Shielding the vulnerable in an epidemic: a numerical approach

TL;DR

This paper presents a numerical approach to epidemic modeling that divides the population into vulnerable and fit groups, using a two-type Reed-Frost model with four parameters to evaluate social distancing strategies and their complex effects.

Contribution

It introduces a simple, fast stochastic model for two-type populations in epidemics, highlighting counterintuitive effects of shielding vulnerable groups.

Findings

Small vulnerable-to-fit infection parameter can increase death toll

Increasing the parameter may sometimes reduce overall deaths

Model enables rapid simulation of epidemic scenarios

Abstract

The death toll for Covid-19 may be reduced by dividing the population into two classes, the vulnerable and the fit, with different lockdown regimes. Instead of one reproduction number there now are four parameters. These make it possible to quantify the effect of the social distancing measures. There is a simple stochastic model for epidemics in a two type population. Apart from the size of the population of the vulnerable and the fit, and the initial number of infected in the two classes, only the four reproduction parameters are needed to run the two type Reed-Frost model. The program is simple and fast. On a pc it takes less than five minutes to do a hundred thousand simulations of the epidemic for a population of the size of the US. Epidemics are non-linear processes. Results may be counterintuitive. The average number of vulnerable persons infected by an infectious fit person is a crucial parameter of the epidemic in the two type population. Intuitively this parameter should be small. However simulations show that even if this parameter is small the death toll may be higher than without shielding. Under certain conditions increasing the value of the parameter may reduce the death toll. The article addresses these blind spots in our intuition.