key: cord-0279699-sb74lmq8
authors: Assamagan, K'et'evi A.; Azote, Somi'ealo; Connell, Simon H.; Haliya, Cyrille E.; Mabote, Toivo S.; Mwale, Kondwani C. C.; Onyie, Ebode F.; Zimba, George
title: A study of COVID-19 data from African countries
date: 2020-07-21
journal: nan
DOI: 10.46882/ijphe/1235
sha: 0b54d6c938f4be89840872ef8c88ed4aa3c88e3d
doc_id: 279699
cord_uid: sb74lmq8

COVID-19 is a new pandemic disease that is affecting almost every country with a negative impact on social life and economic activities. The number of infected and deceased patients continues to increase globally. Mathematical models can help in developing better strategies to contain a pandemic. Considering multiple measures taken by African governments and challenging socio-economic factors, simple models cannot fit the data. We studied the dynamical evolution of COVID-19 in selected African countries. We derived a time-dependent reproduction number for each country studied to offer further insights into the spread of COVID-19 in Africa.

COVID-19 has spread to the entire world within a few months [1] . The World Health Organization (WHO) predicts that 29 to 44 million Africans could be infected with SARS-CoV-2 during the first year of the pandemic and 83 to 190 thousand Africans could die if they don't uphold containment measures [2, 3] .

This grim prediction suggests that most African countries have a lower transmission rate than the other regions of the world such as Europe, the United States of America, and China [2] . However, the low transmission rate may prolong the outbreak over several years, putting pressure on economic resources.

Most African countries are struggling because of lack of essential medical resources such as test kits, personal protective equipments and ventilators. The containment measures such as frequent hand washing, isolation, contact tracing, and social distance are a challenge in Africa-around 60% of the African population lives below the poverty line [4] and cannot afford the basic hygienic amenities. The densely populated slums of Africa make social distancing impossible and burdens the isolation centers. In Africa, the outbreak of COVID-19 has already claimed thousands of lives, rendered millions jobless, increased insecurity and poverty level. A number of studies have been performed on the evolution and impact of COVID-19 in Africa, and on the African responses to the pandemic [5] [6] [7] [8] [9] [10] [11] [12] .

Models for pandemics are necessary for understanding the cause, source, spread, and planning outbreak containment [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] . The simplest of these models is the SIR model; it describes disease transmission and propagation in three categories, namely the susceptible, infected and recovered fractions of a population [23] . An improved version of the SIR model is the SEIR model which proposes four stages: susceptible, exposed, infectious, and removed population densities [24] . Simple models for COVID-19 do not offer reliable insights or predictions to inform African policymakers [23] . The models become complex when one includes more socio-economic factors. One such model is the SIDARTHE [25] which considers eight stages of epidemic evolution.

In this paper, we analyzed COVID-19 data from Benin, Mozambique, Rwanda,

Togo and Zambia. We tested the SIDARTHE model on these data and estimated basic reproduction numbers. This may improve our understanding of the spread of COVID-19 in Africa, although the numbers of tests are small relative to the sizes of the populations. We offer suggestions to keep the basic reproduction number below one, to slow and contain the spread. In Section 2, we present the mathematical model used in the studies reported in this paper. In Section 3, we discuss the analysis strategy and present the results. In Section 4, we discuss the implications of the results, and we offer concluding remarks in Section 5

To have confidence in a model, one needs suitable fits to existing data and verifiable predictions. Here, we describe the SIDARTHE dynamical model, developed to study the spread of COVID-19 in Italy [25] . The strength of this model comes from the fact that it considers the various measures taken by Italian government to contain the disease [25] . It is a mean-field epidemiological model with eight time-dependent compartments, namely Susceptible, Infected, Diagnosed, Ailing, Recognized, Threatened, Healed and Extinct categories, as shown in Figure 1 . This model describes the dynamic spread of the disease when social distancing, lockdown, testing, contact tracing, treatment, curfew, and/or quarantine are implemented as containment strategies in a population. The following mathematical system of eight differential equations describes the SIDARTHE model [25] :

The basic reproduction number, R 0 , is an epidemiological parameter to describe the contagiousness or transmissibility of infections [25] . Biological, socioeconomic, environmental and behavioral factors affect R 0 . It is a parameter used to study the dynamics of an infectious disease. An outbreak ends if R 0 < 1 and continues if R 0 > 1. R 0 indicates of the potential magnitude of an outbreak, and can be used to estimate the fraction of the population to be vaccinated to stop the spread. However, because of its complex dependence on many factors, R 0 is often modeled and, as a result, depends on model parameters and assumptions. Therefore, one must apply R 0 with great caution. The SIDARTHE model defines R 0 as follows [25] :

with r 1 = + ζ + λ,

r 4 = ν + ξ,

We adapted the SIDARTHE model to consider the containment measures taken by African countries and the impact of socio-economic conditions in Africa. In Section 3, we discuss the analyses of data from Benin, Mozambique, Rwanda, Togo and Zambia, and the application of the SIDARTHE model to these data.

We collected the first three months of the official data on COVID-19 from Benin, Mozambique, Rwanda, Togo and Zambia. We got the data from the official website of each country. One team member who is a resident (or is a native) of a country was in charge to compile and follow the measures taken. The same team member was also responsible to understand the tests performed in that country. The data came in categories of active, recovered, dead and total cases.

Compared to the SIDARTHE stages of pandemic evolution, it is straightforward to establish the following associations: the recovered cases correspond to the healed compartment and the dead cases to extinct category shown in Figure 1 .

The active cases do not have a direct correspondence in the model. One needs to understand the tests to define an association of the active cases to the model. In the following subsections, we discuss each country, one-by-one. 29. On May 12, they suspended international flights until May 30, except for humanitarian, cargo or state flights. However, they did not impose a lockdown.

At the time of writing this article, the government and local authorities were studying schools re-opening strategies. Figure 3 shows the COVID-19 data of Mozambique with the modeling of the SIDARTHE; in the top panel, we see good agreement between the model and the data for all the cases of the dead, recovered and active fractions of the population. As a result, the total cumulative cases are also well modeled. In the bottom panel of Figure 3 , we show the extracted R 0 which remains below two for the entire period shown.

The R 0 for Mozambique fluctuates. Between Day 40 and Day 45, it dropped significantly. After Day 45, it stays slightly above one. Table SM3 shows the model parameters that best match the data of Mozambique.

On Figure 4 shows the Rwanda COVID-19 data on the top panel; we superimpose the modeling of the data and see good agreement in the dead, recovered and active cases. As a result, the total cases are also well modeled. From the modeling, we derived R 0 for Rwanda as shown in the bottom panel of Figure 4 . The initial R 0 is above three, but drops well below one after about a week because of the swift reaction of the government and the public.

After a few weeks, the R 0 rose above one, most likely because of the difficulties to observe the measures imposed. We see another reduction in R 0 around Day 47; around Day 64, it went up to about 1.5. Table SM2 shows the model parameters that best match the data of Rwanda.

Togo recorded its first case of COVID-19 on March 6, 2020; the individual was a Togolese national who had traveled abroad. The government implemented effective from March 19. For at least two-and-a-half months, schools, universities, churches, saloons, bars, etc., were closed. They imposed a curfew from 9:00pm to 6:00am. They tested truck drivers crossing the borders; then they allowed the trucks to proceed to their destinations under surveillance. If the drivers had been in contact with confirmed cases, they placed them under quarantine. On April 7, the government started massive tests of both symptomatic and asymptomatic persons in cities with over ten cases. From June 9, they lifted the curfew. However, the government made the wearing of masks compulsory; also, they required hand washing before access to public or private services or markets.

We used the containment measures to tune the model parameters as a function of time. Figure 5 shows Figure 5 shows the reported daily test numbers. Table SM4 shows the model parameters that best match the data of Togo.

On Figure 6 shows the COVID-19 data of Zambia and its SIDARTHE modeling.

The death rate and the total cases are well modeled. The trends of the recovered and active cases are fairly well modeled. The R 0 for Zambia started close to three but dropped below one within a few weeks. It rose again, and around Day 50 it rose to about eight until Day 55. This is because of a significant increase in the reported numbers of daily cases around Day 50. On May 8, the government dispatched a team of health workers to Nakonde-a town next to Tanzania-to provide technical support and enhance port health services, community surveillance and disinfection of public places. They tested truck drivers, community members, health care workers, staff of lodges and the Immigration Department.

The prior number of total cases was 167 and on May 9, they had 85 cases, almost a 50% increase. Seventy-six of the 85 cases were from Nakonde. Between May 9 and 16, they reported high daily cases of 174 and 208. One hundred twenty-six of the 174 cases were from Nakonde and 196 of the 208 cases were also from Nakonde. These increases in the daily cases, concentrated around Nakonde, explain the high R 0 in Day 50-55. The R 0 dropped again around Day 55 until about Day 70 when it increased above one. Table SM5 shows the model parameters that best match the data of Zambia.

For the all the countries studied, R 0 started above one with a few imported cases. Within a few weeks, R 0 dropped below one because of the swift and decisive reactions of the governments and the awareness campaigns. The people reacted well initially and followed the authorities' directives. Unfortunately, R 0 did not stay below one for a long period; in all the cases studied, the basic reproduction number rose again above one after a few weeks-because of difficulties in adhering to the measures when the people face other socio-economic challenges.

The rise of R 0 after it had fallen initially may also because of complacency, fake news, and misinformation-some believe that COVID-19 is a scam, Africans are immune, and/or the disease has no impact in tropical climates, because of the low transmission rate mentioned in Section 1. That the initial responses were effective to bring R 0 below one is an encouragement that African countries can contain the spread. The challenge is to maintain the containment measures long enough to bring R 0 permanently below one. A continuous campaign of community engagement with regular briefings is important; so are an active combat against fake news and misinformation. They should maintain the lockdown and social distance measures notwithstanding the socio-economic adversities. Economic relief is necessary for the people with hardships exacerbated by these measures; this will motivate adherence to the containment plans and that will stop the pandemic [26] [27] [28] [29] .

A comment on the studies reported in this paper is their validity, given the numbers of limited tests performed. We show in Figure 5 that the number of cases are not correlated with the limited number of tests. The statistical samples used are significant; therefore, the conclusions are valid. One may extrapolate these results to the larger populations of the countries studied to determine, for example, the number of people to vaccinate. However, from the limited tests,

we cannot extrapolate to infer the total number of infections in the country. We also caution extrapolating to the future to make predictions; this is because, as we have shown in Figures 2-6 , the basic reproduction number fluctuates. Only detailed modeling from first principles in biology, medicine, physics, epidemiology and sociology may offer a framework for viable predictions.

We have studied COVID-19 data from Benin, Mozambique, Rwanda, Togo and Zambia. We modeled the data from these countries with the SIDARTHE model, and extracted a time-dependent basic reproduction number for each country studied. Our studies showed that at the onset the pandemic, the basic reproduction numbers, R 0 < 4, for all the countries studied. The initial reactions of African governments and populations were effective to bring the basic reproduction number below one after a few weeks. Three months later, R 0 ∼ 1, with fluctuations in between-relaxation and difficulties to maintain the measures over time drove the basic reproduction number in a time-dependent cyclic pattern of rises and falls. We suggest that African countries find satisfactory economic supports for their most disadvantaged populations. This will encourage adherence to the containment plans. of COVID-19 data of Zambia. The uncertainties in these numbers result from the statistical uncertainties in data as shown in Figure 6 . Day 0 is March 18, 2020. The relative uncertainties are large-up to ∼ 80% at the onset of the pandemic, but decrease over time with more data to ∼ 10%.

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We thank Professor John Ellis (University of London) for useful discussions.Toivo S. Mabote would like to thank Professor Doutor Cláudio Moisés Paulo