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Estimation of basic reproduction number
This protocol is extracted from research article:
Effects of population co-location reduction on cross-county transmission risk of COVID-19 in the United States
Appl Netw Sci, Feb 18, 2021;

Procedure

Basic reproduction number ($R0$) is defined as the expected number of secondary cases produced by a single infection in a susceptible population (Dietz 1993). Due to a lack of official estimation and report about this basic reproduction number, we estimated this metric for each county based on the growth of confirmed cases using a simple epidemic model. First, we assume that an individual infects an average of $R0$ new individuals after exactly a time $τ$ (the serial interval) has passed. Then starting with $i0$ individuals, the number of infected individuals will be $it=i0·R0t/τ$ (McCluskey 2010). Hence, by taking logarithm of both sides of the equation, $R0$ can be estimated by

Simplifying the equation with a substitution, we can obtain that

where $K=(logit-logi0)/t$. A simple epidemic contagion model tends to assume that growth of an epidemic in the early stages is exponential in a short period (He et al. 2020). Hence, we adopted CDC data from the date of interest to ten days prior to this day and calculated the values of $K$ for each county per day. Based on the existing studies and models on COVID-19 (Zhang et al. 2019, 2020), we set $τ$ to be 5.1 days. Then, we can estimate $R0$ for each county per day using Eq. (4).

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