Simple SIR models with Markovian control

Krzysztof Bartoszek; Wojciech Bartoszek; Michał Krzemiński

doi:10.1007/s42081-021-00107-1

Simple SIR models with Markovian control

Jpn J Stat Data Sci. 2021;4(1):731-762. doi: 10.1007/s42081-021-00107-1. Epub 2021 Feb 16.

Authors

Krzysztof Bartoszek¹, Wojciech Bartoszek², Michał Krzemiński²

Affiliations

¹ Department of Computer and Information Science, Linköping University, Linköping, 581 83 Sweden.
² Department of Probability and Biomathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80 233 Gdańsk, Poland.

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.

Keywords: Markovian control; SIR models; random dynamical systems.