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Simple SIR models with Markovian control
Krzysztof Bartoszek1, Wojciech Bartoszek2, Michał Krzemiński2
1Department of Computer and Information Science, Linköping University, Linköping, 581 83 Sweden.
Abstract:
We consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving Markov chain. We formulate some questions and conjectures of a purely theoretical nature.
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