A stochastic epidemic model with time delays and unreported cases based on Markovian switching

Disease dynamics are influenced by changes in the environment. In this study, unreported cases (U), environmental perturbations, and exogenous events are included in the epidemic Susceptible–Exposed–Infectious–Unreported–Removed model with time delays. We examine the process of switching from one regime to another at random. Ergodicity and stationary distribution criteria are discussed. A Lyapunov function is used to determine several conditions for disease extinction. The spread of a disease is affected when transitioning from one random regime to another via sudden external events, such as hurricanes. The model and theoretical results are validated using numerical simulations.