Dynamics of Nonlinear Stochastic SEIR Infectious Disease Model with Isolation and Latency Period

This article establishes and studies a SEIR infectious disease model with higher-order perturbation. Firstly, we proved the existence and uniqueness of the overall positive solution of the model. Secondly, by constructing a Lyapunov function, we obtained sufficient conditions for the existence and uniqueness of the ergodic stationary distribution of the positive solution of the model. Then, it was proved that infectious diseases would become extinct under certain conditions. Finally, this article verified the theoretical analysis results by numerically simulating the process of infectious diseases from outbreak to extinction, the numerical simulation results are symmetrical with the theoretical analysis.