Stochastic Delay Differential Model for Coronavirus Infection COVID-19

Rihan, F. A.

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. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.