Optimal Responses to an Infectious Disease

TL;DR

This paper models optimal epidemic control strategies using an SIRS framework, showing how healthcare capacity influences policy strictness and timing, with solutions derived in a spreadsheet environment.

Contribution

It introduces an optimal control approach to SIRS epidemic modeling considering healthcare capacity and seasonality, solved via spreadsheet for practical policy insights.

Findings

High healthcare capacity favors mild, immunity-based policies.

Limited healthcare leads to strict lockdown strategies.

Moderate capacity results in flattening the curve approaches.

Abstract

We analyze an optimal control version of a simple SIRS epidemiology model. The policy maker can adopt policies to diminish the contact rate between infected and susceptible individuals, at a specific economic cost. The arrival of a vaccine will immediately end the epidemic. Total or partial immunity is modeled, while the contact rate can exhibit a (user specified) seasonality. The problem is solved in a spreadsheet environment. A reasonable parameter selection leads to optimal policies which are similar to those followed by different countries. A mild response relying on eventually reaching a high immunity level is optimal if ample health facilities are available. On the other hand limited health care facilities lead to strict lock downs while moderate ones allow a flattening of the curve approach.