Abstract
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.
Acknowledgements
The author thanks S. B. Robinson, F. Chen, S. Raynor, K. Berenhaut, and D. Dolgopyat for discussions and comments.
Notes
No potential conflict of interest was reported by the author.