Modelling the Potential Impact of Social Distancing on the COVID-19 Epidemic in South Africa

Abstract

The novel coronavirus (COVID-19) pandemic continues to be a global health problem whose impact has been significantly felt in South Africa. With the global spread increasing and infecting millions, containment efforts by countries have largely focused on lockdowns and social distancing to minimise contact between persons. Social distancing has been touted as the best form of response in managing a rapid increase in the number of infected cases. In this paper, we present a deterministic model to describe the impact of social distancing on the transmission dynamics of COVID-19 in South Africa. The model is fitted to data from March 5 to April 13, 2020, on the cumulative number of infected cases, and a scenario analysis on different levels of social distancing is presented. The model shows that with the levels of social distancing under the initial lockdown level between March 26 and April 13, 2020, there would be a projected continued rise in the number of infected cases. The model also looks at the impact of relaxing the social distancing measures after the initial announcement of the lockdown. It is shown that relaxation of social distancing by 2% can result in a 23% rise in the number of cumulative cases whilst an increase in the level of social distancing by 2% would reduce the number of cumulative cases by about 18%. The model results accurately predicted the number of cases after the initial lockdown level was relaxed towards the end of April 2020. These results have implications on the management and policy direction in the early phase of the epidemic.

Figure 1

Google mobility report for South Africa from March 1 to April 12, 2020, for (a) retail and recreation, and grocery and pharmacy, (b) workplace and residential, and (c) parks and transit stations.

Figure 2

A decrease in newly infected cases (%) since the lockdown, together with a 7-day moving average, for the 40 data points.

Figure 3

Model diagram for COVID-19 for South Africa with immigration, lockdown, and social distancing.

Figure 4

(a) Influence of parameter values on the cumulative cases before the lockdown. (b) Influence of parameter values on the cumulative cases after the lockdown.

Figure 5

Model fit to data for COVID-19 before the lockdown. The best-fit parameter values are as follows: Λ = 11244, p = 1.7598 × 10⁻⁵, β = 1.1411, κ = 0.655, σ = 0.4482, and ρ = 1.

Figure 6

A simulation model for the SEIR model for all the populations in the absence of any intervention, i.e., ρ = 1. The best fit parameter values are as follows: Λ = 11244, p = 1.7598 × 10⁻⁵, β = 1.1411, κ = 0.655, and σ = 0.4482.

Figure 7

A simulation model for the SEIR model for exposed and infected in the absence of any intervention, i.e., ρ = 1. The best-fit parameter values are as follows: Λ = 11244, p = 1.7598 × 10⁻⁵, β = 1.1411, κ = 0.655, and σ = 0.4482.

Figure 8

The graph shows COVID-19 model fitting for the cumulative infected cases for South Africa before and after lockdown. The red dots are the cumulative reported number of COVID-19 cases before and after lockdown. The red vertical line represents the start of the national lockdown. The continuous curve represents the model fit. The best-fit parameter values are as follows: Λ = 11244, p = 1.7598 × 10⁻⁵, β = 1.1411, κ = 0.655, σ = 0.4482, and ρ = 0.453. Note that ρ = 0.453 represents about 55% compliance in social distancing.

Figure 9

The graph shows COVID-19 model fitting for the cumulative infected cases for various scenarios. The trajectories for different levels of social distancing are shown by the different line types. The red dots are the cumulative reported number of COVID-19 cases in South Africa before the lockdown and two weeks after the lockdown. The red vertical line denotes the time when a lockdown was implemented by the government with a delay of one data point as the reported cases represent posterior data. The best-fit parameter values are as follows: Λ = 11244, p = 1.7598 × 10⁻⁵, β = 1.1411, κ = 0.655, σ = 0.4482, and ρ = 0.453.