Journal of Mathematical Biology

, Volume 66, Issue 7, pp 1527–1553

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

Article

## 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.

### Keywords

Epidemiological games Social distancing Age structure

### Mathematics Subject Classification

91A13 91A10 92D30 92D25

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