Endemic SIR Model in Random Media with Applications

We consider an averaging principle for the endemic SIR model in a semi-Markov random media. Under stationary conditions of a semi- Markov media we show that the perturbed endemic SIR model converges to the classic endemic SIR model with averaged coefficients. Numerical toy examples and their interpretations are also presented for two-state Markov and semi-Markov chains. We also discuss two numerical examples involving real data: 1) Dengue Fever Disease (Indonesia and Malaysia (2009)) and 2) Cholera Outbreak in Zimbabwe (2008-2009). Novelty of the paper consists in studying of an endemic SIR model in semi-Markov random media and in implementations and interpretations of the results through numerical toy examples and discussion of numerical examples with real data.