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

Research output: Contribution to journalArticle

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.
LanguageEnglish
Number of pages13
JournalNonlinear Dynamics
Early online date8 Jul 2019
DOIs
Publication statusE-pub ahead of print - 8 Jul 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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doi = "10.1007/s11071-019-05114-2",
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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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