A model of COVID-19 pandemic evolution in African countries

Abstract

We studied the COVID-19 pandemic evolution in selected African countries. For each country considered, we modeled simultaneously the data of the active, recovered and death cases. In this study, we used a year of data since the first cases were reported. We estimated the time-dependent basic reproduction numbers, $R_0$ , and the fractions of infected but unaffected populations, to offer insights into containment and vaccine strategies in African countries. We found that $R_0\le 4$ at the start of the pandemic but has since fallen to $R_0\sim 1$ . The unaffected fractions of the populations studied vary between $1-10$ % of the recovered cases.

Keywords: Basic reproduction number; COVID-19; SARS-CoV-2; SIDARTHE.

Fig. 1

COVID-19 data and model of South Africa. Active, recovered, death and total cases are shown in the top-left plot. Day 0 is March 5, 2020. The bottom-left plot shows the time-dependent basic reproduction number. The error bands are statistical in the top plot. The bottom-left plot error band includes systematic uncertainty from the infected but unaffected population not counted in the data. The goodness-of-fit of the data modeling is shown as the ratio of the data over the model in the top-right plot. The uncertainty ban contains the statistical uncertainty in the data and the systematic uncertainty on the modeling. The model prediction of the recovered population is shown in the bottom-right plot; also shown, is the undiagnosed fraction of the people that were infected and recovered without symptoms. This fraction, called the unaffected cases, is not measured or included in the data.

Fig. 2

COVID-19 data and model of Ghana. Active, recovered, death and total cases are shown in the top-left plot. Day 0 is March 12, 2020. The bottom-left plot shows the time-dependent basic reproduction number. The error bands are statistical in the top plot. The bottom-left plot error band includes systematic uncertainty from the infected but unaffected population not counted in the data. The goodness-of-fit of the data modeling is shown as the ratio of the data over the model in the top-right plot. The uncertainty ban contains the statistical uncertainty in the data and the systematic uncertainty on the modeling. The model prediction of the recovered population is shown in the bottom-right plot; also shown, is the undiagnosed fraction of the people that were infected and recovered without symptoms. This fraction, called the unaffected cases, is not measured or included in the data.

Fig. 3

COVID-19 data and model of Kenya. Active, recovered, death and total cases are shown in the top-left plot. Day 0 is March 12, 2020. The error bars show the statistical errors between the Model and the Kenya C0VID-19 data. The bottom-left plot shows the time-dependent basic reproduction number and the error band includes systematic uncertainty from the infected but unaffected population not included in the data. The top-right plot shows the goodness-of-fit which is given by the ratio of the data over the model. The uncertainty ban contains the statistical uncertainty in the data and the systematic uncertainty on the modeling. The model prediction of the recovered population is shown in the bottom-right plot; also shown, is the undiagnosed fraction of the people that were infected and recovered without symptoms. This fraction, called the unaffected cases, is not measured or included in the data.

Fig. 4

COVID-19 data and model of Madagascar. Active, recovered, death and total cases are shown in the top-left plot. Day 0 is March 13, 2020. The bottom-left plot shows the time-dependent basic reproduction number. The error bands are statistical in the top plot. The bottom-left plot error band includes systematic uncertainty from the infected but unaffected population not counted in the data. The goodness-of-fit of the data modeling is shown as the ratio of the data over the model in the top-right plot. The uncertainty ban contains the statistical uncertainty in the data and the systematic uncertainty on the modeling. The model prediction of the recovered population is shown in the bottom-right plot; also shown, is the undiagnosed fraction of the people that were infected and recovered without symptoms. This fraction, called the unaffected cases, is not measured or included in the data.

Fig. 5

COVID-19 data and model of Cameroon. Active, recovered, death and total cases are shown in the top-left plot. Day 0 is March 6, 2020. The bottom-left plot shows the time-dependent basic reproduction number. The error bands are statistical in the top plot. The bottom-left plot error band includes systematic uncertainty from the infected but unaffected population not counted in the data. The goodness-of-fit of the data modeling is shown as the ratio of the data over the model in the top-right plot. The uncertainty ban contains the statistical uncertainty in the data and the systematic uncertainty on the modeling. The model prediction of the recovered population is shown in the bottom-right plot; also shown, is the undiagnosed fraction of the people that were infected and recovered without symptoms. This fraction, called the unaffected cases, is not measured or included in the data.