A stochastic vector-borne epidemic model: Quasi-stationarity and extinction

Tom Britton; Ali Traoré

doi:10.1016/j.mbs.2017.05.004

A stochastic vector-borne epidemic model: Quasi-stationarity and extinction

Math Biosci. 2017 Jul:289:89-95. doi: 10.1016/j.mbs.2017.05.004. Epub 2017 May 13.

Authors

Tom Britton¹, Ali Traoré²

Affiliations

¹ Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden.
² Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden; LAboratoire de Mathématiques et Informatique (LAMI), Département de Mathématiques, Université Ouaga I Pr Joseph KI-ZERBO, BP 7021 Ouagadougou, Burkina Faso. Electronic address: traoreali.univ@yahoo.fr.

PMID: 28511957
DOI: 10.1016/j.mbs.2017.05.004

Abstract

We consider a stochastic model describing the spread of a vector borne disease in a community where individuals (hosts and vectors) die and new individuals (hosts and vectors) are born. The time to extinction of the disease, T_Q, starting in quasi-stationary (conditional on non extinction) is studied. Properties of the limiting distribution are used to obtain an approximate expression for E(T_Q), the mean-parameter in the exponential distribution of the time to extinction, for a finite population. It is then investigated numerically and by means of simulations how E(T_Q) and its approximations depend on the different model parameters.

Keywords: Diffusion approximation; Quasi-stationary distribution; Time to extinction; Vector-borne disease.

MeSH terms

Animals
Diffusion
Epidemics*
Host-Pathogen Interactions
Humans
Models, Biological*
Mosquito Vectors
Stochastic Processes