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

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.

Keywords:

• Epidemics
• network model
• infectious disease
• individual risk

AMS Subject Classifications:

• MSC2010
• 37N25
• 92D25
• 60J10

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.