Ecology

Reported SARS-CoV-2 case counts, mortality and testing in SSA as of December 2020
Variables and data sources for reporting data
The numbers of reported cases, deaths and tests for the 48 SSA countries studied (Supplementary Table 1) were sourced from the Africa CDC dashboard on 20 December 2020 (and previously on 23 September and 30 June 2020). The Africa CDC obtains data from the official Africa CDC Regional Collaborating Centre and member state reports. Differences in the timing of reporting by member states results in some variation in the recency of data within the centralized Africa CDC repository, but data should broadly reflect the relative scale of testing and reporting efforts across countries. For Mauritius (https://covid19.mu/) and Rwanda (https://covid19.who.int/region/afro/country/rw), reporting to the Africa CDC was confirmed by comparison to country-specific dashboards.
The countries or member states within SSA in this study follow the United Nations and Africa CDC-listed regions of Southern, Western, Central and Eastern Africa (excluding Sudan). From the Northern Africa region, Mauritania is included in SSA.
For comparison to non-SSA countries, the number of reported cases in other geographical regions were obtained from the Johns Hopkins University Coronavirus Resource Center on 23 September 2020 (https://coronavirus.jhu.edu/map.html).
Case fatality ratios (CFRs) were calculated by dividing the number of reported deaths by the number of reported cases and expressed as a percentage. Positivity was calculated by dividing the number of reported cases by the number of reported tests. Testing and case rates were calculated per 100,000 population using population size estimates for 2020 from the United Nations Population Division (https://population.un.org/wpp/Download/Standard/Population/). Since reported confirmed cases are likely to be an underestimate of the true number of infections, CFRs may be a poor proxy for the IFR, defined as the proportion of infections that result in mortality4.
Variation in testing and mortality rates
Testing rates among SSA countries varied by multiple orders of magnitude as of 30 June and remain highly variable as of 23 September and 20 December 2020. The number of tests completed per 100,000 population ranged from 19.84 in Burundi to 13,508.13 in Mauritius in June 2020; from 65.98 in the Democratic Republic of the Congo to 18,321.83 in Mauritius in September 2020; and from 100.9 in the Democratic Republic of the Congo to 23695.0 in Mauritius in December 2020 (Extended Data Fig. 1a). Tanzania (6.50 tests per 100,000 population) has not reported new tests, cases or deaths to the Africa CDC since April 2020. The number of reported infections (that is, positive tests) was strongly correlated with the number of tests completed in June 2020 (Pearson’s correlation coefficient, r = 0.9667, P 50% coincident with population >50,000) within administrative 2 units61. For some countries, estimates at administrative 2 units were unavailable (Comoros, Cape Verde, Lesotho, Mauritius, Mayotte and Seychelles); estimates at the administrative-1 unit level were used for these cases (these were all island nations, with the exception of Lesotho).
Metapopulation model methods
Once SARS-CoV-2 has been introduced into a country, the degree of spread of the infection within the country is governed by subnational mobility: the pathogen is more likely to be introduced into a location where individuals arrive more frequently than one where incoming travelers are less frequent. Large-scale consistent measures of mobility are rare. However, recently, estimates of accessibility have been produced at a global scale26. Although this is unlikely to perfectly reflect mobility within countries, especially since interventions and travel restrictions are put in place, it provides a starting point for evaluating the role of human mobility in shaping the outbreak pace across SSA. We used the inverse of a measure of the cost of travel between the centroids of administrative level 2 spatial units to describe mobility between locations (estimated by applying the costDistance function in the gdistance package v1.3-6 in R to the friction surfaces supplied in Weiss et al.26). With this, we developed a metapopulation model for each country to develop an overview of the possible range of trajectories of unchecked spread of SARS-CoV-2.
We assumed that the pathogen first arrives in each country in the administrative 2 level unit with the largest population (for example, the largest city) and the population in each administrative 2 level (of size Nj) is entirely susceptible at the time of arrival. We then tracked the spread within and between each of the administrative 2 level units of each country. Within each administrative 2 level unit, dynamics are governed by a discrete time susceptible (S), infected (I) and recovered (R) model with a time step of approximately one week, which is broadly consistent with the serial interval of SARS-CoV-2. Within the spatial unit indexed j, with total size Nj, the number of infected individuals in the next time step is defined by:

$$I_{j,t + 1} = beta I_{j,t}^alpha S_{j,t}/N_j + iota _{j,t}$$

where β captures the magnitude of transmission over the course of one discrete time step; since the discrete time step chosen is set to approximate the serial interval of the virus, this will reflect the R0 of SARS-CoV-2, and is thus set to 2.5; the exponent α = 0.97 is used to capture the effects of discretization62 and Ij,t captures the introduction of new infections into site j at time t. Susceptible and recovered individuals are updated according to:

$$begin{array}{l}S_{j,t + 1} = S_{j,t} + wR_{j,t} – I_{j,t + 1} + b\ R_{j,t + 1} = (1 – w)R_{j,t} + I_{j,t}end{array}$$

where b reflects the introduction of new susceptible individuals resulting from the birth rate, set to reflect the most recent estimates for that country from the World Bank Data (https://data.worldbank.org/indicator/SP.DYN.CBRT.IN), and w reflects the rate of waning of immunity. The population is initiated with Sj,1 = NjRj,1 = 0, and Ij,1 = 0 except for the spatial unit corresponding to the largest population size Nj for each country since this is assumed to be the location of introduction; for this spatial unit, we set Ij,1 = 1.
We made the simplifying assumption that mobility linking locations i and j, denoted as ci,j, scales with the inverse of the cost of travel between sites i and j evaluated according to the friction surface provided in Weiss et al.26. The introduction of an infected individual into location j is then defined by a draw from a Bernouilli distribution following:

$$iota _{j,t} approx {mathrm{Bernouilli}}left( {1 – {mathrm{exp}}left( { – mathop {sum }limits_1^L {c_{i,j}}{I_{i,t}}/{N_i}} right)} right)$$

where L is the total number of administrative 2 units in that country and the rate of introduction is the product of connectivity between the focal location and each other location multiplied by the proportion of population in each other location that is infected.
Some countries show rapid spread between administrative units within the country (for example, a country with parameters that broadly reflect those available for Malawi; Extended Data Fig. 7), while in others (for example, reflecting Madagascar), connectivity may be so low that the outbreak may be over in the administrative unit of the largest size (where it was introduced) before introductions successfully reach other poorly connected administrative units. Where duration of immunity is sufficiently long, the result may be a hump-shaped relationship between the proportion of the population that is infected after five years and the time to the first local extinction of the pathogen (Extended Data Fig. 7, top right). In countries with lower connectivity (for example, resembling Madagascar), local outbreaks can go extinct rapidly before traveling very far; in other countries (for example, resembling Gabon), the pathogen goes extinct rapidly because it travels rapidly and rapidly depletes susceptible individuals everywhere. The U-shaped pattern diminishes as the rate of waning of immunity increases and is replaced by a monotonic negative relationship. With sufficiently rapid waning of immunity, local extinction ceases to occur in the absence of control efforts.
The impact of the pattern of travel between centroids is echoed by the pattern of travel within administrative districts: countries where the pathogen does not reach a large fraction of the administrative 2 units within the country in five years are also those where within-administrative-unit travel is low (Extended Data Fig. 7, right).
These simulations provide a window into qualitative patterns expected for subnational spread of the pandemic virus but there is no clear way of calibrating the absolute rate of travel between regions of relevance for SARS-CoV-2; this is further complicated by the remaining uncertainties around rates of waning of immunity. Thus, the time scales of these simulations should be considered in relative, rather than absolute terms. Variation in lockdown effectiveness, or other changes in mobility for a given country, may also compromise relative comparisons as might large volumes of land border crossings in some settings, which we have not accounted for in this study. Variability in testing and case reporting complicates clarifying this (Extended Data Fig. 7, bottom left and bottom right, respectively) but we have highlighted countries with less connectivity (that is, less synchronous outbreaks expected) relative to the median among SSA countries and with older populations (that is, a greater proportion in higher-risk age groups) (Extended Data Fig. 8).
The University of Oxford’s Blavatnik School of Government generated composite scores of government response, interventions for containment and economic support provided, with each scored from 0 to 100 (Coronavirus Government Response Tracker; https://www.bsg.ox.ac.uk/research/research-projects/coronavirus-government-response-tracker). These data were compared with the day on which ten cases were exceeded in a country according to the Johns Hopkins dashboard data (Johns Hopkins Coronavirus Resource Center; https://coronavirus.jhu.edu/map.html).
While faster waning of immunity will act to increase the rate of spread of the infection, resulting in a higher proportion infected after one year, control efforts will generally act to slow the rate of spread of the infection (Extended Data Fig. 9). Since different countries are likely to have differently effective control efforts (Extended Data Fig. 9), this precludes making country-specific predictions as to the relative impact of control efforts on delay.
Modeling epidemic trajectories in scenarios where transmission rate depends on climate
Climate data sourcing: variation in humidity in SSA
Specific humidity data for selected urban centers comes from the ERA5 using an average climatology (1981–2017)53; we did not consider year-to-year climate variations. Selected cities (n = 56) were chosen to represent the major urban areas in SSA. The largest city in each SSA country was included as well as any additional cities that were among the 25 largest cities or busiest airports in SSA.
Methods for climate-driven modeling of SARS-CoV-2
We used a climate-driven susceptible-infected-recovered-susceptible model to estimate epidemic trajectories (that is, the time of peak incidence) in different cities in 2020, assuming no control measures were in place or a 10 or 20% reduction in R0 beginning 2 weeks after the total reported cases for a country exceeded 10 cases25,63. The model is given by:

$$frac{{mathrm{d}}S}{{mathrm{d}}t} = frac{{N – S – L}}{L} – frac{{beta (t)IS}}{N}$$

$$frac{{mathrm{d}}I}{{mathrm{d}}t} = frac{{beta (t)IS}}{N} – frac{I}{D}$$

where S is the susceptible population, I is the infected population and N is the total population. D is the mean infectious period, set at 5 d following ref. 25.
To investigate the effects on epidemic trajectories of a climate dependency of SARS-CoV-2 on cities with the climate patterns of the selected cities in SSA, we used parameters from the most climate-dependent scenario in ref. 25, based on the endemic betacoronavirus HKU1 in the United States. In this scenario L, the duration of immunity, was 66.25 weeks (that is, >1 year and such that waning immunity did not affect the timing of the epidemic peak). We initially selected a range where R0 declined from R0max = 2.5 to R0min = 1.5 (that is, transmission declined 40% at high humidity) since this exceeds the range observed for influenza and other coronaviruses for which data are available (from the United States). R0max = 2.5 was chosen because 2.5 is often cited as the approximate R0 for SARS-CoV-2. Thus, we initially assumed that the climate dependence of SARS-CoV-2 in SSA would not greatly exceed that of other known coronaviruses from the US context. Then, we explored the effects of different degrees of climate dependency (that is, wider ranges between R0max = 2.5 to R0min = 1.5 and scenarios where R0min approached 1) (Extended Data Fig. 10).
Transmission is governed by β(t), which is related to the basic reproduction number R0 by R0(t) = β(t)D. The basic reproduction number varies based on climate and is related to specific humidity according to the equation:

$$R_0 = {mathrm{exp}}{[a times q(t) + {mathrm{log}}(R_{0{mathrm{max}}} – R_{0{mathrm{min}}})]} + R_{0{mathrm{min}}}$$

where q(t) is specific humidity53 and a is set at −227.5 based on estimated HKU1 parameters25. We assumed the time of introduction for cities to be the date at which the total reported cases for a country exceeded 10 cases.
Sensitivity analysis
Selecting an R0min value of 1, such that epidemic growth stops at high humidities, is likely implausible since simulations indicated no outbreaks would occur in cities such as Antananarivo (countered by the observation that SARS-CoV-2 outbreaks did in fact occur) (Extended Data Fig. 10b; see Supplementary Table 1 for the reported case counts at the country level). Expanding the range between R0min and R0max by increasing R0max resulted in epidemic peaks being reached earlier after outbreak onset but did not increase the difference in timing between cities with different climates (Extended Data Fig. 10c; for example, the difference in timing between peaks in Windhoek and Lomé is similar in 10a and 10c). Finally, we explored scenarios where the R0min was between 1.0 and 1.5. When R0min  > 1.1, epidemic peaks were seen in each SSA city with the difference in timing of the peak growing larger when smaller values of R0min were selected (Extended Data Fig. 10d). However, the difference in timing, even when small values of R0min were selected, was a maximum of 25 weeks and rapidly reduced to only a few weeks when R0min approached 1.5.
Reporting Summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article. More

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