Optimal control of COVID-19 infection rate considering social costs

Abstract

The COVID-19 pandemic has posed a policy making crisis where efforts to slow down or end the pandemic conflict with economic priorities. This paper provides mathematical analysis of optimal disease control policies with idealized compartmental models for disease propagation and simplistic models of social and economic costs. The optimal control strategies are categorized as 'suppression' and 'mitigation' strategies and are analyzed in both deterministic and stochastic models. In the stochastic model, vaccination at an uncertain time is taken into account.

Optimal Control Prevents Itself from Eradicating Stochastic Disease Epidemics

“…This was extended to models with more compartments (Stephenson et al 2017), metapopulations (Ndeffo Mbah and Gilligan 2011, Ögren and Martin 2002), different forms of control (e.g. level of mixing restrictions in Stafford and Kot 2022 vs treatment and inoculation in Sethi and Staats 1978) and different cost functions (Brown and Jane White 2011, Palmer et al 2021). Many papers present results where eradication or infected numbers close to zero is the goal or result of the presented strategies without consideration of the stochastic nature of the problem for both single populations (Saldaña et al 2023, Hamelin et al 2021, Son 2018, Bokil et al 2019) and metapopulations (Ndeffo Mbah and Gilligan 2014, Ögren and Martin 2002).…”