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COVID-19 in Africa: Underreporting, demographic effect, chaotic dynamics, and mitigation strategy impact [1]

['Nathan Thenon', 'Centre D Etudes Spatiales De La Biosphère', 'Cesbio Omp', 'Umr Ups-Cnes-Cnrs-Ird-Inrae', 'Toulouse', 'Animal Santé Territoires Risques Ecosystèmes', 'Astre Cirad', 'Umr Cirad-Inrae-University Of Montpellier', 'Montpellier', 'Marisa Peyre']

Date: 2022-12 

Compared to Europe, the analyses show that the lower proportion of elderly people in Africa enables to explain the lower total numbers of cases and deaths by a factor of 5.1 on average (from 1.9 to 7.8). It corresponds to a genuine effect. Nevertheless, COVID-19 numbers are effectively largely underestimated in Africa by a factor of 8.5 on average (from 1.7 to 20. and more) due to the weakness of the health systems at country level. Geographically, the models obtained for the dynamics of cases and deaths reveal very diversified dynamics. The dynamics is chaotic in many contexts, including a situation of bistability rarely observed in dynamical systems. Finally, the contact number directly deduced from the epidemiological observations reveals an effective role of the mitigation strategies on the short term. On the long term, control measures have contributed to maintain the epidemic at a low level although the progressive release of the stringency did not produce a clear increase of the contact number. The arrival of the omicron variant is clearly detected and characterised by a quick increase of interpeople contact, for most of the African countries considered in the analysis.

The epidemic of COVID-19 has shown different developments in Africa compared to the other continents. Three different approaches were used in this study to analyze this situation. In the first part, basic statistics were performed to estimate the contribution of the elderly people to the total numbers of cases and deaths in comparison to the other continents; Similarly, the health systems capacities were analysed to assess the level of underreporting. In the second part, differential equations were reconstructed from the epidemiological time series of cases and deaths (from the John Hopkins University) to analyse the dynamics of COVID-19 in seventeen countries. In the third part, the time evolution of the contact number was reconstructed since the beginning of the outbreak to investigate the effectiveness of the mitigation strategies. Results were compared to the Oxford stringency index and to the mobility indices of the Google Community Mobility Reports.

In this study, we show (1) that two main factors can explain the lower numbers of cases and deaths per inhabitants in Africa: an underestimation (by a factor 8.5) of the reported cases and deaths which directly results from the under capacities of the health systems at country level, but also a genuine effect by a factor 5.1 directly resulting from the smaller fraction of elderly people. We demonstrate (2) that the dynamics of the epidemic can be approximated deterministically by few variables only. Its time evolution is however highly sensitive to the initial conditions which makes it unpredictable at long term. Moreover, dynamics can largely vary from one country to another. For one country (Ghana), it is shown that very different epidemiological evolution can occur under strictly identical sanitary conditions. Finally, we reveal (3) that the impact of the control measures on the contact number is effective at short term and enabled to maintain the epidemic at a relatively low level, but it is more difficult to identify distinctly the long-term role of mitigation strategy. The omicron variant is very clearly detected in the recent evolution of the epidemic.

Data Availability: Six databases were used. The data used for comparative statistics are provided in S1 File (all taken from these databases). Each database is carefully quoted in the manuscript: (1) DESA, 2019. World Population Prospect 2019: Data Sources, Department of Economic and Social Affairs, Population Dynamics, United Nations. https://population.un.org/wpp (2) IBRD 2020. International Bank for Reconstruction and Development, International Development Association 2020. (3) Dong E., Du H. & Gardner L., 2020. An interactive web-based dashboard to track COVID-19 in real time. The Lancet Infectious Diseases, 20(5), 533 534. https://doi.org/10.1016/S1473-3099(20)30120-1 (4) Mathieu E., Ritchie H., Ortiz-Ospina E., Roser M., Hasell J., Appel C., Giattino C. and Rodés-Guirao L., 2021. A global database of COVID-19 vaccinations. Nature Human Behaviour 2021 May 20. https://doi.org/10.1038/s41562-021-01122-8 (5) Hale T., Angrist N., Cameron-Blake E., Hallas L., Kira B., Majumdar S., Petherick A., Phillips T., Tatlow H. et Webster S., 2020. Oxford COVID-19 Government Response Tracker [en ligne]. 2020. S.l.: Blavatnik School of Government. (6) Google Community Mobility Report. https://www.google.com/covid19/mobility/data_documentation.html?hl=en .

Introduction

Africa has been the subject of relatively less attention in comparison to the other continents since the beginning of the pandemic of COVID-19. One reason for that is the apparent lower magnitude of the epidemic in contrast to what was primarily expected and in comparison to most of the other countries. At present, its specificities remain puzzling and numerous hypotheses have been made to explain this slower propagation [1–5], among which, (1) the relatively good preparation of the African countries after their notable experience of recent emerging epidemics; (2) the demographic age structure characterised by a lower proportion of aged people and a lower population density; (3) the climatic conditions which may foster or hinder the propagation of the disease; (4) a possible pre-existing partial immunity related to the exposure to other zoonotic coronaviruses or a reduced susceptibility to severe forms of the disease together with a specific role of comorbidities [5, 6]; Finally (5) an underascertainment of cases and deaths occurrences [5–8] due to insufficient diagnostic facilities, poorly adapted serological tests to detect the asymptomatic cases (in Africa, these tests give higher seroprevalence than expected which may result from cross-reactions of the test with other viruses and parasites in circulation on the African subcontinent), absence of registration and under-sampling. Although all these factors may have played a significant role, their quantitative influence remains unclear. In terms of total number of cases per inhabitant for instance, the difference with countries of other continents, in particular with Europe, appears considerable (by a factor around 10.9 on average for the cases and 8.4 for the deaths).

The questions about dynamics and dynamical complexity are important issues in epidemiology. The dynamics of epidemics is rarely simple. On the contrary, it is often highly unpredictable—sometimes even at very short term as it is the case for other diseases such as the Ebola Virus Disease [9]—until the propagation of the disease can be completely contained. Most of the epidemiological models can only produce very basic dynamical behaviours (often a single oscillation before converging to a stable situation, or a succession of strictly periodic oscillations) in comparison to the high complexity of the oscillations actually observed. This is an important limitation for epidemiological modelling. For this reason, to detect chaotic behaviours has been expected in epidemiology since the early 1980s. It was proven possible to generate more complex simulations with theoretical epidemiological models by either applying a periodical forcing on models of Susceptible-Exposed-Infected structure [10–12] or by combining predator-prey and Susceptible-Infected models [13, 14].

The possibility to extract chaotic models directly from epidemiological data is more recent [9, 15–17]. To allow valuable analyses of poorly predictable systems, the modelling approach should not use predefined model structure (e.g. models such as the SEIR models have a fixed structure and cannot produce complex dynamics; therefore, they cannot be used to detect chaos, neither to study the dynamics), and should make it possible to overcome the problem of sensitivity to the initial conditions. Based on chaos theory [18, 19], the global modelling technique [20] was designed for this purpose. A chaotic dynamics is defined by two main properties: determinism and high sensitivity to the initial conditions. The initial conditions, here, do not restrictively refer to the conditions at the very beginning of the outbreak. It refers to any initial conditions, be it taken at the earlier origin with the patient zero, after several days or weeks, or once the epidemic has reached its permanent dynamics. In a chaotic system, for a small perturbation, this high sensitivity will result in the exponential divergence of the trajectories, whenever this perturbation will be applied. The problem of modelling (hypothetically) chaotic dynamics can be stated as follows: If small changes in the initial conditions can give rise to completely different time evolution, then the modelling approach should not only enable to reproduce the single time evolution observed in practice, it should retrieve a set of equations able to simulate any of the time evolution made possible by the dynamics. To do so, the global modelling technique takes advantage of the state space (or phase space), an oriented space able to represent—all—the possible states of a given deterministic system. For this reason, this space is independent from the initial conditions. Moreover, as proven by the embedding theorems [21, 22], this state can be reconstructed from observational time series, establishing a powerful bridge between theory and applications.

Thanks to this bridge, the global modelling technique can be used to model chaotic dynamics directly from observational time series [23]; It can also be used to detect directional couplings under chaotic regimes [24] and to obtain interpretable sets of chaotic equations [15] without strong hypotheses. For COVID-19 in China, the approach enabled to obtain a model (M 2 ) characterised by intermittency [17], revealing that, despite a control of high stringency put in place to achieve the zero-COVID strategy, the equilibrium was unstable and restarts were to be expected after an undetermined time. Facilitated by the emergence of the omicron variant, such a situation was confirmed almost two years later by a restart that broke out by the beginning of 2022. Such a restart appears fully expected now, but it was not at all at the time this model was obtained (06 April 2020). Of course, the approach can also be applied under non chaotic conditions.

Face to emerging or re-emerging diseases, in particular under a pandemic context, the question of the efficacy of the mitigation strategy is of first importance. This question has been investigated using different approaches. For the epidemic of COVID-19, most of the studies on the impact of mitigation strategies have been prospective and based on scenarios. Scenarios can help in determining the measures to be fostered. However, their ability to assess the genuine impact of the intervention policies highly depends on the hypotheses the scenarios have been built for (this limitation is not specific to epidemic scenarios [25]). Therefore, other approaches should be preferred to make a diagnostic of their impact a posteriori.

Day-by-day estimates of the effective reproduction number (the average number of secondary cases contaminated at time t by an infectious individual) is commonly used to track the evolution of epidemics. Various techniques were developed for this purpose [26]. However, the main aim of this number is to determine if the epidemic is on either growing or decreasing stage, but it cannot distinguish the effect of pharmaceutic versus non-pharmaceutic interventions. Therefore, it is not adapted to estimate the impact of control measures.

Some approaches have been developed to estimate the impact of non-pharmaceutical interventions, either by trying to separate the effect of less/more restrictive non-pharmaceutical interventions according to the growth rate [27], or by analysing the reproduction number in relation to the physical distancing and other control measures [28], or by reconstructing the infection rate functions [29] in SEIR models.

The aim of the alternative approach introduced in the present work is to reconstruct β(t) the time evolution of the average contact number directly from the daily evolution of newly infected cases. Such a reconstruction can be of particular interest to understand the efficacy of the mitigation strategy since one main role of the non-pharmaceutical strategies is precisely to reduce the interindividual contacts.

The purpose of the present study is to provide an overall perspective on the epidemic of COVID-19 in Africa since it broke out. Three main objectives are considered. The first one is to understand the low numbers of cases and deaths due to COVID-19 in Africa in comparison to the other continents, and their geographical variability at intracontinent scale. The second objective is to investigate the dynamics of the epidemics in Africa at the country scale, to explain its low predictability and to investigate its intercountry variability. The third objective is to assess the impact of the mitigation strategies by the reconstruction of the average contact number at the country scale from the earlier beginning of the outbreak.

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[1] Url: https://journals.plos.org/plosntds/article?id=10.1371/journal.pntd.0010735

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