Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 60, Issue 2, Pages S92-S118Publisher
SIAM PUBLICATIONS
DOI: 10.1137/20M1376923
Keywords
epidemics on networks; temporal networks; game theory; bounded rationality; stochastic systems
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This article investigates the evolution of epidemics over dynamical networks when nodes choose to interact with others in a selfish and decentralized manner. The authors propose activity-driven networks and a game-theoretic model to analyze the epidemic evolution. The numerical results provide compelling insights into the impact of game-theoretic activation on epidemic dynamics.
We investigate the evolution of epidemics over dynamical networks when nodes choose to interact with others in a selfish and decentralized manner. Specifically, we analyze the susceptibleasymptomatic-infected-recovered (SAIR) epidemic in the framework of activity-driven networks with heterogeneous node degrees and time-varying activation rates and derive both individual- and degreebased mean-field approximations of the exact state evolution. We then present a game-theoretic model where nodes choose their activation probabilities in a strategic manner using current state information as feedback, and we characterize the quantal response equilibrium (QRE) of the proposed setting. We then consider the activity-driven susceptible-infected-susceptible (SIS) epidemic model, characterize equilibrium activation probabilities, and analyze epidemic evolution in closed-loop. Our numerical results provide compelling insights into epidemic evolution under game-theoretic activation. Specifically, for the SAIR epidemic, we show that under suitable conditions, the epidemic can persist, as any decrease in infected proportion is counteracted by an increase in activity rates by the nodes. For the SIS epidemic, we show that in regimes where there is an endemic state, the infected proportion could be significantly smaller under game-theoretic activation if the loss upon infection is sufficiently high.
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