Stationary solution, extinction and density function for a high-dimensional stochastic SEI epidemic model with general distributed delay

Bingtao Han, Baoquan Zhou, Daqing Jiang, Tasawar Hayat and Ahmed Alsaedi

Applied Mathematics and Computation, 2021, vol. 405, issue C

Abstract: A stochastic SEI (Susceptible-Exposed-Infected) epidemic model with general distributed delay is studied in this paper. First, we prove the existence and uniqueness of a global positive solution to the stochastic system. By means of the Lyapunov method, we verify the existence of a stationary distribution of the positive solution under a stochastic criterion R0p>1, which is known as stationary solution. Moreover, if R0p>1, two exact probability density functions around the quasi-stable equilibrium are obtained by solving the corresponding Fokker-Planck equation. Notably, both the explicit expression of density function and the existence of stationary distribution suggest the disease persistence in biological sense. For completeness, some sufficient conditions for disease extinction are established. At last, several numerical simulations are provided to verify our analytical results and reveal the impact of stochastic perturbations on disease transmission.

Keywords: Stochastic SEI model; General distributed delay; Stationary solution; Extinction; Density function (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:405:y:2021:i:c:s009630032100326x

DOI: 10.1016/j.amc.2021.126236

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