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09.04.2020 Opinion

The Mathematics Of Social Distancing – The Case In Ghana

By Samuel Asante Gyamerah
The Mathematics Of Social Distancing – The Case In Ghana
LISTEN APR 9, 2020

Social distancing, defined as a measure taken to prevent and reduce the spread of infectious disease (such as SAS, COVID-19, etc.) by reducing the number of times individuals come into contact with each other and maintaining the physical distance between individual.

Social distancing interventions are significant as they depict the only measure guaranteed to be accessible against a novel strain of influenza (e.g. COVID-19) in the initial phases of a pandemic (Kelso et al., 2009).

To help understand the effect this measure can have on the COVID-19 pandemic, “Basic reproduction number” shows how a reduction in social activities can contain the spread of the pandemic.

Basic reproduction number R0 is the average number of secondarily infected individuals generated from one primary infected individual in a population where all individuals are susceptible to disease. The reproductive number for COVID-19 was estimated to be 2.5 (Zhang et al., 2020) during the early stages. That is, on average, an infected individual will spread the disease to 2.5 other people.

Now suppose, each infected person unintentionally spread COVID-19 over a median 5-day incubation period. Assume that after this period, the infected person begins to develop symptoms and is immediately self-isolated from the populace.

However, it should be noted that after the 5 days period, one infected individual will have infected 2.5 more individuals and the network continues. Also, assume that there is a direct relationship between the reproduction number and social interaction. That is as the social interaction increases, the reproduction number R0 increases and vice versa. For better illustration, consider table 1 below:

Table 1: No social distancing measures

Days 1 6 11 16 21 26 31 Total Case
R0 = 2.5 1 2.5 6.25 15.63 39.06 97.66 244.14 406

From table 1, one individual can only infect 2.5 other individuals on average and there would be 406 infected people in 30 days period.

Now, assume that the reproduction number is reduced to half (social exposure is reduced to 50%). That is each infected individual can only infect 1.25 more individuals because of a reduction of social exposure of that individual.

Table 2: Reducing social exposure by 50%

Days 1 6 11 16 21 26 31 Total Case
R0 = 1.25 1 1.25 1.56 1.95 2.44 3.05 3.81 15

From table 2, one individual can only infect 1.25 other individuals on average and there would be 15 infected people in 30 days period.

The total number of infected cases in Ghana on 07/05/2020 excluding those that were quarantined on arrival at the Kotoka International Airport-Ghana just before they made any social contacts and the previously recorded cases through contact tracing were 73.

If each individual can infect 406 more individuals before experiencing the symptoms or being tested for the virus, then the total number of individuals affected for a month period is 29638. Assume, these individuals practiced social exposure by 50% even before they got infected, then the total number of individuals infected by these individuals for the same period are 1095. Suppose, these individuals even practiced an enhanced social distancing by 25%, then the total number of individuals infected by these individuals for the same period will drastically reduce to 146.

Clearly, the mathematics of social distancing supports the decision (minimizing the physical contact between individuals, banning of social activities, and the partial lockdown of prime areas) of the Government. In conclusion, it can be stated that social distancing is a powerful disease control strategy to reduce the number of infections.

Author: Samuel Asante Gyamerah (Ph.D.)
1. Kelso, J. K., Milne, G. J., & Kelly, H. (2009). Simulation suggests that rapid activation of social distancing can arrest epidemic development due to a novel strain of influenza. BMC public health, 9(1), 117.

2. Zhang, S., Diao, M., Yu, W., Pei, L., Lin, Z., & Chen, D. (2020). Estimation of the reproductive number of Novel Coronavirus (COVID-19) and the probable outbreak size on the Diamond Princess cruise ship: A data-driven analysis. International Journal of Infectious Diseases, 93, 201-204.

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