title: Games of age-dependent prevention of chronic infections by social distancing.
abstract: 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.
authors.affiliation: Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. timothy@reluga.org
authors.forename: Timothy C
authors.initials: TC
authors.lastname: Reluga
authors.forename: Jing
authors.initials: J
authors.lastname: Li
mesh_terms: D000367:Age Factors; D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission*; D005716:Game Theory; D006801:Humans; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D012929:Psychological Distance