Dynamics and optimal control of a stochastic coronavirus (COVID-19) epidemic model with diffusion

In view of the facts in the infection and propagation of COVID-19, a stochastic reaction-diffusion epidemic model is presented to analyse and control this infectious diseases. Stationary distribution and Turing instability of this model are discussed for deriving the sufficient criteria for the persistence and extinction of disease. Furthermore, the amplitude equations are derived by using Taylor series expansion and weakly nonlinear analysis, and selection of Turing patterns for this model can be determined. In addition, the optimal quarantine control problem for reducing control cost is studied, and the differences between the two models are compared. By applying the optimal control theory, the existence and uniqueness of the optimal control and the optimal solution are obtained. Finally, these results are verified and illustrated by numerical simulation.

Automated summary

A stochastic reaction-diffusion epidemic model is used to analyze and control the infectious disease COVID-19, discussing the stationary distribution and Turing instability. The derivation of amplitude equations, determination of Turing patterns, study of optimal quarantine control, and comparison between models are also conducted. Optimal control theory is applied to obtain the existence and uniqueness of the optimal control and solution, which are then verified through numerical simulation.