Approximating individual risk of infection in a Markov chain epidemic network model with a deterministic system

摘要

In the Markov chain model of infectious diseases in a connected network of heterogeneous individuals, the computation of the risk of infection for each individual and the expected size of the infected population over time is an NP-hard problem. We show that the individual risk of infection over time can be approximated by orbits of a nonlinear discrete dynamical system on a phase space of dimension equal to the number of individuals in the network. An upper bound for the eradication rate of the infectious disease in the network is also obtained.