On the basic reproduction number in semi-Markov switching networks

Basic reproduction number $ \mathcal {R}_0 $ in network epidemic dynamics is studied in the case of stochastic regime-switching networks. For generality, the dependence between successive networks is considered to follow a continuous time semi-Markov chain. $ \mathcal {R}_0 $ is the weighted average of the basic reproduction numbers of deterministic subnetworks. Its position with respect to 1 can determine epidemic persistence or extinction in theories and simulations.