Differential Games in the spread of Covid-19
Sushant Vijayan

TL;DR
This paper models Covid-19 spread as a differential game between governments and individuals, incorporating disease dynamics, asymptomatic carriers, and detection issues to analyze equilibrium behaviors and control strategies.
Contribution
It introduces a novel differential game framework for Covid-19 spread, including undetected infections and individual decision-making based on reported data.
Findings
Population behavior significantly impacts disease spread.
Detection rates and trust influence the effectiveness of control measures.
Extended model captures the delay in optimal control due to undetected cases.
Abstract
Given the ongoing Covid-19 pandemic, it is of interest to understand how the infections spread as the combined result of measures taken by central planners (governments) and individual behavior. In this work, the spread of Covid-19 is modelled as a differentiable game between the planner and population with appropriate disease spread dynamical equations. We first characterise the equilibrium dynamics of only the population with modifed Susceptible-Infected-Recovered (SIR) equations to highlight the qualitative nature of the equilbrium. Using this result, we formulate the joint equilibrium exposure profile between the planner and population. Additionally, as in case of Covid-19, the role of asymptomatic carriers, inadequacies in testing, contact tracing and quarantining can lead to a significant underestimate of the true infected numbers as compared to just the detected numbers.…
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