Impacts of Game-Theoretic Activation on Epidemic Spread over Dynamical Networks

TL;DR

This paper models how individual strategic behavior influences epidemic spread on dynamic networks, revealing that game-theoretic activation can sustain or reduce infection levels depending on conditions.

Contribution

It introduces a game-theoretic framework for node activation in epidemic models on dynamic networks, providing equilibrium analysis and insights into epidemic persistence and control.

Findings

Epidemic persistence can occur due to increased activity when infection decreases.

Game-theoretic activation can significantly reduce infected proportions in endemic regimes.

Strategic behavior impacts epidemic evolution and control strategies.

Abstract

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 susceptible-asymptomatic-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 degree-based 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 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.