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Dynamics of stochastic SEIS epidemic model with varying population size. (English) Zbl 1400.92512

Summary: 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.

MSC:

92D30 Epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
92D25 Population dynamics (general)
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References:

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