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Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching. (English) Zbl 1400.92484
Summary: We discuss the effect of introducing telegraph noise, which is an example of an environmental noise, into the susceptible-infectious-recovered-susceptible (SIRS) model by examining the model using a finite-state Markov Chain (MC). First we start with a two-state MC and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence. We then explain how the results can be generalised to a finite-state MC. The results for the SIR (Susceptible-Infectious-Removed) model with Markovian Switching (MS) are a special case. Numerical simulations are produced to confirm our theoretical results.

MSC:
92D30 Epidemiology
34F05 Ordinary differential equations and systems with randomness
60J28 Applications of continuous-time Markov processes on discrete state spaces
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