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

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Abstract

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
Volume97
Issue number4
Early online date8 Jul 2019
DOIs
Publication statusPublished - 30 Sep 2019

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SIS Model
Brownian movement
Epidemic Model
Stochastic Equations
Brownian motion
Differential equations
Differential equation
Perturbation
Deterministic Model
Extinction
Persistence
Computer Simulation
Computer simulation
Model

Keywords

  • correlated Brownian motions
  • extinction
  • persistence
  • stationary distribution

Cite this

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title = "A stochastic differential equation SIS epidemic model with two correlated Brownian motions",
abstract = "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.",
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author = "Siyang Cai and Yongmei Cai and Xuerong Mao",
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A stochastic differential equation SIS epidemic model with two correlated Brownian motions. / Cai, Siyang; Cai, Yongmei; Mao, Xuerong.

In: Nonlinear Dynamics, Vol. 97, No. 4, 30.09.2019, p. 2175-2187.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A stochastic differential equation SIS epidemic model with two correlated Brownian motions

AU - Cai, Siyang

AU - Cai, Yongmei

AU - Mao, Xuerong

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N2 - 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.

AB - 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.

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KW - persistence

KW - stationary distribution

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