Stochastic Delay Differential Model for Coronavirus Infection COVID-19

Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of coronavirus COVID-19 to humans. In this chapter, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number R0s for the stochastic model which is smaller than R₀ of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. We provide a stochastic SIRC model with time delay in Sect. 13.2. In Sect. 13.3, we study the existence and uniqueness of a global positive solution for the stochastic delayed SIRC model. In Sects. 13.4 and 13.5, a stationary distribution and extinction analysis of the underlying model are investigated. Some virtual numerical examples are presented in Sect. 13.6. Finally, concluding remarks are provided in Sect. 13.7.