Act Now or Forever Hold Your Peace: Slowing Contagion with Unknown Spreaders, Constrained Cleaning Capacities and Costless Measures

Abstract

What can be done to slow contagion when unidentified healthy carriers are contagious, total isolation is impossible, cleaning capacities are constrained, and contamination parameters and even contamination channels are uncertain? Short answer: reduce variance.
In the oft-analyzed reciprocal contamination framework, convexity of expected contamination is verified for a limited number of users and spreaders, but concavity occurs for many users (except with linear effect of additional spreaders). Conversely, when people are contaminated by successively using a device, expected contamination is always a convex function of the number, n, of users, and can therefore be reduced by limiting the variance of n. Furthermore, in that case, individuals’ optimizing behavior may not suffice to enforce optimal organization.
Gains form better organization are bounded, but substantial and costless. Still, they decrease when the proportion of spreaders increases: Optimal organization is more beneficial at the beginning of an epidemic, which calls for early action.

Keywords: coronavirus, epidemic, contagion, healthy carrier, spreaders, cleaning, convexity, restroom

JEL Classification: I12, I18, L23, M50