Abstract

Given the ongoing Covid-19 pandemic, it is of interest to understand how the disease spread is affected by by planner (government) intervention and population behaviors. In this work, the spread of Covid-19 is modeled as a differentiable game between the planner and population. Susceptible-Infected-Recovered (SIR) disease dynamics are modified to incorporate these choices. In this framework we characterize 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. Therefore, it is vital to model the true infected numbers within the context of choices made by individuals within the population. To incorporate this, we extend our framework by modifying the dynamics to include additional sub-compartments of ‘undetected infected’ and ‘detected infected’ in the disease dynamics.

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