Stochastic epidemic models with random environment: quasi-stationarity, extinction and final size
We investigate stochastic $$SIS$$ and $$SIR$$ epidemic models, when there is a random environment that influences the spread of the infectious disease. The inclusion of an external environment into the epidemic model is done by replacing the constant transmission rates with dynamic rates governed by an environmental Markov chain. We put emphasis on the algorithmic evaluation of the influence of the environmental factors on the performance behavior of the epidemic model.