Journal of Mathematical Biology

, Volume 66, Issue 7, pp 1527–1553

Games of age-dependent prevention of chronic infections by social distancing


DOI: 10.1007/s00285-012-0543-8

Cite this article as:
Reluga, T.C. & Li, J. J. Math. Biol. (2013) 66: 1527. doi:10.1007/s00285-012-0543-8


Epidemiological games combine epidemic modelling with game theory to assess strategic choices in response to risks from infectious diseases. In most epidemiological games studied thus-far, the strategies of an individual are represented with a single choice parameter. There are many natural situations where strategies can not be represented by a single dimension, including situations where individuals can change their behavior as they age. To better understand how age-dependent variations in behavior can help individuals deal with infection risks, we study an epidemiological game in an SI model with two life-history stages where social distancing behaviors that reduce exposure rates are age-dependent. When considering a special case of the general model, we show that there is a unique Nash equilibrium when the infection pressure is a monotone function of aggregate exposure rates, but non-monotone effects can appear even in our special case. The non-monotone effects sometimes result in three Nash equilibria, two of which have local invasion potential simultaneously. Returning to a general case, we also describe a game with continuous age-structure using partial-differential equations, numerically identify some Nash equilibria, and conjecture about uniqueness.


Epidemiological gamesSocial distancingAge structure

Mathematics Subject Classification


Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA