### Abstract

Original language | English |
---|---|

Pages (from-to) | 218-238 |

Number of pages | 21 |

Journal | Applied Mathematics and Computation |

Volume | 276 |

Early online date | 7 Jan 2016 |

DOIs | |

Publication status | Published - 5 Mar 2016 |

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### Keywords

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

### Cite this

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*Applied Mathematics and Computation*, vol. 276, pp. 218-238. https://doi.org/10.1016/j.amc.2015.11.094

**SDE SIS epidemic model with demographic stochasticity and varying population size.** / Greenhalgh, D.; Liang, Y.; Mao, X.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Greenhalgh, D.

AU - Liang, Y.

AU - Mao, X.

PY - 2016/3/5

Y1 - 2016/3/5

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

KW - varying population size

KW - extinction

KW - stochastic differential equation

KW - Brownian motion

UR - http://www.sciencedirect.com/science/journal/00963003

U2 - 10.1016/j.amc.2015.11.094

DO - 10.1016/j.amc.2015.11.094

M3 - Article

VL - 276

SP - 218

EP - 238

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -