A stochastic differential equation SIS epidemic model with two independent Brownian motions

Siyang Cai, Yongmei Cai, Xuerong Mao

Research output: Journal PublicationArticlepeer-review

33 Citations (Scopus)

Abstract

In this paper, we introduce two perturbations in the classical deterministic susceptible–infected–susceptible epidemic model. Greenhalgh and Gray [4] in 2011 use a perturbation on β in SIS model. Based on their previous work, we consider another perturbation on the parameter μ+γ and formulate the original model as a stochastic differential equation (SDE) with two independent Brownian Motions for the number of infected population. We then prove that our Model has a unique and bounded global solution I(t). Also we establish conditions for extinction and persistence of the infected population I(t). Under the conditions of persistence, we show that there is a unique stationary distribution and derive its mean and variance. Computer simulations illustrate our results and provide evidence to back up our theory.

Original languageEnglish
Pages (from-to)1536-1550
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume474
Issue number2
DOIs
Publication statusPublished - 15 Jun 2019
Externally publishedYes

Keywords

  • Extinction
  • Independent Brownian motion
  • Persistence
  • SIS model
  • Stationary distribution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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