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

Siyang Cai, Yongmei Cai, Xuerong Mao

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In this paper, we introduce two perturbations in the classical deterministic susceptible-infected-susceptible epidemic model with two correlated Brownian Motions. We consider two perturbations in the deterministic SIS model and formulate the original model as a stochastic differential equation (SDE) with two correlated Brownian Motions for the number of infected population, based on previous work from Gray et al. in 2011 and Hening’s work in 2017. Conditions for the solution to become extinction and persistence are then stated, followed by computer simulation to illustrate the results.
Original languageEnglish
Pages (from-to)2175-2187
Number of pages13
JournalNonlinear Dynamics
Issue number4
Early online date8 Jul 2019
Publication statusPublished - 30 Sep 2019


  • correlated Brownian motions
  • extinction
  • persistence
  • stationary distribution

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