Approximation of the invariant probability density function for a stochastic SEIR epidemic model with infectivity during the latent, infectious, and immune periods

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Abstract

In this paper, we proposed and studied a stochastic SEIR epidemic model with infectivity during the latent, infectious, and immune periods. First, the existence of a stationary distribution for the model was verified using the Lyapunov method. Then, by solving the corresponding Fokker-Planck equation, the explicit expression of the probability density function around the quasi-stable equilibrium point was obtained. Furthermore, the global approximation of the invariant probability density function for the model was explored. In addition, sufficient conditions for disease extinction were derived by constructing a suitable Lyapunov function. Finally, numerical simulations are presented to illustrate the analytical results and to reveal the impact of stochastic perturbations on disease transmission.

Keywords

stochastic SEIR epidemic model / infectious force in latent, infected and immune period / stationary distribution / probability density function / global approximation / extinction

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