Games of age-dependent prevention of chronic infections by social distancing
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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.
KeywordsEpidemiological games Social distancing Age structure
Mathematics Subject Classification91A13 91A10 92D30 92D25
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- Arias E (2006) United states life tables, 2003. National Vital Statistics Reports 54(14)Google Scholar
- Aubin JP (1979) Mathematical methods of game and economic theory, DoverGoogle Scholar
- Clark CW, Mangel M (2000) Dynamics State Variable Models in Ecology: Methods and Applications. Oxford University Press, New York, NYGoogle Scholar
- Cornforth DM, Reluga TC, Shim E, Bauch CT, Galvani AP, Meyers LA (2011) Erratic flu vaccination emerges from short-sighted behavior in contact networks. PLOS Comput BiolGoogle Scholar
- Donoghue JF, Golowich E, Holstein BR (1996) Dyamics of the standard model. Cambridge University Press, CambridgeGoogle Scholar
- Houston A, McNamara J (1999) Models of adaptive behaviour. Cambridge University Press, CambridgeGoogle Scholar
- Rzewuski J (1969) Field theory. Hafner Publishing Company, New YorkGoogle Scholar