A Model for the Testing and Tracing Needed to Suppress COVID-19

This paper presents the first analytical model for calculating how many tests and tracing needed to suppress COVID-19 transmission. The number of people needs to be tested daily is given by: <disp-formula id="ueqn1"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20120568v3_ueqn1.gif" position="float" orientation="portrait"/></alternatives></disp-formula> Where

N is the size of the population in consideration

A_r is the attack rate at any given time

T_p is the test-positive rate

ρ is the percentage of infectious people that have to be detected per day. To make the effective reproduction number R_e below 1, ρ must satisfy the following equation: <disp-formula id="ueqn2"><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20120568v3_ueqn2.gif" position="float" orientation="portrait"/></alternatives></disp-formula>

Where

R₀ is the basic reproduction number,

S/N is the percentage of the susceptible population over the entire population,

D is the length of the infectious period, and

η is the percentage of close contacts that have to be traced.

This model provides insights and guidance to deploy the testing and tracing resources optimally. An Excel model is attached to facilitate easy calculation of the number of tests and tracing needed. This model is also applicable to any infectious disease that can be suppressed by testing and tracing.