Dynamics of stochastic SEIS epidemic model with varying population size

Jiamin Liu and Fengying Wei

Physica A: Statistical Mechanics and its Applications, 2016, vol. 464, issue C, 241-250

Abstract: We introduce the stochasticity into a deterministic model which has state variables susceptible–exposed–infected with varying population size in this paper. The infected individuals could return into susceptible compartment after recovering. We show that the stochastic model possesses a unique global solution under building up a suitable Lyapunov function and using generalized Itô’s formula. The densities of the exposed and infected tend to extinction when some conditions are being valid. Moreover, the conditions of persistence to a global solution are derived when the parameters are subject to some simple criteria. The stochastic model admits a stationary distribution around the endemic equilibrium, which means that the disease will prevail. To check the validity of the main results, numerical simulations are demonstrated as end of this contribution.

Keywords: Extinction; Persistence; Stochastic SEIS model; Varying population size; Stationary distribution (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:464:y:2016:i:c:p:241-250

DOI: 10.1016/j.physa.2016.06.120

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