Modeling local coronavirus outbreaks

Abstract

This article presents an overview of methods developed for the modeling and control of local coronavirus outbreaks. The article reviews early transmission dynamics featuring exponential growth in infections, and links this to a renewal epidemic model where the current incidence of infection depends upon the expected value of incidence randomly lagged into the past. This leads directly to simple formulas for the fraction of the population infected in an unmitigated outbreak, and reveals herd immunity as the solution to an optimization problem. The model also leads to direct and easy-to-understand formulas for aligning observable epidemic indicators such as cases, hospitalizations and deaths with the unobservable incidence of infection, and as a byproduct leads to a simple first-order approach for estimating the effective reproduction number $R_t$ . The model also leads naturally to direct assessments of the effectiveness of isolation in preventing the spread of infection. This is illustrated with application to repeat asymptomatic screening programs of the sort utilized by universities, sports teams and businesses to prevent the spread of infection.

Keywords: COVID-19; Epidemic indicators; OR in health services; Renewal model; Repeat testing.

Fig. 1

Herd immunity in the basic renewal model ($R_0=2.5$, ${\mu }_F=8.9$, $s\left(t^{*}\right)=0.4$).

Fig. 2

Three approaches to herd immunity.

Fig. 3

Comparing estimated $R_t$ from Connecticut hospitalizations to covidestim.org and RT.live.

Fig. 4

How testing and isolation reduce infections: For a person isolated a random amount of time $T$ after infection, the gray shaded area shows the expected number of further infections whose transmissions are prevented.

Fig. 5

Test sensitivity function as estimated by Kucirka et al. (2020).

Fig. 6

Model projections for the number of infections in 80 days as a function of the testing interval $\delta$ for a student body of size 3500 in a scenario described by (i)-(iv) in the text.