Dynamical analysis of a stochastic delayed epidemic model with levy jumps and regime switching

In this paper a delayed stochastic SLVIQR epidemic model, which can be applied for modeling the new coronavirus COVID-19 after a calibration, is derived. Model is constructed by assuming that trans-mission rate satisfies the mean-reverting Ornstain-Uhlenbeck process and, besides a standard Brownian motion, another two driving processes are considered: a stationary Poisson point process and a con-tinuous finite-state Markov chain. For the constructed model, the existence and uniqueness of positive global solution is proven. Also, sufficient conditions under which the disease would lead to extinction or be persistent in the mean are established and it is shown that constructed model has a richer dy-namic analysis compared to existing models. In addition, numerical simulations are given to illustrate the theoretical results.(c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a delayed stochastic SLVIQR epidemic model is derived, which can be applied to model the new coronavirus COVID-19 after calibration. The model assumes that the transmission rate follows a mean-reverting Ornstain-Uhlenbeck process and considers two additional driving processes: a stationary Poisson point process and a continuous finite-state Markov chain. The existence and uniqueness of the positive global solution are proven for the constructed model. Sufficient conditions for disease extinction or persistence in the mean are established, and the model is shown to have a richer dynamic analysis compared to existing models. Numerical simulations are provided to illustrate the theoretical results.