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

Siyang Cai, Yongmei Cai, Xuerong Mao

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
14 Downloads (Pure)

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
Early online date13 Feb 2019
DOIs
Publication statusPublished - 15 Jun 2019

Keywords

  • SIS model
  • independent Brownian motion
  • extinction
  • persistence
  • stationary distribution

Fingerprint Dive into the research topics of 'A stochastic differential equation SIS epidemic model with two independent Brownian motions'. Together they form a unique fingerprint.

Cite this