A Stochastic Epidemic Model with Constant Immigration and Multi-Dimensional Noises

DOI

10.2991/cisia-15.2015.202How to use a DOI?

Keywords

SIS model; brownian motion; stochastic differential equations; extinction; basic reproduction number

Abstract

In this paper we extend a classical SIS epidemic model from a deterministic framework to a stochastic one by introducing two random perturbations in the model for transmission parameter and cure parameter, and formulate it as stochastic differential equation (SDE) for the number of infectious individuals I(t). Then we prove that this SDE has a unique global positive solution and establish conditions for extinction. So it is clear that the basic reproductive number R0D for the deterministic SIS model is larger than the basic reproductive number R0S for the SDE model, which means for the sake of extinction of I(t), the condition of stochastic SIS model may be weaker than that of the deterministic SIS model. The results are illustrated by computer simulations.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - L.J Hu
AU  - W.Q Shen
PY  - 2015/06
DA  - 2015/06
TI  - A Stochastic Epidemic Model with Constant Immigration and Multi-Dimensional Noises
BT  - Proceedings of the International Conference on Computer Information Systems and Industrial Applications
PB  - Atlantis Press
SP  - 742
EP  - 745
SN  - 2352-538X
UR  - https://doi.org/10.2991/cisia-15.2015.202
DO  - 10.2991/cisia-15.2015.202
ID  - Hu2015/06
ER  -