Revisiting SIR in the Age of COVID-19: Explicit Solutions and Control Problems

The nonpopulation conserving SIR (SIR-NC) model to describe the spread of infections in a community is studied. Unlike standard model, this does not assume population conservation. Although similar form SIR, SIR-NC admits closed solution while allowing us mortality and also provides different, arguably more realistic, interpretation parameters. Numerical comparisons with standard, conserving, are provided. Extensions include imported infections, interacting communities, models that births deaths presented analyzed. Several numerical examples illustrate these models. A discrete time control problem for epidemic which cost function depends on variables correspond levels lockdown, level testing quarantine, number infections. We switching moving between lockdown levels. experiments presented.