Different Type of Epidemic Models

Total Page：16

File Type：pdf, Size：1020Kb

Different types of epidemic models Tommi Asikainen Unit I. 2 Foresight, Modelling, Behavioural Insights & Design for Policy Overview • Compartmental models • Stochastic models • Agent based models Compartmental models(Kermack, W. O.; McKendrick, A. G.) SIR model • Assume a homogenously mixing population • Divide the population into different groups • S(t) • I(t) • R(t) • Infectious process as below: In differential equation form Exact solutions exist, we need also S(0), I(0) and R(0) N = Population size β= Number of infectious contacts per timeunit ɤ = recovery rate From this basic reproduction number R0 is derived as β / ɤ Limitations and use of this SIR model • Is used for seasonal influenza, less good for pandemics • Limitations: • Does not incorporate latent / incubation period • Does not incorporate heterogenous mixing (age groups for example) • Does not incorporate pandemic situation importation of infectious cases Extension: SEIR model Λ= Birth rate β = Infection rate a = Latent to infectious rate ɤ = Recovery rate µ = Deathrate SEIR model continued SEIR model many times applied to pandemics Limitation: 1. Lack of heterogenity • Adressed later 2. Numbere of imported infectious not constant • Numeric solution by assuming time dependant importation rate (Ferguson et al. 2006) Stochastic SIR / SEIR model • The deterministic model assumes all rates are exponentially distributed • If the exponential distribution does not fit other distributions can be used • Does this matter? • Depends what you want to model • Beginning of an outbreak -> stochasticity can have a large impact • To estimate the size of a larger outbreak, the deterministic model works rather well • When are stochastic models used? • At a beginning to estimate the inputparameters (beta, gamma) needed • Approach by estimating doubling time of the epidemic (assuming proportion asymptomatic is constant) • Has been ”successfull” with H1N1pdm, covid-19 Agent based models (ABM) • Can follow groups or individuals, throughout the pandemic • Each individual assigned to household, school, workplace etc. • Can incorporate movement and travel patterns • Can provide a lot of insight on very specific interventions or places of infection • Needs a lot of inputdata, many times all data not available • Syntetic populations, generate a population based on official statistics, household size, workplace size etc. Can generate many syntetic populations and see how dependent outputs are on these Basic reproduction number R0 • How many infectious one infectious individual causes in average in a totally susceptible population • In SIR model defined as • In SEIR model defined as • Effective reproduction number Re = Realtime value of R0 • If proportion susceptible reduce or contactrates reduce -> Re reduces • Critical value Re = 1, if below epidemic in control • For covid-19 many countries try estimating this after lockdown. Heterogenity • Different age structures in the populations, how is infection spread between these? • WAIFW – matrix (Who Acquires Infection from Whom), by studying age dependent, proportion infected in a population (for example antibodies in bloodsamples) • POLYMOD project .

Copy Link

Recommended publications

Contact Patterns and Their Implied Basic Reproductive Numbers: an Illustration for Varicella-Zoster Virus
Epidemiol. Infect. (2009), 137, 48–57. f 2008 Cambridge University Press doi:10.1017/S0950268808000563 Printed in the United Kingdom Contact patterns and their implied basic reproductive numbers: an illustration for varicella-zoster virus T. VAN EFFELTERRE1*, Z. SHKEDY1,M.AERTS1, G. MOLENBERGHS1, 2 2,3 P. VAN DAMME AND P. BEUTELS 1 Hasselt University, Center for Statistics, Biostatistics, Diepenbeek, Belgium 2 University of Antwerp, Epidemiology and Social Medicine, Center for Evaluation of Vaccination, Antwerp, Belgium 3 National Centre for Immunization Research and Surveillance, University of Sydney, Australia (Accepted 25 February 2008; first published online 9 May 2008) SUMMARY The WAIFW matrix (Who Acquires Infection From Whom) is a central parameter in modelling the spread of infectious diseases. The calculation of the basic reproductive number (R0) depends on the assumptions made about the transmission within and between age groups through the structure of the WAIFW matrix and different structures might lead to different estimates for R0 and hence different estimates for the minimal immunization coverage needed for the elimination of the infection in the population. In this paper, we estimate R0 for varicella in Belgium. The force of infection is estimated from seroprevalence data using fractional polynomials and we show how the estimate of R0 is heavily influenced by the structure of the WAIFW matrix. INTRODUCTION and social factors affecting the transmission rate be- tween an infective of age ak and a susceptible of age a An essential assumption in modelling the spread of [1, 2]. For the discrete case with a population divided infectious diseases is that the force of infection, which into a finite number, say n, of age groups, Anderson & is the probability for a susceptible to acquire the May [3] introduced the WAIFW (Who Acquires infection, varies over time as a function of the level of Infection From Whom) matrix in which the ij th entry infectivity in the population [1].
[Show full text]
Supplementary Information Methods Supplement
1 SUPPLEMENTARY INFORMATION 2 METHODS SUPPLEMENT 3 4 Description of Model Structure 5 A frequency-dependent SIRS-type metapopulation model was used to explore the effect of enhanced 6 shielding with three population categories being modelled: 7 8 Vulnerable population (Nv) - Those who have risk factors that place them at elevated risk of 9 developing severe disease if infected with COVID-19 and so would remain shielded whilst the 10 rest of the population is gradually released from lockdown. 11 Shielders population (Ns) - Those who have contact with the vulnerable population and include 12 carers, certain care workers and healthcare workers. It is expected that they would also 13 continue some shielding whilst the rest of the population is released from lockdown. 14 General population (Ng). The population that are not vulnerable or shielders. 15 16 For the baseline scenario, a population structure of 20% vulnerable, 20% shielders and 60% general 17 was used (Table M1). A total infectious fraction of 0.0001 (split equally across the population) was 18 used as the initial conditions to seed infection. Model parameters were chosen to best describe the 19 transmission dynamics of COVID-19 in the UK using current assumptions (as of publication) regarding 20 the values of key epidemiological parameters (Table M2). 21 22 The SIRS model assumes that the number of new infections in a sub-population is a function of the 23 fraction of the sub-population that is susceptible (SX), the fraction of the sub-population that is 24 infectious (IX) and the rate of infectious transmission between the two sub-populations (βX).
[Show full text]
The Basic Reproduction Number of an Infectious Disease in a Stable Population: the Impact of Population Growth Rate on the Eradication Threshold
Math. Model. Nat. Phenom. Vol. 3, No. 7, 2008, pp. 194-228 The Basic Reproduction Number of an Infectious Disease in a Stable Population: The Impact of Population Growth Rate on the Eradication Threshold H. Inabaa1 and H. Nishiurab a Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan b Theoretical Epidemiology, Faculty of Veterinary Medicine, University of Utrecht, Yalelaan 7, 3584 CL, Utrecht, The Netherlands Abstract. Although age-related heterogeneity of infection has been addressed in various epidemic models assuming a demographically stationary population, only a few studies have explicitly dealt with age-speci¯c patterns of transmission in growing or decreasing population. To discuss the threshold principle realistically, the present study investigates an age-duration- structured SIR epidemic model assuming a stable host population, as the ¯rst scheme to account for the non-stationality of the host population. The basic reproduction number R0 is derived using the next generation operator, permitting discussions over the well-known invasion principles. The condition of endemic steady state is also characterized by using the e®ective next generation operator. Subsequently, estimators of R0 are o®ered which can explicitly account for non-zero population growth rate. Critical coverages of vaccination are also shown, highlighting the threshold condition for a population with varying size. When quantifying R0 using the force of infection estimated from serological data, it should be remembered that the estimate increases as the population growth rate decreases. On the contrary, given the same R0, critical coverage of vaccination in a growing population would be higher than that of decreasing population.
[Show full text]
Who Acquires Infection from Whom and How? Disentangling Multi-Host and Multi- Mode Transmission Dynamics in the 'Elimination
Downloaded from http://rstb.royalsocietypublishing.org/ on March 22, 2017 Who acquires infection from whom and how? Disentangling multi-host and multi- rstb.royalsocietypublishing.org mode transmission dynamics in the ‘elimination’ era Review Joanne P. Webster1, Anna Borlase1 and James W. Rudge2,3 1 Cite this article: Webster JP, Borlase A, Department of Pathology and Pathogen Biology, Centre for Emerging, Endemic and Exotic Diseases, Royal Veterinary College, University of London, Hatfield AL9 7TA, UK Rudge JW. 2017 Who acquires infection from 2Communicable Diseases Policy Research Group, London School of Hygiene and Tropical Medicine, whom and how? Disentangling multi-host and Keppel Street, London WC1E 7HT, UK multi-mode transmission dynamics in the 3Faculty of Public Health, Mahidol University, 420/1 Rajavithi Road, Bangkok 10400, Thailand ‘elimination’ era. Phil. Trans. R. Soc. B 372: JPW, 0000-0001-8616-4919 20160091. http://dx.doi.org/10.1098/rstb.2016.0091 Multi-host infectious agents challenge our abilities to understand, predict and manage disease dynamics. Within this, many infectious agents are also able to use, simultaneously or sequentially, multiple modes of transmission. Accepted: 25 August 2016 Furthermore, the relative importance of different host species and modes can itself be dynamic, with potential for switches and shifts in host range and/ One contribution of 16 to a theme issue or transmission mode in response to changing selective pressures, such as ‘Opening the black box: re-examining the those imposed by disease control interventions. The epidemiology of such multi-host, multi-mode infectious agents thereby can involve a multi-faceted ecology and evolution of parasite transmission’.
[Show full text]
Generating a Simulation-Based Contacts Matrix for Disease Transmission Modeling at Special Settings
Generating a Simulation-Based Contacts Matrix for Disease Transmission Modeling at Special Settings Mahdi M. Najafabadi a*, Ali Asgary a, Mohammadali Tofighi a, and Ghassem Tofighi b Author Affiliations: a Advanced Disaster, Emergency and Rapid Response Simulation (ADERSIM), York University, Toronto, Canada; b School of Applied Computing, Sheridan College, Toronto, Canada Abstract Since a significant amount of disease transmission occurs through human-to-human or social contact, understanding who interacts with whom in time and space is essential for disease transmission modeling, prediction, and assessment of prevention strategies in different environments and special settings. Thus, measuring contact mixing patterns, often in the form of a contacts matrix, has been a key component of heterogeneous disease transmission modeling research. Several data collection techniques estimate or calculate a contacts matrix at different geographical scales and population mixes based on surveys and sensors. This paper presents a methodology for generating a contacts matrix by using high fidelity simulations which mimic actual workflow and movements of individuals in time and space. Results of this study show that such simulations can be a feasible, flexible, and reasonable alternative method for estimating social contacts and generating contacts mixing matrices for various settings under different conditions. Keywords: Agent-Based Modeling, ABM, Contact Matrices, COVID-19, Disease Transmission Modeling, High Fidelity Simulations, Proximity Matrix, WAIFW Page 1 1. Introduction and Background Person-to-person disease transmission is largely driven by who interacts with whom in time and space (Prem et al., 2020). Past and current studies, especially those conducted during the COVID- 19 pandemic have further revealed that individuals who have more person-to-person contact per period have higher chances of becoming infected, infecting others, and being infected earlier during pandemics (Smieszek et al., 2014).
[Show full text]
Quantifying How Social Mixing Patterns Affect Disease Transmission
Quantifying How Social Mixing Patterns Affect Disease Transmission ∗ S.E. LeGresley1;2, S.Y. Del Valle1, J.M. Hyman3 1 Energy and Infrastructure Analysis Group (D-4), Los Alamos National Laboratory, Los Alamos, NM 87545 2 Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66046 3 Department of Mathematics Tulane University, New Orleans, LA 70118 ∗Corresponding author. E-mail address: [email protected](S.E. LeGresley). 1 1 Abstract 2 We analyze how disease spreads among different age groups in an agent-based com- 3 puter simulation of a synthetic population. Quantifying the relative importance of differ- 4 ent daily activities of a population is crucial for understanding the disease transmission 5 and in guiding mitigation strategies. Although there is very little real-world data for these 6 mixing patterns, there is mixing data from virtual world models, such as the Los Alamos 7 Epidemic Simulation System (EpiSimS). We use this platform to analyze the synthetic 8 mixing patterns generated in southern California and to estimate the number and du- 9 ration of contacts between people of different ages. We approximate the probability of 10 transmission based on the duration of the contact, as well as a matrix that depicts who 11 acquired infection from whom (WAIFW). We provide some of the first quantitative esti- 12 mates of how infections spread among different age groups based on the mixing patterns 13 and activities at home, school, and work. The analysis of the EpiSimS data quantifies 14 the central role of schools in the early spread of an epidemic.
[Show full text]
Approximate Bayesian Computation for Infectious Disease Modelling
Epidemics 29 (2019) 100368 Contents lists available at ScienceDirect Epidemics journal homepage: www.elsevier.com/locate/epidemics Approximate Bayesian Computation for infectious disease modelling T ⁎ Amanda Mintera,1, , Renata Retkuteb,1 a Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK b The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, UK ARTICLE INFO ABSTRACT Keywords: Approximate Bayesian Computation (ABC) techniques are a suite of model fitting methods which can be im- Approximate Bayesian Computation plemented without a using likelihood function. In order to use ABC in a time-efficient manner users must make R several design decisions including how to code the ABC algorithm and the type of ABC algorithm to use. Epidemic model Furthermore, ABC relies on a number of user defined choices which can greatly effect the accuracy of estimation. Stochastic model Having a clear understanding of these factors in reducing computation time and improving accuracy allows users Spatial model to make more informed decisions when planning analyses. In this paper, we present an introduction to ABC with a focus of application to infectious disease models. We present a tutorial on coding practice for ABC in R and three case studies to illustrate the application of ABC to infectious disease models. 1. Introduction able to defend, and is responsible for all of these choices. There is an existing body of literature on ABC tutorials. In particular, for an starting Mathematical models can be used to predict infectious disease dy- introduction to ABC in general Sunnåker et al.
[Show full text]
Based Pandemic Influenza Mitigation Strategies
Cost-effectiveness of Pharmaceutical- based Pandemic Influenza Mitigation Strategies Technical Appendix 1. Description of the transmission model Model structure The model was structured as a set of “Susceptible, Exposed, Infected, Removed” (SEIR)- type deterministic differential equations: r Sd r r = −λ *. S dt r dE r r r =λ*. SE − ω dt r Id r r =ωEI − γ dt r dR r = γI dt The states are vector structures containing 12 elements representing 3 possible vaccination groups (no-vaccine (i=1), pre-vaccine and matched vaccine (i=2) or matched vaccine only (i=3)) and 3 population groups (0-19 years (j=1), 20-64 years (j=2), and 65+ (j=3)). Susceptible states, j for example, can be written as Si , i,j=1..3. The parameters ω and γ were fixed constants representing the rate of progression from exposure to becoming infectious and the rate of recovery from infection respectively. Births and deaths were assumed to make a negligible contribution over the time-scale of the epidemic. We also assumed that there are a growing number of imported cases during the early stages of the pandemic (discussed below). See Appendix 2 for parameter values and ranges. r The force of infection vector λ was dependent on several time-dependent factors including the prevalence of infection and the timing of vaccination programs. We defined r r λ= βˆIN/ , where βˆ is the who-acquires-infection-from-whom (WAIFW) matrix and N was the Page 1 of 5 population size. The mixing between population groups without considering interventions was defined as: ⎛ β β β ⎞ ⎜ 11 12 13 ⎟ ˆ β0 = ⎜ β21 β 22 β 23 ⎟ ⎜ ⎟ ⎝ β31 β 32 β 33 ⎠ Mixing Matrix ˆ The matrix β 0 was calculated using data from a recent POLYMOD survey of contacts conducted in the European Union (1).
[Show full text]
Pulse Mass Measles Vaccination Across Age Cohorts (Age Structure/Mathematical Model/Israel/Dirac Function/Campaign Strategy) Z
Proc. Natl. Acad. Sci. USA Vol. 90, pp. 11698-11702, December 1993 Population Biology Pulse mass measles vaccination across age cohorts (age structure/mathematical model/Israel/Dirac function/campaign strategy) Z. AGURtt§, L. COJOCARUt, G. MAZOR1, R. M. ANDERSONII, AND Y. L. DANONtt tDepartment of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel; *Department of Zoology, Oxford University, South Parks Road, Oxford OX1 3PS, United Kingdom; lDepartment of Statistics, School of Mathematical Sciences, Tel-Aviv University 69978, Israel; IlDepartment of Biology, Imperial Coilege of Science, Technology and Medicine, Prince Consort Road, London SW7 2BB, United Kingdom; and ttThe Children's Medical Center, Kipper Institute of Immunology, The Beilinson Medical Center, Petach-Tikva, 49104, and Sackler School of Medicine, Tel Aviv University, Israel Communicated by Robert M. May, August 2, 1993 (receivedfor review December 18, 1992) ABSTRACT Although vaccines against measles have been a resurgence of measles in the United States is likely without routinely applied over a quarter of a century, measles is still sustained and improved immunization effort (6). persistent in Israel, with major epidemics roughly every 5 The current situation concerning the prospects of measles years. Recent serological analyses have shown that only 85% of eradication in Israel stimulated the production of new guide- Israelis aged 18 years have anti-measles IgG antibodies. Con- lines for measles immunization. A first dose is recommended sidering the high transmissibility ofthe virus and the hih level at 15 months of age and a second dose at 6 years. These of herd immunity required for disease eradication, the Israeli guidelines are based on the conventional concept of a con- vaccination policy against measles is now being reevaluated.
[Show full text]
Estimating Infectious Disease Parameters from Data on Social
The definitive version of this manuscript is available in the Journal of the Royal Statistical Society, Series C, at www3.interscience.wiley.com/journal/117997424/home, 2010, Vol. 59, Part 2, p. 255-277. Estimating infectious disease parameters from data on social contacts and serological status Nele Goeyvaerts1∗, Niel Hens1,2, Benson Ogunjimi2, Marc Aerts1, Ziv Shkedy1, Pierre Van Damme2, Philippe Beutels2 1Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Agoralaan 1, B3590 Diepenbeek, Belgium 2Centre for Health Economics Research and Modeling Infectious Diseases (CHERMID) & Centre for the Evaluation of Vaccination (CEV), Vaccine & Infectious Disease Institute, University of Antwerp, Belgium Abstract In dynamic models of infectious disease transmission, typically various mixing patterns are imposed on the so-called Who-Acquires-Infection-From-Whom matrix (WAIFW). These imposed mixing patterns are based on prior knowledge of age- related social mixing behavior rather than observations. Alternatively, one can assume that transmission rates for infections transmitted predominantly through non-sexual social contacts, are proportional to rates of conversational contact which can be estimated from a contact survey. In general, however, contacts reported in social contact surveys are proxies of those events by which transmission may occur and there may exist age-specific characteristics related to susceptibility and infec- tiousness which are not captured by the contact rates. Therefore, in this paper, transmission is modeled as the product of two age-specific variables: the age-specific contact rate and an age-specific proportionality factor, which entails an improve- ment of fit for the seroprevalence of the varicella-zoster virus (VZV) in Belgium. Furthermore, we address the impact on the estimation of the basic reproduction number, using non-parametric bootstrapping to account for different sources of variability and using multi-model inference to deal with model selection uncer- tainty.
[Show full text]
Population Heterogeneity, Structure, and Mixing
Outline Population heterogeneity, structure, Introduction: Heterogeneity and population structure and mixing Models for population structure Structure example: rabies in space Models for heterogeneity Jamie Lloyd-Smith • individual heterogeneity and superspreaders Center for Infectious Disease Dynamics • group-level heterogeneity Pennsylvania State University Population structure and mixing mechanisms Pair formation and STD transmission Heterogeneity and structure – what’s the difference? Modelling heterogeneity Group-level heterogeneity and multi-group models Tough to define, but roughly… Heterogeneity describes differences among individuals or groups in Break population into sub-groups, each a population. of which is homogeneous. (often assume that all groups mix randomly) Population structure describes deviations from random mixing in a population, due to spatial or social factors. However, epidemiological traits of each host individual are due to a complex blend of host, pathogen, and environmental factors, The language gets confusing: and often can’t be neatly divided into groups - models that include heterogeneity in host age are called (or predicted in advance). “age-structured”. Individual-level heterogeneity - models that include spatial structure where model parameters differ through space are called “spatially heterogeneous”. Allow continuous variation among individuals. Models for population structure Models for population structure Random mixing Multi-group Spatial mixing Random mixing or mean-field • Every individual in population has equal probability of contacting any Network Individual-based model other individual. • Mathematically simple – “mass action” formulations borrowed from chemistry – but often biologically unrealistic. • Sometimes basic βSI form is modified to power law βSaIb as a phenomenological representation of non-random mixing. 1 Models for population structure Models for population structure Multi-group Spatial mixing or metapopulation • Divides population into multiple discrete groupings, based on spatial or social differences.
[Show full text]
Models of Hospital Acquired Infection
3 Models of Hospital Acquired Infection Pietro Coen University College London Hospitals NHS Trust United Kingdom 1. Introduction This chapter will not dwell on how mathematical models are built, better covered elsewhere (Bailey, 1975; Renshaw, 1991; Scott & Smith, 1994; Coen, 2007). It will focus on the impact of mathematical models on the understanding of infections spread in hospitals and their control. Hospital Acquired Infections (HAIs) made their first appearance with the invention of hospitals, mostly associated with surgical operations carried out when germ theory and hand-hygiene were unheard of and post-surgical mortality could be as high as 90% (La Force, 1987). The invention of antibiotics reduced mortality, but subsequently led to the emergence of infections adapted to survival in the antimicrobial-rich hospital environment. An arms race ensued where the bacterium and the pharmacist are to this day fighting to outwit each other (Sneader, 2005). Bacteria like Meticillin-resistant Staphylococcus aureus (MRSA) and Vancomycin-resistant Enterococci (VRE) were detected in UK hospitals as early as the 1960s (Stewart & Holt, 1962), but it was not until the mid 1990s that they ‘took off’ as a significant problem for hospital managers and inpatients (Austin & Anderson, 1999). If only 10% of adult HAI infections could be prevented, £93 million could be saved in England and Wales alone (Plowman et al., 1999). Hospital inpatients are difficult subjects for study. They are only ‘available’ for a short time window, measured in days; too debilitated to all cooperate to the same degree; an extremely heterogeneous population; and major ethical issues are met when it comes to experimentation, especially when infection is asymptomatic.
[Show full text]