Dynamics and simulations of a second order stochastically perturbed SEIQV epidemic model with saturated incidence rate

• DOI: 10.1016/j.chaos.2021.111312
• Publication Date: 2021-08-15T02:47:48Z
• Authors: Chun Lu; Honghui Liu; De Zhang
• Keywords: Epidemic model; Stationary distribution; Basic reproduction number

Abstract A second order stochastically perturbed SEIQV epidemic model is studied in this paper. Firstly, we derive sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the model by establishing a suitable stochastic Lyapunov function. Secondly, we obtain adequate conditions for completing eradication and wiping out of the infectious disease from the basic reproduction number of corresponding deterministic model. Thirdly, distinguished from the previous literatures, the equilibrium stability is investigated by combining Hasminskii theory of stability with Lyapunov function. The new method can also be successfully used for some classical epidemic models. Finally, our analytical results are illustrated by computer simulations, including three examples based on disease originated from reality.