SDE SIS epidemic model with demographic stochasticity and varying population size

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this paper we look at the two dimensional stochastic differential equation (SDE) susceptible-infected-susceptible (SIS) epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size. First we look at the SDE model for the total population size and show that there exists a unique non-negative solution. Then we look at the two dimensional SDE SIS model and show that there exists a unique non-negative solution which is bounded above given the total population size. Furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely. Lastly, we support our analytical results with numerical simulations using theoretical and realistic disease parameter values.
LanguageEnglish
Pages218-238
Number of pages21
JournalApplied Mathematics and Computation
Volume276
Early online date7 Jan 2016
DOIs
Publication statusPublished - 5 Mar 2016

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Stochasticity
Epidemic Model
Population Size
Stochastic Equations
Differential equations
Nonnegative Solution
Differential equation
Random processes
Stochastic Processes
Contact
Numerical Simulation
Computer simulation
Model

Keywords

  • two dimensional SIS epidemic model
  • demographic stochasticity
  • varying population size
  • extinction
  • stochastic differential equation
  • Brownian motion

Cite this

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title = "SDE SIS epidemic model with demographic stochasticity and varying population size",
abstract = "In this paper we look at the two dimensional stochastic differential equation (SDE) susceptible-infected-susceptible (SIS) epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size. First we look at the SDE model for the total population size and show that there exists a unique non-negative solution. Then we look at the two dimensional SDE SIS model and show that there exists a unique non-negative solution which is bounded above given the total population size. Furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely. Lastly, we support our analytical results with numerical simulations using theoretical and realistic disease parameter values.",
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author = "D. Greenhalgh and Y. Liang and X. Mao",
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SDE SIS epidemic model with demographic stochasticity and varying population size. / Greenhalgh, D.; Liang, Y.; Mao, X.

In: Applied Mathematics and Computation, Vol. 276, 05.03.2016, p. 218-238.

Research output: Contribution to journalArticle

TY - JOUR

T1 - SDE SIS epidemic model with demographic stochasticity and varying population size

AU - Greenhalgh, D.

AU - Liang, Y.

AU - Mao, X.

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N2 - In this paper we look at the two dimensional stochastic differential equation (SDE) susceptible-infected-susceptible (SIS) epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size. First we look at the SDE model for the total population size and show that there exists a unique non-negative solution. Then we look at the two dimensional SDE SIS model and show that there exists a unique non-negative solution which is bounded above given the total population size. Furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely. Lastly, we support our analytical results with numerical simulations using theoretical and realistic disease parameter values.

AB - In this paper we look at the two dimensional stochastic differential equation (SDE) susceptible-infected-susceptible (SIS) epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size. First we look at the SDE model for the total population size and show that there exists a unique non-negative solution. Then we look at the two dimensional SDE SIS model and show that there exists a unique non-negative solution which is bounded above given the total population size. Furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely. Lastly, we support our analytical results with numerical simulations using theoretical and realistic disease parameter values.

KW - two dimensional SIS epidemic model

KW - demographic stochasticity

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KW - extinction

KW - stochastic differential equation

KW - Brownian motion

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