VECTOR-BORNE AND ZOONOTIC DISEASES Volume 4, Number 1, 2004 © Mary Ann Liebert, Inc. Research Paper Mapping Rift Valley Fever Vectors and Prevalence Using Rainfall Variations D.J. BICOUT and P. SABATIER ABSTRACT High activity of the Rift Valley Fever (RVF) virus is related to a tremendous increase of associated mosquito vec- tors, which follows periods of high rainfall. Indeed, rainfall creates an ecologically humid environment that in- sures the proliferation of breeding sites and the development of RVF vectors. Data collected by Fontenille et al. (1998) from 1991 to 1996 in the Barkedji area in the northern Senegal are employed to discuss and quantify the in- cidence of rainfall upon the abundances of RVF vectors. We have constructed a non-linear mapping of vector abundances versus rainfall variations, and developed a stochastic model and a corresponding algorithm allowing on output the simulation of RVF mosquito vectors as a function of rainfall trajectories in the course of time. This stochastic mapping of vector abundance is subsequently used to assess the prevalence of RVF in a population of susceptible hosts as a consequence of rainfall. Keywords: Arboviruses—Stochastic dynamics—Rainfall— Vectors— RVF prevalence. Vector-Borne Zoonotic Dis. 4, 33–42. INTRODUCTION severe disease with high mortality and abor- tions in pregnant females. Human infection IFT VALLEY FEVER (RVF) is an arboviral dis- with RVF virus is characterized by the onset of Rease that causes epizootics and associated high fever, hepatitis, encephalitis, haemor- human epidemics throughout Africa (Meegan rhagic fever orocular disease and sometimes and Bailey 1988, Peters and Linthicum 1994). leading to death (Laughlin et al. 1979, Meegan RVF virus belongs to the genus Phlebovirus , et al. 1980, McIntosh et al. 1980). family Bunyaviridae . It is transmitted to verte- RVF outbreaks are commonly correlated brates by infected floodwater mosquitoes Aedes with periods of widespread and heavy rainfall spp. and other Culex spp. Humans can also be (Meegan and Bailey 1988, Wilson et al. 1994, infected via inhalation of aerosols of vireamic Digoutte and Peters 1989, Linthicum et al. blood during slaughtering, or other direct con- 1999). It is assumed that ecologically wetter tact with infected animals. Vertical transmis- conditions increases the number of breeding sion from mosquito to mosquito also occurs in sites for mosquitoes resulting in an increase in some species (Meegan and Bailey 1988, Davies the number of vectors and therefore more in- and Highton 1980, Wilson et al. 1994, Fontenille tense virus transmission and circulation. Rain- et al. 1998). The RVF virus affects domestic an- fall floods the mosquito breeding habitats imals, specially sheep, cattle and goats, causing which contain eggs of the primary vector Unité Biomathé matiques et Epidémiologie, Ecole Nationale Vété rinaire de Lyon–INRA, Marcy L’Etoile, France. 33 34 BICOUT AND SABATIER species and reservoirs (transovarially infected fluential since maximum vector-host contact Aedes spp.), and these subsequently serve as a occurs during periods when vectors are active habitat for development of secondary vectors and their populations are high. To address the (e.g., Culex spp.). It follows that excessive flood- issue of direct influence of rainfall on RVF virus ing allows for massive hatching and a tremen- circulation we have focused our analysis on m. dous increase of the number of both primary We have used real data collected in Barkedji and secondary vectors, which may results in an area in the northern Senegal during 1991–1996 outbreak (Davies et al. 1985, Zeller et al. 1997, (Fontenille et al. 1998) to construct a framework Woods et al. 2002). Although other weather fac- for a rational study of correlation between rain- tors may be important, this paper focuses on fall and vector abundance in a region where analysing and modelling the relationship be- temperature shows little variation. Our ap- tween rainfall, vector abundance, and the oc- proach is fundamentally stochastic. It consists currence and maintenance of RVF outbreaks. of a statistical analysis for determining firstly In general, the importance of climate condi- the distribution laws describing the data and tions to vector-borne diseases is highlighted in secondly, constructing the correlations be- the basic reproductive number given ( R0) in the tween observable components of the problem. formula below (Macdonald 1957, Anderson In this context, the observable factors are the and May 1991): rainfall and vectors abundances over the course 2 of time. The parameters obtained from the sta- C0 a mbc R0 5 } 5 RvRh 5 } exp(2mtx) (1) tistical analysis are next used to formulate a sto- a am chastic model describing the dynamics of the where a is the vector biting rate, m the number observables and, to develop an algorithm for of vectors per host, b the transmission proba- stochastic simulations. Accordingly, we derive bility from vector to vertebrate, c the transmis- mathematical expressions allowing for the sto- sion probability from vertebrate to vector, a the chastic mapping of vectors abundance versus rate of recovery of the vertebrate from infec- rainfall over the course of time. Numerical re- tiousness, m the vector mortality rate, and tx the sults are compared to collected data and, sim- extrinsic incubation period. The basic repro- ulated stochastic trajectories of vector popula- ductive number is the product of the vectorial tion densities are used to generate the pattern capacity C0 and the duration of the infectious of the prevalence of RVF virus infection and period in the vertebrate hosts. The vectorial ca- immunity in a population of hosts. pacity is defined as the mean number of po- tentially infective contacts made by a mosquito population per infectious host and per unit MATERIALS AND METHODS time (Garrett-Jones 1964) and the R0 yields the average number of secondary host infections Data characterization which one infected host could produce during the duration of the infection among a suscep- The Barkedji area (15°17 9N, 14°179W) is lo- tible host population. The R0 comprises of two cated in the northern Senegal in the Sahelian components: Rv 5 (ac/m)exp(2mtx) the num- Ferlo region. This area was found to sustain a ber of infective contacts for transmission from focus of an enzootic maintenance of the RVF vertebrate to vector and Rh 5 mab/a the num- virus in 1993 (Zeller et al. 1997). Rainfall in this ber of infective contacts for transmission from region averages 250–350 mm annually, and oc- vector to vertebrate. If R0 . 1 each infected host curs in a short rainy season (July to September) will generate on average, a further case and an which fills the temporary ground pools. These epizootic or epidemic can occur (with proba- latter remain the only source of water until to bility 1 2 1/R0). When R0 , 1 the outbreak can- January during the 6th-month dry season (De- not maintain itself and will stutter to extinction. cember through May). After the first rains, the Among all parameters influencing C0 and R0, number of mosquitoes dramatically increases. vector mortality (or survival) rates and vector More than 228,000 mosquitoes from 52 species density (m) are strongly related to environ- were collected in Barkedji and tested for virus mental conditions. Rainfall is particularly in- isolation (Fontenille et al. 1998). Aedes species RVF VECTORS AND PREVALENCE VERSUS RAINFALL 35 represented 28.8% of the mosquitoes collected, among which the Ae. vexans was the most abun- dant, followed by Ae. ochraceus . Other Aedes species like, for example, Ae. mcintoshi and Ae. dalzieli, were rare but Culex species and sand flies were very abundant during the dry season. Records of monthly rainfall and the distrib- utions of RVF vectors ( Aedes vexans and Culex poicilipes) abundances captured in Barkedji, Senegal, over 6 years from 1991 to 1996 (Fonte- nille et al. 1998) were used for the statistical analyses (Fig. 1). Simple inspection of the data shows that periods of greater mosquito abun- dances coincide with that of heavy rainfall in amount and the maximum numbers of Culex is FIG. 2. Monthly reduced mean values fi(t) of the rain- attained couple months after that of Aedes. To fall, Aedes and Culex. Filled triangles, circles, and squares are calculated using the field data from Fontenille et al. characterize the intra- and inter-annual varia- (1998), while the solid, dashed, and dot-dashed lines rep- tion of the data, we calculate the between-year resent formula in Eqs. 3 and 5, respectively. monthly means and variances of the rainfall and vector abundance. Let r (t) be the observable vector (in the math- i mum value of kr (t)l given by R 5 128.67 mm, ematical sense) at time t (measured in months) i 1 R 5 4981.48 and R 5 5814.82. If it is assumed with i 5 1,2,3 corresponding to the rainfall, 2 3 that the population of hosts within the study Aedes and Culex abundances, respectively. We area is almost constant during the period of the calculate for each month the average kri(t)l and study, then the Aedes and Culex densities are standard deviation s2(t) 5 kr2(t)l 2 kr (t)l2 over i i i calculated as m (t) 5 r (t)/N and m (t) 5 all the years under study. As a result, we find 2 2 3 r (t)/N, respectively, where N is a population for all three variables, that s (t) < kr (t)l for all 3 i i scaling constant. t such that 0 # t # T 5 12 months. Figure 2 dis- These findings indicate firstly that as s (t) < plays the reduced mean f 5 kr (t)l/R (sym- i i i i kr (t)l then the inter-annual values of r (t), at bols) as a function of t, where R is the maxi- i i i each month t within a year, can be described by the non-stationary exponential distribution, P(r1,r2,r3;t) 3 exp{2ri/kri(t)l} 5 P } } for t 5 1,2,…,12 (2) 3i 5 1 kri(t)l 4 Secondly, kri(t)l describes an average of the in- tra-annual variation of ri(t) and correlations be- tween coordinates.