Downloaded by guest on September 30, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1803264115 Iacono Lo Giovanni models mechanistic revealed ecoepidemiological fever using Valley Rift of limits Environmental etrbrediseases vector-borne VBDs. important other many behaviors of and up emergence epidemics the opens of of here predictions improve developed to approach ability the the sometimes Using emergence periods. intermittent long the after with under detection, circulation low-level of as threshold RVF explained of is nature intermittent which the occurrence, captures threshold model the The the with persistence. overlaps when of variables arise environmental the the Instabilities of of regimens). range endemicity (persistent the infection and/or long-term consequently, RVF populations of and establishment mosquito populations the of mosquito or extinction regimens) seasonally (nonpersistent the that RVF of either availability range to water-body and the leads temperatures identify data ambient environmental and we varying empirical Importantly, availability using setting Kenya. water realistic from a and to temperature it apply ambient (RVF), of ecoepi- fever an the dynamics to Valley develop coupled We Rift model mathematical Africa. of compartmental, to demiological, study these endemic case disease examine a high-burden we the a using Here, and detail unstable. complex, in highly problems be at are reliable can systems broader are dynamics resulting models important infection theoretical which VBDs; An to forecasting persistence. extent the disease is concern and environmen- including conditions between are link dynamics, tal unclear VBDs the an transmission of of and complex epidemics requirements cycles intermittent ecological in transmission the resulting The by vectors, poverty. mediated and disease strongly of of often driver burden global animals key the 2018) domestic of 23, a February and component review significant humans for (received a of 2018 are 19, (VBDs) June approved diseases and FL, Vector-borne Gainesville, Florida, of University Singer, H. Burton by Edited Kingdom United 6BT, WC1E London London, Kingdom; and United 4RY, Kenya; NW1 00100 London Nairobi, London, of Society Kingdom; Zoological Zoology, United 0RQ, OX11 Oxford Didcot, a Wood N. L. James and min eprtrs(,5.Fo eeo,w ee o“ambient at to refer replication “temperature.” we as on, pathogen temperature” here From require 5). (4, usually temperatures ambient climate which incu- the extrinsic by both periods, pathogen affects and influenced bation infection temperature to is instance, vectors of for ecology susceptibility well; Pathogen as estab- weather areas. and and reach new to in vectors animal for lish opportunity and the mobility increasing human trade and habitats vectors; new new instance, disease-competent creating for for constructions, via, dam vectors; bodies and the water patterns of of irrigation availability rates conditions the biting weather to and in changes reproduction variability survival; geographic the mech- alter to of the that changes variety affect a as through to change such (3) anisms, use expected species land are arthropod and of pre- globalization distribution Climate rate is as (2). accelerating that well century the change as next to environmental the due other over future and dicted the climate in global occurrence change of VBD to of likely patterns con- Current are significant poverty. a are global they to and tributor (1), year per deaths human million V analysis stability eateto eeiayMdcn,DsaeDnmc nt nvriyo abig,CmrdeC30S ntdKingdom; United 0ES, CB3 Cambridge Cambridge, of University Unit, Dynamics Disease Medicine, Veterinary of Department netosdsae,wt vr1blinhmncssad1 and cases human of billion class 1 important over an with diseases, form infectious (VBDs) diseases ector-borne | lqe analysis Floquet | zoonosis a,b,c,1 f etefrBoiest n niomn eerh eateto eeis vlto n niomn,Uiest College University Environment, and Evolution Genetics, of Department Research, Environment and Biodiversity for Centre a nrwA Cunningham A. Andrew , | rs-pce transmission cross-species c colo eeiayMdcn,Uiest fSre,GidodG27L ntdKingdom; United 7AL, GU2 Guildford Surrey, of University Medicine, Veterinary of School | d enr Bett Bernard , e nmladHmnHat rga,ItrainlLvsokRsac Institute, Research Livestock International Program, Health Human and Animal 1073/pnas.1803264115/-/DCSupplemental hsatcecnan uprigifrainoln at online information supporting contains article This 1 the under Published Submission. Direct PNAS a G.L.I., is and article This data; interest. of analyzed conflict no G.L.I. declare paper. authors data; the The wrote the performed J.L.N.W. collected and G.L.I. D.W.R., D.W.R. research; D.G., B.B., and designed A.A.C., J.L.N.W. B.B., and G.L.I., A.A.C., research; G.L.I., contributions: Author huh ob h otipratfrvrstasiso to transmission virus for important most the people. and trans- livestock be of 40 to capable than be thought to more (16), known play Although RVFV are might hosts. mitting species (15)] midge reservoir rodents and as mosquito and role (14) important although buffalos an ruminants, [e.g., domestic in animals significant wild species. most when of is range RVFV wide disease a by transmit The infecting potentially directly mosquitos meal, blood occasionally, Infected a taking fluids. and body mosquitos animal biting in by disease transmitted fatal cause on Val- can impact Rift and economic (10–12). Africa significant (13). world in humans a industry the has livestock of (RVFV) the regions virus facilitat- new or fever to areas ley endemic spread in changes its RVF ing environmental/climatic of impact for increased potential causing the been about has concern raised Furthermore, in (7–10). occurrence Yemen and epidemic Arabia recent by Saudi shown and epi- as (6) expanding major be analysis to for seems phylogeographic range responsible its and is Africa, virus in demics mosquito-borne causative important The an zoonosis. (RVF), viral fever Valley Rift on focus owo orsodnesol eadesd mi:[email protected] Email: addressed. be should correspondence whom To oe,teeoe fesa motn olt etrunder- eradication better effective design to programs. to and tool Our diseases returns important vector-borne stops. quickly an stand intervention offers system the therefore, the after model, control as configuration health original fail, short-term the likely scenario, will latter conditions measures the Impor- of transmission. popula- under sets disease tantly, of those vector oscillations importantly, ambient stable sea- mosquito in and and resulting how persist the bodies show will when to water tions of able dictate of are dynamics availability temperatures we key varying the the fever, sonally for Valley and advance the Rift this species between disease, making vector By relationship transmission. of the pathogen been limits capture have formally ecological models to epidemiological unable previous transmis- systems; infection sion complex represent diseases Vector-borne Significance VVhsacmlx utseiseieilg,adi is it and epidemiology, multispecies complex, a has RVFV We here. reported work the of basis the provide issues These e ei Grace Delia , NSlicense. PNAS e ai .Redding W. David , Aedes sp., . Mansoni www.pnas.org/lookup/suppl/doi:10. b f ulcHat England, Health Public , NSLts Articles Latest PNAS p,and sp., d nttt of Institute Culex p are sp. | f9 of 1

POPULATION BIOLOGY P Climatic drivers, such as temperature and rainfall, have a water bodies (i.e., parameters Tm and Sm in Eqs. 5 and 6); for strong impact on the complex ecology of both RVFV and its each simulation, we ascertained whether the predictions result vectors (17–20). Thus, the epidemiology of RVFV is likely to be in sustained fluctuations in populations of Culex sp. or Aedes sp. strongly impacted by climate change (21). Other environmental, [the dominant vectors in Kenya (57)] or in the prevalence of cultural, and socioeconomic factors, such as gathering of large RVFV in livestock. All other parameters were kept the same, numbers of people and domestic animals during religious fes- and the surface area of water bodies and temperature were tivities, have relevant implications for the infection dynamics of allowed to fluctuate in phase with annual periodicity (e.g., the RVFV, including driving epidemics (22–25). parameters φS = φT = π in Eqs. 5 and 6) (SI Appendix, SI Text The complex features of RVFV infection dynamics have led discusses a situation where this constraint was relaxed). We con- to many studies. Empirical statistical approaches have identified ducted analyses in both the theoretical and realistic models using key environmental variables (e.g., temperature and rainfall) that different initial conditions and numbers of livestock. How fre- are associated with disease epidemics, enabling disease risk to quently the surface areas of water bodies change is likely to be mapped (11, 18, 19, 22, 23, 25–35). Mechanistic models have have an impact on mosquito populations. Thus, for the theo- added crucial insights for understanding links between disease retical model, we varied the frequency of water bodies’ body transmission and the environment by exploring the impact of surface area fluctuation (i.e., ωS in Eqs. 5 and 6) while ensur- seasonality and studying the processes leading to epidemic trans- ing the same overall annual surface area of water bodies. To mission (24, 36–52). Despite progress, these approaches are still investigate the intermittent nature of observed RVF epidemics, subject to important limitations: the earlier mechanistic mod- we assumed that, when the mean number of infected livestock els do not incorporate seasonality; most models tend to include is below a certain threshold, the epidemic is not detected. This either only rainfall or only temperature as a contributing factor; is a reasonable assumption considering the frequency of sub- and if included, seasonality is usually incorporated only as an clinical infections and the limited diagnostic facilities available ad hoc periodic variation in the response (e.g., oviposition rate) in endemic areas. Cases detected within 30 d are assumed to rather than in the causative variable, undermining the realism of be part of the same epidemic. We then ran the realistic model the approaches. 100 times with the initial number of livestock and with infec- A further critical limitation of these studies is that they rely on tion prevalence in the livestock randomly drawn from uniform rainfall data. In empirical statistical approaches, rainfall is often distributions (100–5,000 for the number of livestock and 5–20% considered a “predictor variable” [with the commonly associated for the infection prevalence, respectively). All other parame- problem of collinearity (53)]. In mechanistic models, rainfall is ters were kept the same. The simulation was also run in the usually a proxy for breeding sites. In complex hydrogeological absence of transovarial transmission. In each case, we then models, rainfall is merely an input to represent water bodies; estimated the periods of time during which RVFV was not the major problem with this approach is that the dependence of detected. Predictions of the duration of interepidemic periods RVFV on rainfall varies widely across countries and ecoregions for the realistic model were compared with historical data of due to, for example, different types of terrain, evaporation rates, RVF epidemics that had occurred in Kenya from 2004 to 2013 delay between rainfall occurrence and establishment of water obtained from the Global Animal Disease Information System, bodies, etc. EMPRES-i (58). To overcome these limitations, we developed a unified, pro- cess-based model built on a realistic representation of how the Results dynamics of water bodies obtained from satellite images (rather Influence of the Seasonal Patterns of Temperature and Water Bod- than rainfall) and temperature influence the ecology of the ies on the Quantitative Dynamics of RVFV. The theoretical model primary mosquito vectors and the epidemiology of RVFV. A shows (Fig. 1; more details are in SI Appendix, Fig. S19) that critical feature of using this approach is our ability to investi- different amplitudes and frequencies of fluctuations in temper- gate the combined impact of seasonality on both water avail- ature and water availability within the system result in different ability and temperature, allowing us to (i) capture the influ- disease patterns. It is possible, for example, that one or both ence of seasonal patterns of temperature and water bodies on mosquito species might go extinct, that there could be stable the quantitative transmission dynamics of RVFV, (ii) quan- oscillations with one or more annual peaks in the mosquito pop- tify the environmental drivers that lead to regional endemicity ulation but in an RVFV-free situation, that there could be stable of RVFV, (iii) assess if transovarial transmission in Aedes sp. mosquito populations with sporadic RVFV epidemics, or that (the only species of mosquitos for which ovarian transmission RVFV might become endemic. is known) is necessary for RVFV persistence, (iv) isolate the mechanisms allowing virus reemergence after long periods of Quantifying the Environmental Drivers Leading to Regional En- inactivity in endemic regions (43, 54), and (v) identify if and demicity of RVFV. The theoretical model predicts the existence under which conditions the complex patterns of RVFV epi- of a temperature-dependent threshold in mean surface area demics resemble chaotic behavior [i.e., the system being highly of water bodies below which mosquito populations and RVFV sensitive to initial conditions (55), rendering disease predictions always fade out (gray areas in Fig. 1, which are referred to as the difficult]. “nonpersistent regimen”). The model also showed the param- eter space (i.e., the set of all possible combinations of values Analysis for the different parameters) resulting in a “persistent regimen” Our analyses were conducted within two main contexts: a the- (i.e., sustained oscillations in the vectors and RVFV) (colored oretical case, represented by a simple sinusoidal variation of areas in Fig. 1). The intensity of the color reflects the yearly the surface area of water bodies and of temperature (repre- averaged population of the mosquitos or the yearly averaged sented by Eqs. 5 and 6), and a realistic situation, where we prevalence of RVFV in livestock. The optimal conditions for used empirical data for Kenya viz., spatially averaged temper- mosquito occur when the mean body surface area is at its greatest ature (56) and the total surface area of water bodies over the and when the mean temperature is ∼26 ◦C for Culex and ∼22 ◦C entire territory divided by the surface of Kenya] (SI Appendix, for Aedes (Fig. 1). The prevalence of RVFV in livestock is pre- SI Text). Here and throughout, we refer to these two situa- dicted to be highest when temperature is ∼26 ◦C. The ranges of tions as “theoretical model” and “realistic model,” respectively. mean annual temperature and mean annual water-body surface We first ran the theoretical model by systematically changing area resulting in sustained fluctuations in mosquito abundance, the mean annual temperature and mean annual surface area of in particular for Aedes sp., differ from those causing sustained

2 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1803264115 Lo Iacono et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 ne osattmeaueof S19 popula- temperature Fig. constant Appendix, mosquito (SI a persistent endemicity Under a RVFV support where not of situations does absence tion few the a in are possible there where regions is some endemicity are There RVFV livestock. in RVFV of oscillations in dots black The livestock. in prevalence stabilize). infection to or periodic prevalence solution mosquitos a the of infection around number for averaged system average short yearly linearized yearly too the the the is or of to population exponents corresponds Floquet mosquitos color largest the the (negative where of B phase parameters intensity transient of The a space solution). gray after the cycle oscillations The limit in sustained simulations. establish region the (A, always a in population will to changed livestock mosquitos correspond are in the dots that black parameters where only no parameters the with of are regions space these the area; surface in (C bodies’ region livestock water a in to peaks seasonal correspond of areas number annual the shows axis 1. Fig. oIcn tal. et Iacono Lo functions sinusoidal by described is area surface bodies’ Water mosquitos. of sinusoidal population by the described on are area (ω surface temperature frequency bodies’ Eq. and the water to area while in according simulations surface oscillations the bodies’ of in Water frequency changed of prevalence. are RVFV that parameters and only mosquitos the of Eqs. population to according the functions on temperature mean and and E niomna osrit edn opritn n opritn eiesmsutsadRF.(A–C RVFV. and mosquitos regimens nonpersistent and persistent to leading constraints Environmental dniyargo ntesaeo aaeesweeteslto susal pstv ags lqe xoet;ti sbcuetetm considered time the because is this exponents; Floquet largest (positive unstable is solution the where parameters of space the in region a identify and F 5 rp ozr fe rnin hs ngtv ags lqe xoet ftelnaie ytmaon h ulslto) h colored The solution). null the around system linearized the of exponents Floquet largest (negative phase transient a after zero to drops ) with φ S = 5 π and hl h eprtr skp osat(T constant kept is temperature the while , The 6. 25 x xssostema ae ois ufc area surface bodies’ water mean the shows axis ◦ ,teaeaeabundance average the C, Aedes p,and sp., ). = 25 p bnac nrae ihtefeunyo siltosin oscillations of frequency the with contrast, In increases decreasing. abundance starts bodies when sp. water times of at sizes surface interactions population the nontrivial mosquito to particular due from is arising This 1D). (Fig. availability water of ◦ S ) The C). = Culex ω T = x 6)adpae(φ phase and 365) 2π/ p erae ihicesn rqec foclainin oscillation of frequency increasing with decreases sp. xssostema ae ois ufc area surface bodies’ water mean the shows axis S m P hl the while , B, and D, y E rteyal vrgdifcinpeaec in prevalence infection averaged yearly the or ) xssostema temperature mean the shows axis mato enwtrbde’sraearea surface bodies’ water mean of Impact ) S = φ T = π r etcntn.(D–F constant. kept are ) NSLts Articles Latest PNAS S m P T hl the while , m hs are these ; Impact ) | Aedes f9 of 3 y

POPULATION BIOLOGY water-body surface area (Fig. 1E). This is not surprising, as in different values of the initial infection prevalence lead to quali- contrast to Culex sp., the hatching of Aedes sp. eggs is driven by tatively different solutions (Fig. 2B), a phenomenon resembling flooding and desiccation cycles. In the extreme case of no water- chaotic systems observed in meteorology. This phenomenon can body fluctuation, Aedes sp. is expected to go extinct, although be stronger for different parameter values, leading to situations this does not always occur, as a small proportion of Aedes where the overall mosquito populations as well as their infection eggs hatches spontaneously without desiccation/flooding (59) prevalence are asymptotically different (SI Appendix, Fig. S26). (SI Appendix, Fig. S20). The domain of the RVFV persistent conditions is dependent on the abundance of livestock, NL, in Is Transovarial Transmission in Aedes Necessary for RVFV Persis- particular when this impacts on the biting and oviposition rate tence? The simulations of RVFV dynamics showed persistence (SI Appendix, Figs. S21–S23). The intensity of the fluctuations in Culex sp. in the absence of Aedes mosquitos (Fig. 3) over 15 y in temperature and in the surface area of water bodies seems in the realistic model. The numerical simulation shows that per- to have little impact on mosquito abundance and on whether sistent patterns of RVFV occur in the absence of Aedes sp. In RVFV becomes endemic (SI Appendix, Fig. S24). the theoretical model, the use of Floquet theory should pre- vent the problem of infection persistence at unrealistic low levels When Does the Complexity of RVFV Dynamics Resemble Chaotic [“atto-fox problem” (60)], as the theory focuses on the stability Behavior? Stability refers to the property of an ecosystem to of the precise zero or periodic solution (although here, the stabil- return to equilibrium if perturbed (55) or equivalently, that ity of RVFV was studied only numerically). In general, random the system will always reach the equilibrium state regardless extinctions of RVFV preclude persistence of infection, although of the initial conditions. In the theoretical model, the equilib- one could argue that deterministic models mimic the fact that ria are represented by extinction of mosquito species and/or random extinctions are compensated by random immigration RVFV infection (nonpersistent regimen) or more or less com- of infected mosquitos or livestock. Incorporating demographic plex periodic oscillations (persistent regimen). For the mosquito stochasticity and spatial immigration would address this con- populations, Floquet analysis (Materials and Methods and SI cern. Taking all of this into account, we cautiously conclude Appendix, SI Text) shows that the long-term mathematical solu- that the transovarial transmission of RVFV in Aedes sp. is not a tions are stable. For RVFV infection, numerical computations prerequisite for RVFV persistence over time, although the mod- show that the solutions are stable after the initial conditions (i.e., els provide no evidence to discount this as an important (49) the initial number of livestock) are fixed (SI Appendix, Fig. S25). transmission route in reality. Changing the initial number of livestock has no practical effect on the overall population of mosquitos when the impact of live- Isolate the Drivers Enabling the Virus to Reemerge After Long Periods stock on mosquito oviposition and biting rate is assumed to be of Inactivity in Endemic Regions. Here, we assumed that, when the negligible (i.e., for very large values of the parameter q as in this mean number of infected livestock is below a certain threshold case, but other scenarios are shown in SI Appendix, Fig. S23). (chosen to be 50) (SI Appendix, SI Text discusses 5 infected ani- The number of livestock, however, predictably impacts the tem- mals and 1% infection prevalence), the epidemic is not detected poral patterns of infected mosquitos and infected livestock (SI by routine surveillance. The patterns of the distribution of these Appendix, Fig. S25), and the system can no longer be considered disease-undetected times (Fig. 4) are similar for the situations stable if the number of livestock is externally perturbed. Accord- where both mosquitos species are present and where Aedes sp. ingly, animal movements, including the immigration of infected and thus, transovarial transmission are absent. The empirical animals, might have a significant impact on the pattern of RVFV interepidemic periods observed in Kenya from 2004 to 2013 (58) infection. Similar behavior is observed for the realistic model, are shown for comparison. The similarity of the patterns suggests where simulations show that, regardless of the initial conditions, a strong impact of external drivers and variation in immunity in the system approaches the same asymptotic limit, with only the livestock populations compared with the impact of the mosquito initial number of livestock having a direct impact on the pat- species. Both distributions are multimodal (Fig. 4), with several terns of infections (SI Appendix, Fig. S25). The property that the peaks occurring; interestingly, several small peaks occur over system always reverts to the same asymptotic solution (after fix- long time periods (> 10 y). This shows that RVFV can circu- ing the initial number of livestock) is not general. An important late in the system at very low, undetectable levels, emerging counterexample is shown in Fig. 2 (SI Appendix, Fig. S26). In this unexpectedly after very long time periods. For a lower level of simulation experiment, we consider the two scenarios illustrated threshold (SI Appendix, Fig. S29), the probability of observing by path A and path B in Fig. 1C: first, when the mean tempera- long interepidemic periods is smaller. This further highlights the ture and mean surface area of water bodies are always within the importance of including stochasticity in the diagnostic (the detec- RVFV persistent regimen, and second, when these values tran- tion threshold). As discussed above, demographic stochasticity sit from RVFV persistence to RVFV nonpersistence and then allows for the extinction of the infection, and other factors, such back again. To do so, we divided the entire time (32 y) into eight as spatial immigration, would allow reemergence. Incorporating cycles; each 4-y cycle (described either by path A or by path B in this mechanism would likely have a detectable impact on patterns Fig. 1C) consists of four intervals of 1 y each (represented by the of the interepidemic periods. segments in the paths). For each interval, we let the mean values P Tm or Sm in Eqs. 5 and 6 change year by year (SI Appendix, Fig. Discussion S27). For each situation, represented by paths A and B (Figure We identified the range of seasonally varying temperatures and 2A and 2B respectively), we then considered two scenarios (sce- water-body extent leading either to extinction of mosquito pop- nario 1 and scenario 2 in Figure 2 A and B) by imposing different ulations and/or RVFV or to established mosquito populations initial conditions in the infection prevalence but the same total and endemicity of the infection. These results allow prediction number of livestock, i.e., we kept the total number of livestock of future geographic distribution of RVFV due to changes in 500, but the infection prevalence for scenario 1 was set to 1% environmental and climatic conditions across the globe. (5 infected livestock out of 495) and the infection prevalence for To achieve this, we developed a process-based mathemati- scenario 2 was set to 4% (20 infected livestock out of 480). When cal model, which unifies environmental factors, the ecology of the mean temperature and mean surface area of water bodies mosquitos, and the epidemiology of RVFV. vary within the RVFV persistent regimen (path A), the system reaches the same limit irrespective of the different initial condi- A Unified Framework for the Dynamics of VBDs. A key advantage tions (Fig. 2A). In contrast, for the situation described by path B, of this model is its conceptual simplicity, with the undeniable

4 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1803264115 Lo Iacono et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 oIcn tal. et Iacono Lo water of area surface m mean 18 the 4,000 between of and is range ture 3,000 the but between A, is path m bodies for 6,500 as at same constant the is a is bodies to water 25 according of from increasing area interval is face 2-mo temperature a mean in the function stepwise when year, to fourth 7,500 a from interval by 4-mo a in m function 6,500 from stepwise interval a 2-mo to according a decreases in function stepwise a m 30 to 7,500 according at decreasing bodies is water ture of area 4-mo surface a mean 30 in at function constant stepwise is perature a to Appendix according B (SI increases interval and bodies A water paths of to area 1C according Fig. changing cyclic in are illustrated temperature mean and ies 2. Fig. VVifcini ietc hnma eprtr n ensraearea surface mean and temperature mean when livestock in infection RVFV ◦ o25 to C 2 uigtesmlto 3 ) h ensraeae fwtrbod- water of area surface mean the y), (32 simulation the During n h entmeauei osata 25 at constant is temperature mean the and , ◦ .Drn h hr er h ensraeae fwtrbodies water of area surface mean the year, third the During C. ◦ n 22 and C o ahA uigtefis er h ensurface mean the year, first the during A, path For . rm650t ,0 m 7,500 to 6,500 from S27) Fig. , ◦ ;ti sfloe yascn erwt constant with year second a by followed is this C; ◦ yaiso oqio ouainand population mosquitos of Dynamics (A) C. 2 n h ag o entempera- mean for range the and ◦ o30 to C 2 hl h entempera- mean the while , 2 o ahB h dynamics the B, path For . 2 ◦ n h entem- mean the and , n h ensur- mean the and C ◦ ;ti sfollowed is this C; rao ae oiscag codn opt .Teaypoi behavior asymptotic The scenarios. B. different path the to for different according is change bodies water of area narios. eggs slk cnro1btwith livestock but infected 1 scenario and like susceptible is the for except stages and mosquitos zero, condi- all to initial and livestock different set removed two are and for exposed A 1, path scenario In to tions. according change bodies water of transmission very Transovarial not drought. of are flooding in by periods typically provoked protracted are and epidemics after intermittent Severe 54). are (43, predictable RVFV Predictability. of of Problem the demics and RVFV of Nature Intermittent environment. regimen, new persistent this in the established in become will temperature are they with that then region parameters a water-body into Sim- imported and stops. are measures mosquitos control perma- if of ilarly, a the application to in after return values to result expected original is not abundance mosquito will as water solution, mosquito control) of nent the chemical area reduce (e.g., surface to aiming average population perma- measure (e.g., temporary a drivers any is the bodies), there unless in that, change imply nent oscillations population stable mosquito example, the For in stability important. of extremely reflecting interpretation is biophysical num- livestock, analysis The livestock in critical. Here, also disease. RVFV were the bers of of persistence distribution geographic the the for occur ies dry especially of very dynamics, importance water-body or the in for cold fluctuations showed very of reflecting also in frequency values, analysis the survive upper The not temperatures. and do hot mosquitos lower that between fact confined the is temperature, this it mean of and the value on The nonmonotonically oscillation. depends sustained threshold in extinct; result go will will it populations mosquito Floquet sur- otherwise, the water-body using which mean by below in areas, threshold system face lower the a of showed This stability analysis. the theoretical proved the in we numerically; systems, the shown In of was conditions. this sta- area scenarios, initial a surface realistic of in results irrespective the that population (i.e., and capacity mosquito carrying eggs area) ble a surface in of resulting unit bodies, density per water maximum eggs of the number by constrained Popula- Persistence. ultimately Mosquito Viral and Established tions Allowing Conditions situation, Environmental RVFV-free disease. an the of in effects tested the including be subsequently can only example, For model validation. mosquito and the calibration of its nature modular facilitates The model and peaks. the annual mosquitos more or (in of one prevalence with oscillations livestock) RVFV sustained with and abundance but or mosquito scenario populations, RVFV-free mosquito both an or established one extinct, including becoming these regimens, of mosquitos different sur- combinations qualitatively different water-body in the of result temperature, variation and area sinusoidal system face theoretical simple a in by even system; represented the of trivial area nonlinearity not surface the are to however, water-body due patterns, in resulting The seasonality is temperature. the and prevalence by infection The governed and RVFV. largely abundance on thus, mosquito and cascades of population parameters mosquito seasonality these the incubation of of extrinsic impact dynamics the the The as RVFV. well as of rates period fac- biting and and fundamental rates, survival developmental few their mosquito a affecting oviposition temperature mosquito to governing rates, bodies reduced water of area system surface tors: the of complexity Aedes Aedes I L O = C B = ,rsetvl,admsutseggs mosquitos and respectively, 5, stesm as same the is 100, oqio samcaimo VVpritne(61) persistence RVFV of mechanism a is mosquitos p iia hehlsi eprtr n ae bod- water and temperature in thresholds Similar sp. O I = 0.Teaypoi eairi h aei ohsce- both in same the is behavior asymptotic The 100. u h entmeaueadma surface mean and temperature mean the but A, S L = 8 and 480 h bnac fmsut gsis eggs mosquito of abundance The I L = 0 epciey n mosquitos and respectively, 20, O C NSLts Articles Latest PNAS = 100, O I = 0.Seai 2 Scenario 100. S | L = f9 of 5 Epi- 495

POPULATION BIOLOGY (24)] and transitions across persistent and nonpersistent regi- mens are additional causes of the intermittent patterns in the epidemics of RVFV.

A Program for Future Work. This work identified important chal- lenges that could be addressed by further theoretical work and model-guided fieldwork. Fieldwork can be designed to test well- defined hypotheses that emerge from the model, such as the predicted larger abundance of Aedes sp. in regions where water bodies are fluctuating more frequently and the existence of thresholds in surface area of water bodies and temperature con- fining the domain of the persistent regimens for mosquito species and RVFV infection. Further experiments to gauge the impact of livestock density on mosquito oviposition and biting rates (66) are crucial, as this will have an important effect on the mosquito population and on patterns of RVFV infection (SI Appendix, SI Text). In most cases, we focus on one host only. Copresence of multiple hosts can dilute or amplify the disease. Further inves- tigations on host feeding preference (67) and the relationship between mosquito abundance and host population size are crit- ical to estimate this effect (68). A challenging point is the large uncertainty associated with many parameter values; in particular, the life history parameters of mosquitos stage are often based on laboratory conditions and inferred for different species of mosquitos. Theoretical works like this can steer future fieldwork and experimentation to reduce the knowledge gaps that emerged Fig. 3. Assessing the impact of transovarial transmission. Dynamics of Culex from the model. sp. population and RVFV infection in livestock in the absence of Aedes sp. population for the realistic model. The theoretical case is exemplified in SI The potential impacts of multiple hosts, including wildlife Appendix, Fig. S19B. hosts (e.g., buffalo), also need to be investigated. We assumed uniform mixing between mosquitos and livestock. As a result, the predicted patterns of infection in Aedes sp., Culex sp., and live- and a possible explanation for the intermittent nature of RVFV stock are qualitatively similar. The model should be generalized epidemics, as presumably infected Aedes sp. eggs can survive for to incorporate heterogeneity occurring in nature. Furthermore, several years. Another explanation is that RVFV is always cir- the model needs to be refined to incorporate the impact of veg- culating in the population, perhaps in a cryptic reservoir (14, etation and natural predators on the ecology of mosquitos. This 15, 62), at very low level and is not detected. This is sup- could be done, for example, by allowing the birth and mortality ported by evidence of interepidemic RVFV seropositivity among humans and animals (63, 64) and the indication of subclinical infection in livestock (65). Our model suggests that transovar- ial transmission is not necessary for interepidemic persistence of RVFV and that the infection may continuously circulate at low and largely undetectable levels in between irregular epi- demics; change in immunity in livestock populations is playing an important role in the irregularity of the infection patterns. This result is strictly valid, however, when all animals and mosquitos are well-connected (e.g., through animal movement), as our deterministic model is based on the assumption of uniform mixing. Our theoretical model shows that, after the initial num- ber of livestock is fixed, the solution is stable, and long-term behavior can be accurately predicted even if the initial con- ditions, such as the exact number of infected animals or the abundance of mosquitos at a given time, are not known. If the number of livestock, however, is perturbed, the solutions are qualitatively and quantitatively different even if all other conditions are kept identical. Thus, for reliable predictions, accu- rate information on the demography of livestock is necessary (the impact of the livestock size on infection is discussed in SI Appendix, SI Text). In some situations, however, this is not suffi- cient. The mean surface areas of water bodies and temperatures can change (as in Kenya, where mean surface area of water bod- ies decreased during 2003 − 2007) (SI Appendix, Fig. S4) and transit from the persistent to nonpersistent regimen and vice versa. In such situations, the system becomes highly sensitive to the initial values of infection prevalence, a situation that resem- Fig. 4. Assessing the intermittent nature of RVFV. The histograms represent bles chaotic behavior. Thus, the irregularity of the system can the distribution of duration of interepidemic periods for empirical data, for arise even from small variations in the infection prevalence due the model where Aedes spp. is absent (origin due only to undetected cases) to, for example, immigration of a few infected livestock. Varia- and where both mosquitos species are present (origin due to undetected tions in the demography of livestock [such as occurs in festivals cases and transovarial transmission).

6 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1803264115 Lo Iacono et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 h rtgntohccce(.. edn nbodma n aigo eggs) of (F laying flyer and After a meal becomes females. blood female are on nulliparous adults feeding the ends, (i.e., emerging cycle the gonotrophic of first one-half the only and (A included, eggs itly laid having adults female (L larvae tively), (C the eggs laid ing ave(L larvae Model. Ecoepidemiological is empha- framework we the Below, of formulation livestock. detailed of a in density while presented model, the the on of (iii aspects batch (i and size per eggs, are eggs immature (72) of and number al. mature into et eggs (ii surface, Otero sp. bodies’ addi- water of Important the on model mosquitos. process of oviposition the the effect of the to includes rate be which tions development (72), is al. can the et mosquitos on Otero model the of temperature model of the the dynamics on cat- although population based goats, largely stage-structured (e.g., host, The hosts one sheep). heterogeneous multiple tle, only include to assume extended readily we populations. simplicity, mosquito two For the and for livestock model susceptible–exposed–infectious the a for model compartmental dynamics exposed–infectious–recovered population stage-structured the ecological, for model an combines model The Methods and behavior.Materials chaotic to subject of is presence/absence epidemiology on the when based cases models on statistical questions of theoretical reliability and the practical of important prevalence. raises infection space also its con- and This initial the population the livestock only of as distribution such not ditions, plausible the exploring also, required, but sen- parameters are and uncertainty analysis and robust sitivity persistent more between then interface regimens, envi- the nonpersistent the at If such are areas). measures, variables nonendemic ronmental short-term in movement, and animal areas limiting as endemic of size in the bodies, reducing long-term as water such at conditions, aiming VBDs environmental (e.g., other of effectively or control more RVFV interventions for generate plan regions to endemic to used potentially be per- of could the map to approach a within calibrated the are Then, carefully variables regimens. be sistent environmental could the data, model whether vegetation the pro- assess of resolution census, natural type spatiotemporal (56), animal the temperature high and is (71), using bodies variability By water work. spatial of Extension this include research. of to future gression model in the consider These to of settings. questions spatial crucial different are at in variability diagnostics stochastic periods and account interepidemic into demography taking the by epidemiology assessed of the be patterns should and Furthermore, mosquitos of RVFV. can ecology of with the bodies) (70), on water ecosystem effects the of of large frequencies area natural the surface with sea- and resonate (e.g., temperature drivers in periodic sonality external and stochasticity ronmental infected of number the and batch. each imports is in these this animals RVFV of research how size and of Future the immigration epidemiology by livestock 69). affected of the ref. presence how the in in instance, changes discussion for and of address, 34 climate epidemiology should (ref. of driver the crucial RVFV another impact and is of movement the mosquitos animal of of of impact The ecology analysis RVFV. the accurate on more change a the into for incorporated fre- readily model not and be in intensity can rainfall projections increase Climate also, an quency. but cause temperature to average In the expected only (68). is change relationships climate ratio general, CO vector-to-host via density-dependent attract areas might a animals neighbor other from and livestock mosquitos of accord- model presence the The calibrating and ingly. factors such on depend to rates oIcn tal. et Iacono Lo u nlsswsdn sn eemnsi oe,btenvi- but model, deterministic a using done was analysis Our Aedes C ,ppe(P pupae ), p ossso maueadmtr gs(O eggs mature and immature of consists sp. IAppendix SI Aedes A 1 ] yr (F flyers )], ,ppe(P pupae ), p and sp. C ,nliaosfmls[.. eaeaut o hav- not adults female [i.e., females nulliparous ), , IText SI The Culex C A ,adfml dlshvn adeg (C eggs laid having adults female and ), ,nliaosfmls(A females nulliparous ), Culex . 2 p iha pdmooia susceptible– epidemiological an with sp. .Autml oqio r o explic- not are mosquitos male Adult ). p ouain oss feg (O eggs of consist populations sp. C 2 and h eedneo the of dependence the ) msin eutn in resulting emission, h eednyo the of dependency the ) h eaainof separation the ) F A nsac fbreed- of search in ) 1 ,fles(F flyers ), I and O M respec- , A ,and ), Aedes C 2 ); ), g odrts(.. h ubro gsli yalflesprtm unit) time per flyers all by laid eggs of the number in the capacity as (i.e., carrying rates a introduced load prevent therefore, egg eggs the we, by occupied of ovipositions; already species further sites Breeding common (17). that (dambos) depressions fact etc., and the gutters, circumluteolus, by rain Aedes justified clogged is cans, containers tin This genus artificial pots, included. small flower not of tires, is suitable as contribution nearest such the the water, simplicity, to with For m surface 1,500 (71). time-varying to the images up (76); be body would water mosquitos of activity the area of region flyer a as a in dispersed by sites scanned breeding and terrain the sites the breeding of suitable size detect as typical to modeled the eggs to is of corresponds rate batch mosquito) the a oviposition reducing lays the flyer site, a Thus, breeding that unit). scale, times suitable P field time of a number at per for the conditions; (i.e., search ideal rate to be oviposition need to is mosquitos assumed deposition are the egg which for time conditions, average tory Appendix the (SI 75, body ref. water to the surrounding water high second the by regulated transitions (C cyclic (F stage adult of the series to cycle a gonotrophic by followed sites ing yaiso utbebedn ie ie,tmoaywtrbde (dambos) with bodies trast water temporary [i.e., Appendix sites (SI breeding suitable of dynamics the of emergence the with (72). associated adult mortality additional an is there stage, variable response Text the SI as squares rate (15 least mortality temperature Ordinary with and fitted 74. were ref. models from regression conditions laboratory (SI standard 74 under ref. and from Sharpe data quinquefasciatus by model on the based of development Appendix (73) according poikilotherm al. modeled et for were Schoolfield DeMichele stages by other simplification the parametrization the (42); on to based literature were the meal, in blood presented available infinitely of limit the fmtr n maueeg repcieo hi netdstatus. infected their of irrespective eggs b immature and mature of case, first the In laid. already O r h aiu ubr of numbers maximum the are factors by rescaled num- addi- are the triatomines, In for bodies). 66 of thus, ref. water meals; bers in blood presented the argument ingesting of same without the area eggs following produce surface cannot total areas mosquitos surface the tion, both that to assumed we proportional for (here, and are body body, water the water around the soil of moist edge the for around survival; area and deposition eggs for water and (either unit surface surface over its laid be by can limited that and is eggs of body number water maximum a the that account into take eid hyaerayt ac rvddta hyaesbegdin submerged are they that (59); provided flooding without hatch taneously to 19.7% ready although water, are they period, drop rate biting the and batch per eggs zero. host of to of number absence the biting the meal), the in blood as Accordingly, no manner. same (i.e., same the the be in to rescaled assumed were total are rates, which the cycles, consider gonotrophic we of then rates present, be are to by species ratio divided mosquitos vector-to-host is both fecundity if vector (but which for two Appendix ratio (SI vector-to-host particular livestock) the of is 1% number the be divided to mosquitos assumed of (here respectively. ratios resources, vector-to-host infinite culated of limit the in batch ˜ A Culex C P h ouaindnmc feg srgltdb h viaiiyand availability the by regulated is eggs of dynamics population The in cycles, gonotrophic the for rates development Temperature-dependent Aedes ξ ≈ A r h ubr feg e ac,adtecryn capacities carrying the and batch, per eggs of numbers the are and S Culex K κ P A (t Aedes Aedes and .Ohrta h al otlt ntepupal the in mortality daily the than Other S18). and S17 Figs. and 1E ≈ )/(At F Culex = A , P p gsrqieamnmmdscainperiod desiccation minimum a require eggs sp. 6 ). Culex S IText SI b ˜ O − P C P yial omdb ev anal.I con- In rainfall]. heavy by formed typically S14) and S13 Figs. , (t Aedes novdi h rnmsino VV uhas such RVFV, of transmission the in involved dep η 2E ρ ersn h rcin ftebedn iesial for suitable site breeding the of fractions the represent ) p and sp. Culex A ,where ), m 6 κ sp., and Aedes .Lf tg-pcfi otlt ae for rates mortality stage-specific Life S6). Table and r h oa ubr of numbers total the are  2 Aedes 1 ◦ ae nsm niainta h pta ag of range spatial the that indication some on based − S b ee aegypti Aedes o34 to C Aedes P fnwyembryonated newly of C (t O /(1 A m ,where ), Culex K re ntmoaygrassland temporary in breed ochraceus, Aedes p a hi gsi h os ol bv mean above soils moist the in eggs their lay sp. C C O asmdt etesm o ohseisof species both for same the be to (assumed + + Culex p gsprbatch, per eggs sp. ◦  m Culex Culex m IAppendix (SI variable explanatory the as C) and C Aedes A and /q) = .Bsdo h aeagmn 6) the (66), argument same the on Based ). Culex ρ C O S ξ p and sp. p rsi for soil or sp. P eeetatdfo aacollected data from extracted were and C 2 Aedes S (t n ntescn ae ti h sum the is it case, second the in and , and p gscnsriedscainfor desiccation survive can eggs sp. P steoealsraea time at surface overall the is ) (t p,ti orsod oa inner an to corresponds this sp., b ρ ,namely ), = A S A A /(1 P Culex Aedes b ˜ 2 (t r h este feg per eggs of densities the are n akt h yrstatus flyer the to back and ) A NSLts Articles Latest PNAS a bandb satellite by obtained was ) Aedes hsrgo sestimated is region This A. η + Aedes Aedes t m b ˜ dep p and sp. m C p gspoue per produced eggs sp. A Aedes K C ,where /q), .According S14). Fig. , and p gshthspon- hatch eggs sp.  ftettlnumber total the of = C and 1 ≈ 2 nlabora- in d 0.229 p,i steouter the is it sp., − ee mcintoshi, Aedes P η b ˜ , Aedes m sp.). Culex A O IText SI P T Aedes respectively, , A K d ρ A fe this after ; r h cal- the are C = K κ κ b  C C Culex Culex p eggs sp. η where , | ,and ), b and ˜ and Aedes C Culex f9 of 7 S S and t P P K b (t (t of ≈ q A A ) ) ,

POPULATION BIOLOGY several years. Therefore, we distinguish two egg stages OI and Om, with exposed and infectious populations will lead to the exposed and infec- Exp Inf Exp Inf development time of newly laid eggs OI conditioned to tious flyer populations (FC and FC for Culex sp. and FA and FA for Aedes sp.) followed by cyclic transitions to the corresponding exposed ! 1 1 and infectious adult stages and back to the exposed and infectious flyer ≈ max Td, , [1] Exp θAedes θAedes[T(t)] stages. Furthermore, infected Aedes sp. flyers [i.e., either exposed (FA ) O1 O Inf Inf or infectious (FA )] will deposit infectious eggs OI , which will turn into infectious larvae LInf, infectious pupae PInf, infectious nulliparous adults where θAedes[T(t)] is the temperature dependency of development rate of A A O AInf, etc. The explicit set of differential equations is presented in SI the eggs (72) (SI Appendix, Eqs. S14 and S21 and Table S6). 1 Appendix, SI Text. Parameters are based on data presented in the liter- Aedes sp. eggs will hatch at the time of the first flood [e.g., at time t ature (refs. 40, 42, and 72 and references therein) (SI Appendix, Tables when SP (t) − SP (t − ∆t) > 0], Thus, during a small time ∆t, the variation in S3–S5) and adapted to the Kenya situation [e.g., temperature (56) and water the number of mature eggs due to hatching can be modeled as bodies (71)].

OM(t) − OM(t − ∆t) ≈ Stability Analysis for Seasonal Systems: Floquet Theory. Floquet analysis is Number of submerged eggs a well-established tool suitable to study the stability of seasonal systems z }| { h   i (77, 78). In the simplest scenarios, temperature and water bodies can be − max ρ (t) κAedesSP (t) − κAedesSP (t − ∆t) , 0 [2] A approximated by the periodic functions

(i.e., if the water body is shrinking, no eggs will be submerged, and thus, no P P P S (t) = Sm + SA cos (ωSt + φS) [5] eggs will hatch). This leads to T(t) = T + T cos (ω t + φ ), [6]     m A T T SP (t) − SP (t − ∆t) ω ω O (t) − O (t − ∆t) = − max , 0 O (t), [3] where S and T are the frequencies of oscillations in surface areas of water M M  P  M P S (t) bodies and temperature; the terms Sm and Tm represent the mean surface area of water bodies and mean temperature during periods 2π/ωS and P 2π/ωT , respectively; S and TA are the maximum amplitudes in the oscil- where the superficial density of eggs at time t was estimated as ρA(t) ≈ A Aedes P lations; and φS and φT are the respective phases. Then, we ran the model OM(t)/(κ S (t)). The continuous counterpart of the above equation leads to and calculated the corresponding Floquet multipliers for a range of frequen- P ! cies, mean surface areas of water bodies, and mean temperatures to explore Aedes 1 dS (t) τO = max , 0 , [4] which of these parameters lead to stable solutions. More details are in SI SP (t) dt Appendix, SI Text. P where the term dS (t) represents the rate of change of the surface area of a dt ACKNOWLEDGMENTS. We thank Dr. Erasmus Zu Ermgassen for his help dur- water body. ing the preliminary stages of the work. This work was mainly conducted within the Dynamic Drivers of Disease in Africa Consortium, Natural Environ- Combined Mosquito and Livestock Population Model in the Presence of ment Research Council (NERC) Project NE-J001570-1, which was funded with Infection. RVFV transmission in Aedes mosquitos can be transovarial or support from the Ecosystem Services for Poverty Alleviation (ESPA) program. horizontal, while only horizontal transmission, mediated by biting infec- The ESPA program is funded by the Department for International Develop- tious hosts, is possible for Culex sp. Both adult Culex sp. and Aedes sp. ment, the Economic and Social Research Council, and the NERC. The work can become infected after feeding on infectious livestock I . More pre- was partially supported by the National Institute for Health Research (NIHR) L Health Protection Research Unit in Environmental Change and Health at the cisely, for Culex sp., the movements out from the susceptible categories, London School of Hygiene and Tropical Medicine in partnership with Pub- and , are θ˜Culex and θ˜Culex , respectively; of these, λ and C1 C2 C1 C1 C2 C2 L→C1 C1 lic Health England (PHE) and in collaboration with the University of Exeter, λ mosquitos move to the exposed flyer category, Exp. The remain- University College London, and the Met Office. A.A.C. and J.L.N.W. are also L→C2 C2 FC ing (θ˜Culex − λ )C and (θ˜Culex − λ )C move to the susceptible flyer supported by European Union FP7 Project ANTIGONE (Contract 278976). C1 L→C1 1 C2 L→C2 2 A.A.C. was supported by a Royal Society Wolfson Research Merit Award. category, FC . Similar arguments apply to Aedes sp., but in this case, there Inf J.L.N.W. is supported by the Alborada Trust. D.W.R. is supported by a Med- is an additional infectious category for nulliparous mosquitos, A1 , emerg- ical Research Council UK Research and Innovation/Rutherford Fellowship ing out of infectious eggs due to transovarial transmission. The exposed (MR/R02491X/1). The views expressed are those of the author(s) and not Inf Inf categories then transit to the adult infectious categories (C1 and C2 for necessarily those of the National Health Service, the NIHR, the Department Inf Inf Culex and A1 and A2 for Aedes) with rates C and A, respectively. The of Health, or PHE.

1. WHO (2016) Vector-borne diseases. Available at www.who.int/en/news-room/fact- 13. Gerdes GH (2004) Rift Valley fever the importance of Rift Valley fever for animal and sheets/detail/vector-borne-diseases. Accessed June 13, 2018. public. Rev Sci Tech 23:613–623. 2. IPCC (2014) Summary for Policymakers, eds Core Writing Team, Pachauri R, Meyer L 14. Beechler BR, et al. (2015) Rift Valley fever in Kruger National Park: Do buffalo (IPCC, Geneva), pp 2–26. play a role in the inter-epidemic circulation of virus? Transbound Emerg Dis 62: 3. Semenza JC, Menne B (2009) Climate change and infectious diseases in Europe. Lancet 24–32. Infect Dis 9:365–375. 15. Gora D, et al. (2000) The potential role of rodents in the enzootic cycle of Rift Valley 4. Brubaker JF, Turell MJ (1998) Effect of environmental temperature on the suscepti- fever virus in Senegal. Microbes Infect 2:343–346. bility of Culex pipiens (Diptera: Culicidae) to Rift Valley fever virus. J Med Entomol 16. Meegan J, Bailey C, eds (1989) Rift Valley Fever. The Arboviruses: Epidemiology and 35:918–921. Ecology (CRC, Boca Raton, FL). 5. Turell MJ (1993) Effect of environmental temperature on the vector competence 17. Davies FG, Linthicum KJ, James AD (1985) Rainfall and epizootic Rift Valley fever. Bull of Aedes taeniorhynchus for Rift Valley fever and Venezuelan equine encephalitis World Health Organ 63:941–943. viruses. Am J Trop Med Hyg 49:672–676. 18. Linthicum KJ (1999) Climate and satellite indicators to forecast Rift Valley fever 6. Soumare´ POL, et al. (2012) Phylogeography of Rift Valley fever virus in Africa reveals epidemics in Kenya. Science 285:397–400. multiple introductions in Senegal and Mauritania. PLoS One 7:23–26. 19. Anyamba A, et al. (2009) Prediction of a Rift Valley fever outbreak. Proc Natl Acad Sci 7. Balkhy HH, Memish ZA (2003) Rift Valley fever: An uninvited zoonosis in the Arabian USA 106:955–959. peninsula. Int J Antimicrob Agents 21:153–157. 20. Anyamba A, et al. (2012) Climate teleconnections and recent patterns of human and 8. Abdo-Salem S, et al. (2006) Descriptive and spatial epidemiology of Rift Valley fever animal disease outbreaks. PLoS Negl Trop Dis 6:e1465. outbreak in Yemen 2000-2001. Ann New York Acad Sci 1081:240–242. 21. Martin V, Chevalier V, Ceccato P, Anyamba A, Simone LD (2008) The impact of climate 9. Chevalier V, Pepin´ M, Plee´ L, Lancelot R (2010) Rift Valley fever–a threat Europe? Euro change on the epidemiology and control of Rift Valley fever vector-borne diseases Surveill Bull Europeen´ sur les maladies transmissibles. Eur Commun Dis Bull 15:19506. Rift Valley fever and climate change. Rev Sci Tech 27:413–426. 10. Rolin AI, Berrang-Ford L, Kulkarni Ma (2013) The risk of Rift Valley fever virus intro- 22. Abdo-Salem S, et al. (2011) Can environmental and socioeconomic factors explain the duction and establishment in the United States and European Union. Emerg Microbes recent emergence of Rift Valley fever in Yemen, 2000-2001? Vector Borne Zoonotic Infect 2:e81. Dis 11:773–779. 11. Taylor D, et al. (2016) Environmental change and Rift Valley fever in eastern Africa: 23. Metras´ R, et al. (2015) Risk factors associated with Rift Valley fever epidemics in South Projecting beyond health futures. Geospat Health 11:115–128. Africa in 2008-11. Sci Rep 5:9492. 12. Golnar AJ, Kading RC, Hamer GL (2018) Quantifying the potential pathways and loca- 24. Xiao Y, et al. (2015) Modelling the effects of seasonality and socioeconomic tions of Rift Valley fever virus entry into the United States. Transbound Emerg Dis impact on the transmission of Rift Valley fever virus. PLoS Negl Trop Dis 9: 65:85–95. e3388.

8 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1803264115 Lo Iacono et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 5 edn W id ,L aooG etB oe E(07 pta,saoa n cli- and seasonal Spatial, (2017) KE Jones B, Bett G, Iacono Lo S, Tiedt DW, Redding 25. 6 lmnsA,Pefe U atnV teM 20)ARf alyfvralsfrAfrica. for atlas fever Valley Rift A (2007) MJ Otte V, Martin DU, Pfeiffer AC, Clements 26. 5 lv M ta.(07 eosrcino itVle ee rnmsindynamics transmission fever Valley Rift of Reconstruction (2017) al. et MM, Olive fever Valley 35. Rift for mapping risk and factors Predictive (2016) al. et PM, Munyua 33. knowledge-based geographic a of assessment and Kenya Development in (2016) outbreaks al. fever et Valley A, Rift Tran for model 32. risk Dynamic (2016) al. et D, Gikungu related 31. and fever Valley Mauritania Rift for suitability in habitat of outbreaks heterogeneity Spatial fever (2016) al. valley et C, Sindato Rift (2014) 30. al. et C, fever Valley Caminade Rift 29. with associated Aedes features by landscape occupied Identifying potentially (2013) zone al. a et in V, fever Soti Valley 28. Rift (2009) al. et C, Vignolles 27. 6 pseS,Hai ,TheceJ 21)Amteaia oe fRf alyfever Valley Rift of model mathematical A (2011) JM Tchuenche H, Haario SC, Mpeshe 36. Madagascar. in epidemics Fever Valley Rift of Drivers (2017) al. et R, Lancelot 34. 7 u ,SotH,Chsad W cgi 21)Antokbsdmeta-population network-based A (2012) C Scoglio LW, Cohnstaedt HM, Scott L, Xue 37. 0 akrC,NuT esnW,HrlyD 21)Dt-rvnmdln oassess to modeling Data-driven (2013) DM Hartley WK, Reisen T, Niu CM, Barker 40. identify to models population mosquito and hydrology Combining (2012) Valley al. et Rift V, of Soti model epidemiological An 39. (2012) DM Hartley YE, Papelis HD, Gaff T, Niu 38. 2 ice A one J oeikG eKejrA,vnRemn J(03 h trans- The (2013) HJ Roermund van of AA, spread Koeijer spatial de G, the Nodelijk Modeling GJ, (2013) Boender EA, S Fischer Ruan JC, 42. Beier RS, Cantrell C, Cosner D, Gao 41. 4 hti ,HmnJ,Mnr A(03 oeln etcltasiso nvector- in transmission vertical Modelling (2013) CA Manore JM, Hyman N, Chitnis of 44. persistence between-season and Inter-epidemic (2015) BR Beechler CA, Manore 43. 1 io E iraoG,Kae D mt J(06 utsao rnmsinfrRift for transmission Multiseason (2016) RJ Smith AD, Kealey GA, Giordano RE, against Miron strategies vaccination 51. Modelling (2016) B Bett P, Kitala MK, Njenga J, Gachohi 50. inter-epidemic fever Valley Rift Rift Predicting the (2016) HEZ of Tonnang S, analysis Abelman Stability SA, Pedro (2014) YAW 49. Nkansah-gyekye LS, Luboobi SC, Mpeshe 48. Bifur- Stability, (2014) HEZ Tonnang R, Sang outbreaks FT, Ndjomatchoua epizootic S, investigate Abelman to SA, Pedro approach modeling 47. A (2014) al. et F, Chamchod popula- of 46. modelling Simulation (2014) SI Kimera LEG, Mboera N, Holst CN, Mweya 45. oIcn tal. et Iacono Lo ai rdciemdl fRf alyfvrdsaears Africa. across disease Sci fever Biol Valley Rift of models predictive matic rvVtMed Vet Prev nMdgsa:Etmto ffreo neto rmsrpeaec uvy using surveys seroprevalence from infection of modelling. force Bayesian of Estimation Madagascar: in USA Sci Acad Natl Kenya. in epidemics Africa. Eastern in transmission fever Dis Valley Trop Rift Negl for PLoS areas suitable mapping for model data. outbreak disease and climate on based approach. modelling Niche 10:e0005002. ecological An Tanzania: in occurrence conditions. environmental satellite resolution spatial high very using Senegal, imagery. region, Ferlo transmission, virus mapping. risk and Dynamics Senegal: in vexans ihhmnhost. human with praht oe itVle ee epidemics. fever Valley Rift model to approach eetvt o itVle ee virus. fever Valley Rift for Africa. receptivity West of regions semi-arid in emergence Dis fever Trop Valley Negl Rift of drivers the dynamics. spatial with fever iso oeta fRf alyfvrvrsaoglvsoki h ehrad:A Netherlands: The in livestock among virus fever Valley study. modelling Rift of potential mission Egypt. in fever Valley Rift on iesswt plctost itVle fever. Valley Rift to applications with diseases borne cycling? cryptic or transmission Vertical 62:13–23. fever: Valley Rift alyfvri ot mrc utsao rnmsinfrRf alyfvri North in fever Valley Rift for transmission multiseason America. America North in fever Valley Kenya. in livestock in fever Valley Rift model. host-vector stochastic a Dis from Trop Insights Negl patterns: outbreak and activities Rift model. to dynamical fever application Valley with model disease vector-borne of fever. analysis Valley Chaos and cation virus. fever Valley epidemic Rift of disease maintenance a enzootic and in virus fever Valley Rift for vectors setting. mosquito of dynamics tion 372:20160165. LSOne PLoS n elhGeogr Health J Int ahPplStud Popul Math LSOne PLoS 6:e1795. 10:e0005167. 82:72–82. e Res Vet 9:e108430. caBiotheor Acta 114:938–943. 10:e0004999. LSOne PLoS c Rep Sci 9:e108172. 44:58. ulMt Biol Math Bull n nio e ulcHealth Public Res Environ J Int 23:71–94. 12:10. 7:39870. optMt ehd Med Methods Math Comput 11:e0144570. ahCmu Sci Comput Math J 59:231–250. LSNg rpDis Trop Negl PLoS LSNg rpDis Trop Negl PLoS 75:523–542. esa Health Geospat ho Bio Theor J esa Health Geospat 4:740–762. ulMt Biol Math Bull ilDyn Biol J 7:e2515. 10:e0005049. 2012:138757. 11:903–918. 306:129–144. rnbudEegDis Emerg Transbound 11:377. 7:11–40. 3:211–220. hlsTasRScB. Soc R Trans Philos LSNg rpDis Trop Negl PLoS 76:2052–2072. PLoS PLoS Proc 5 a MM(2001) RMRM May 55. (2014) the P Vuren quantifying van for Jansen JT, methods Paweska developing 54. in Challenges (2017) al. et model G, network Iacono Lo Individual-based 53. informed Biologically (2016) al. et CM, Scoglio 52. 8 lumirC 20)Foutter:Aueu olfrudrtnignonequilibrium understanding for tool useful A theory: Floquet (2008) CA Klausmeier 78. (1990) R Grimshaw the of 77. abundance of pattern spatial and distribution Temporal (2011) al. et D, Diallo 76. devel- Temperature-dependent (1960) R (1990) Christophers RE 75. Stinner RC, Axtell KJ, Patel LM, Rueda biological 74. of regression Non-linear (1981) CE Magnuson PJ, for Sharpe model dynamical RM, spatial Schoolfield stochastic A 73. (2008) HG crop Solari N, to Schweigmann land.copernicus.eu/ M, resistance at Otero Available Durable 72. service. (2013) land global CA Copernicus (2016) Gilligan Anonymous F, 71. Bosch den van G, zoonotic of Iacono dynamics infection Lo the for 70. framework unified A (2016) al. et G, Iacono Lo 69. horses? the are Where (2013) JLN Wood S, Gubbins JR, Newton CA, Valley Robin Rift G, Iacono of Lo amplifiers livestock 68. on choices host Mosquito (2016) al. environ- et and DP, Tchouassi strategies 67. risk-spreading vectors’ in of virus Influence Fever (2013) Valley al. Rift et of P, survey Pelosse Seroepidemiological 66. (2016) seropositivity, al. et virus inter- during M, livestock fever in Nanyingi virus fever Valley 65. Valley Rift of Rift Seroprevalence (2017) Interepidemic al. et C, (2008) Mroz 64. al. A et virus: fever AD, Valley Rift LaBeaud (1997) 63. research: E Ryst fever der Valley van Rift MS, Smith in MJ, Advances Oelofsen basic A, (2010) on Pretorius CH velocities 62. King population JW, Kazura and AD, epidemic LaBeaud of 61. Dependence (1991) D Mollison for model 60. table life Dynamic (1993) GA Mount E, Daniels empres- DG, at Haile Available DA, system. Focks information disease 59. animal Global (2017) fever al. Valley et Rift R, Sang of vectors 58. key of abundance and Distribution (2017) al. et R, Sang 57. global the of overview An (2012) TG Houston BE, Gleason RS, Vose I, Durre MJ, Menne 56. nEegn ia Diseases Viral review. Emerging in systematic A diseases: water-associated Dis on Trop climate Negl PLoS and strategies. weather mitigation of of effects evaluation and US the in fever 11:e0162759. Valley Rift for dynamics. Oxford). Senegal. Barkedji, in vectors 436. fever Nile West and fever Valley Rift UK). Cambridge, Press, and quinquefasciatus Culex of rates Culicidae). survival and opment theory. reaction-rate Biol absolute on based models rate temperature-dependent aegypti Aedes 2016. 2, June Accessed global/. uncertainty. under risk predict to Biol Comput framework epidemiological An pathogens: spread. and spillover Britain. Great the in and transmission preferences sickness vector-feeding horse African location, of host risk Uncertain cows? or sheep the With Kenya. in virus fever The disease. diseases: vector-borne Chagas’ of of evolution example and epidemiology the on stochasticity mental Kenya. Garissa, in ruminants 2014/15. Egypt, in period epidemic Kenya. northeastern Africa. South in vertebrates Hyg terrestrial Med small of study seroepidemiologic prevention. disease for Insights parameters. Entomol aegypti 2017. 28, June Accessed i.fao.org/eipws3g/. Kenya. in counties distinct ecologically Dis two in arboviruses other and database. 910. network-daily climatology historical Ed. 2nd Princeton), Press, 11:e0005341. 88:719–731. Dpea uiia) nlsso h ieaueadmdldevelopment. model and literature the of Analysis Culicidae): (Diptera: 30:1003–1017. 57:693–698. ho Ecol Theor e Entomol Med J ahBiosci Math 9:e1002870. . ulMt Biol Math Bull 11:e0005659. tblt n opeiyi oe Ecosystems Model in Complexity and Stability olna riayDfeeta Equations Differential Ordinary Nonlinear aai Vectors Parasit mr netDis Infect Emerg LSNg rpDis Trop Negl PLoS 1:153–161. ee eyt L) h elwFvrMosquito Fever Yellow The (L.), aegypti Aedes 107:255–287. 27:892–898. Aaei,Bso) p169–200. pp Boston), (Academic, LSOne PLoS etrBreZooi Dis Zoonotic Vector-Borne 70:1297–1325. urOi netDis Infect Opin Curr M e Res Vet BMC 9:184. 14:1240–1246. 8:e70830. itVle ee iu nteRl fAnimals of Role the in Virus Fever Valley Rift 10:e0004957. 13:87. to cai Technol Oceanic Atmos J NSLts Articles Latest PNAS 23:403–408. 7141–146. 17 o Interf Soc R J ee aegypti Aedes BakelScientific, (Blackwell etrEcol Vector J CmrdeUniv (Cambridge PictnUniv (Princeton LSNg Trop Negl PLoS 10:20130194. mJTrop J Am LSOne PLoS | (Diptera: 36:426– 29:897– Theor J f9 of 9 Aedes Med J PLoS

POPULATION BIOLOGY