Optimal illness policy for an unethical daycare center

TL;DR

This paper models an unethical daycare strategy where keeping sick children increases profits, revealing how disease infectiousness influences optimal sick child attendance and profit maximization.

Contribution

It introduces a modified SIR model to determine the optimal number of sick children a daycare should keep for maximum profit, highlighting ethical concerns.

Findings

Higher disease infectiousness leads to fewer sick children being kept.

Profit increases as the number of sick children maintained rises.

Optimal sick child attendance approaches zero with increased infectiousness.

Abstract

While businesses are typically more profitable if their workers and communities are minimally exposed to diseases, the same is not true for daycare centers. Here it is shown that a daycare center could maximize its profits by maintaining a population of sick children within the center, with the intention to infect more children who then do not attend. Through a modification of the Susceptible-Infected-Recovered (SIR) model for disease spread we find the optimal number of sick children who should be kept within the center to maximize profits. We show that as disease infectiousness increases, the optimal attendance rate of sick children approaches zero, while the potential profit increases.