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The spread of an epidemic: a game-theoretic approach

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  31 January 2025

Sayar Karmakar ,
Moumanti Podder ,
Souvik Roy  and
Soumyarup Sadhukhan Open the ORCID record for Soumyarup Sadhukhan [Opens in a new window]
Sayar Karmakar*
Affiliation:
University of Florida
Moumanti Podder*
Affiliation:
Indian Institute of Science Education and Research Pune
Souvik Roy*
Affiliation:
Indian Statistical Institute, Kolkata
Soumyarup Sadhukhan*
Affiliation:
Indian Institute of Technology Kanpur
*
*Postal address: University of Florida, 230 Newell Drive, Gainesville, FL 32603, USA. Email address: [email protected]
**Postal address: Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, Maharashtra, India. Email address: [email protected]
***Postal address: Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700108, West Bengal, India. Email address: [email protected]
****Postal address: Indian Institute of Technology, Kalyanpur, Kanpur, Uttar Pradesh 208016, India. Email address: [email protected]
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Abstract

We introduce and study a game-theoretic model to understand the spread of an epidemic in a homogeneous population. A discrete-time stochastic process is considered where, in each epoch, first, a randomly chosen agent updates their action trying to maximize a proposed utility function, and then agents who have viral exposures beyond their immunity get infected. Our main results discuss asymptotic limiting distributions of both the cardinality of the subset of infected agents and the action profile, considered under various values of two parameters (initial action and immunity profile). We also show that the theoretical distributions are almost always achieved in the first few epochs.

Keywords

Game-theoretic modelspread of infectious diseases in networksspread of an epidemicutility functions

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60G50: Sums of independent random variables; random walks
Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 62
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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