We consider the classical deterministic susceptible-infective-susceptible epidemic model, where the infection and recovery rates depend on a background environmental process that is modeled by a continuous time Markov chain. This framework is able to capture several important characteristics that appear in the evolution of real epidemics in large populations, such as seasonality effects and environmental influences. We propose computational approaches for the determination of various distributions that quantify the evolution of the number of infectives in the population.
Keywords: Color noise; Embedded distribution; Markov chain; Markovian switching; Number of infectives; Random environment; SIS epidemic model; Steady-state distribution; Telegraph noise.