Pan-African evolution of within- and between-country COVID-19 dynamics

As of August 13, 2020, the 55 AU Member States had reported over 1,000,000 cases and 20,000 deaths from COVID-19. The southern region had the most cases, reporting over 50% (over 560,000 cases and 11,000 deaths) of the total for the continent. North Africa carries the highest regional case fatality rate (4%) but contributes 20% of the continent’s cases, with countries such as Egypt (102 cases per 100,000), Morocco (94 cases per 100,000), and Algeria (83 cases per 100,000) driving the overall numbers (Fig. 1). As more countries conduct targeted mass screening and testing, these figures continue to change. The spatial distribution of cases per 100,000 displays no clear geographical pattern (Fig. 1). South Africa, Djibouti, Equatorial Guinea, Gabon, and Egypt carry the largest burden of cases per capita, ranging from 100 to 500 per 100,000. The epidemiological curves for the African countries display varying shapes, mostly driven by the frequency and intensity of testing. For example, the epidemiological curve of South Africa is similar to those of the United Kingdom and the United States (SI Appendix, Fig. S1). An exception is Tanzania, which stopped reporting new cases in late April of 2020 (SI Appendix, Fig. S1).

Time series for case incidence and temporally varying model inputs are shown for selected countries in Fig. 1A. The full set of case incidence time series for all countries can be found in SI Appendix, Fig. S1. A majority of the countries imposed containment policies, including lockdowns and curfews, in early March 2020 to prevent further COVID-19 transmission within their borders. These social policy interventions remained in effect through August 2020 for most countries (SI Appendix, Fig. S2). Testing policies, which were restrictive at the beginning of the pandemic due to inadequate testing infrastructure, have become more open as testing is made widely available (SI Appendix, Fig. S3). As expected, spatiotemporal distribution of temperatures, rainfall, and specific humidity are very heterogeneous across the continent (Fig. 1 and SI Appendix, Figs. S4–S6). Population-weighted averages of these three meteorological variables were calculated for each country and day. This type of weighting prioritizes the human–climate interaction over the land–climate interaction (SI Appendix, Figs. S7–S9).

The spatiotemporal dynamics of reported cases are modeled as additive components. Two epidemic sources capture infections coming from within the country and from all other countries. An endemic component includes all contributions to the reported number of cases that are not taken into account by the epidemic part. The endemic part is not driven by previous case counts but may account for factors such as seasonality, sociodemography, animal reservoirs, and population. The epidemic part of the model has an autoregressive nature, meaning that the past number of COVID-19 cases reported both within a specific country and in the rest of the continent will be used to forecast the trend of COVID-19 cases. How much the past observations contribute to the future disease count depends on two parameters, $\lambda$ for the local transmission and $\varphi$ for the external transmission, and will be estimated from the data. In particular, the impact of cases reported in the neighboring countries depends also on a set of weights that modulate the spatial connectivity of the countries in the continent (see Materials and Methods). These two parameters are also functions of social policy, testing availability, and meteorological and demographic factors whose association with transmission we aim to determine. The model specification reported in Eqs. 3–5 representing the endemic, within-, and between-country component of the model, respectively, is the result of a model selection procedure based on the Akaike Information Criterion (AIC) (38). A summary of model comparison and selection process is presented in SI Appendix, Table S1. We began with an intercept-only model (model 1) with a population offset in the endemic component of the model and country’s measure of connectivity based on a power law. More complicated versions of the epidemic component were evaluated by sequentially adding weather, demographic, stringency index, and testing policy in the formula for the within- ($\lambda$) and between-country ($\varphi$) components of the model. We also tested whether multiple lags for cases and covariates better described the observed patterns: considering lags d = 1, …, D, where D = 14 days. Exploration of the higher-order model with Poisson and geometric lag weights revealed that, relative to the first-order model, the largest improvement in AIC ($\mathrm{\Delta }$AIC = −1,560) was achieved with a model with D = 7 for all variables (SI Appendix, Fig. S10). Therefore, the model with lag 7 d for cases, testing policy, stringency index including Human Development Index (HDI), landlocked status, and population in the between-country component, and with meteorology factors, HDI, landlocked status, stringency index, and testing policy in the within-country component, yielded the lowest AIC (from 48,824 in model 1 to 48,437 in model 5 without random effects; SI Appendix, Table S1).

Due to the high spatiotemporal heterogeneity of reported cases across Africa and to better capture country-specific transmission dynamics and incidence levels not explained by observed covariates, we allowed the intercept (mean levels of $\lambda$ and $\varphi$) in the local (4) and neighbor-driven (5) sources of infections to vary for each country as random effects. The relative risks for each explanatory variable included in this final model and the associated 95% CIs are reported in Table 1. Landlocked status, stringency index, and testing policy were significant contributing factors for the local transmission of cases. SI Appendix, Fig. S11 shows the actual contribution of the time-constant and time-varying covariates to the transmission parameters.

In addition, higher lagged mean temperature was a positive contributing factor, but higher specific humidity had a negative effect on the transmission of cases. For example, a 1 SD increase in the lagged mean temperature results in 11% higher contribution to the within-country transmission (P = 0.023, relative risk [RR] 1.11, 95% CI 1.01 to 1.21). However, a 1 SD increase in the 7-d lag mean specific humidity resulted in a 14% lower contribution on the local transmission of cases (P = 0.001, RR 0.86, 95% CI 0.78 to 0.94). Greater accessibility of testing remained the only significant contributing factor explaining the numbers of cases from the neighboring countries. With each level increase in the openness of the testing policy from zero to four, the contribution to the transmission of cases from neighboring countries was higher by twofold (P < 0.0001). The overdispersion parameter decreased from the fixed effects model (1.95, 95% CI 1.87 to 2.03) to random effects model (1.70, 95% CI 1.63 to 1.78) as a sign that the random effects absorbed part of the unexplained variability between countries.

Fig. 2 shows country-specific random effects, which we used to capture unexplained contributions to transmission. A value higher (lower) than one means that a country has an average transmission rate that is higher (lower) than the rest of the continent. This may be interpreted as a country-specific propensity to generate more or fewer cases given the past number of reported infected individuals. With respect to the within-country contributions to transmission, South Africa and Djibouti are the only African countries with an effect significantly higher than one. On the other hand, the Republic of Congo is the only country with a within-country transmission rate significantly lower than the continental-level mean. With respect to the between-country contributions to transmission of cases, Benin, Cameroon, Central African Republic, Ethiopia, Gabon, Ghana, Guinea, Malawi, Republic of Congo, and Senegal had significantly higher rates of between-country transmission than the continental-level mean. Angola, Chad, Lesotho, Namibia, and Tanzania had lower between-country transmission rates compared to the continental-level mean. The estimated variation of these country-specific effects in the within-country component of the model is small (${\widehat{\sigma }}_{\lambda }^2=0.07$) compared with their variation in the neighborhood component (${\widehat{\sigma }}_{\varphi }^2=2.3$). Although the between-country variability of transmission resulting from cases reported outside of the country was larger, the between-country intercept (Table 1) is very small, and so the neighborhood component is, in general, a small contributor to the fit.

We distinguish between endemic, within-country, and between-country contributions to the mean number of cases. Fitted values for all components according to model formulations in Eq. 1 are shown in Fig. 3, with a complete listing in SI Appendix, Fig. S12. The number of cases attributed to within- and between-country transmission of cases during the entire study period varied greatly. Across countries, the contribution from the endemic component was found to be minimal. Of the 46 countries analyzed, 16 of them are landlocked, and 13 (81%) of these had a substantial contribution of cases from their neighboring countries: Botswana, Burkina Faso, Burundi, Central African Republic, Ethiopia, Lesotho, Malawi, Rwanda, South Sudan, Swaziland, Uganda, Zambia, and Zimbabwe.

We keep the last 7 d of data out of the fitting procedure in order to use them as a forecast validation dataset. We produce 1-wk-ahead predictions and compare them with the reported data to check the quality of the model forecast. The results show that the majority of individual country case count data are captured well within model prediction intervals (Fig. 4 and SI Appendix, Fig. S13). Across countries, the model predictive performance was assessed with a calibration test based on proper scoring rules as described in ref. 39. A map of P values for the calibration test is shown in SI Appendix, Fig. S14. Overall, model predictions are well calibrated, and a misalignment between forecast and observations was only detected for a few countries ($p<0.05$, Burundi, Cameroon, Somalia, and Botswana).

A number of assumptions in our analysis reflect practical limitations. We used aggregated data at the country level to ensure continental coverage, but fitting this model at different spatial scales would require reformulation of the neighborhood structure and the model parameters. It is difficult to obtain accurate mobility data within and between countries throughout Africa, necessitating an indirect estimation of contact probabilities. Although our use of higher-order neighborhood (beyond sharing a border) contact patterns led to improved model fit compared to an assumption of first-order neighbors (bordering countries) only, more-accurate mobility data would improve these estimations. Because ground truth data on within-country vs. imported cases are not available, we cannot validate case origins in our model fits. Other assumptions related to the testing and stringency policies are coarse approximations of governmental response to the surveillance and control of disease transmission. The absence of quantifiable tests per capita limits all such approaches. We excluded Equatorial Guinea, Guinea-Bissau, and Western Sahara, due to missing stringency index, and excluded the six island nations (Madagascar, Comoros, Mauritius, Seychelles, Cape Verde, São Tomé, and Príncipe), due to the lack of connectivity to mainland Africa which prevented model convergence.

SARS-CoV-2 is often carried by otherwise healthy-appearing individuals who unknowingly transmit the pathogen. In the present analysis, we could not disentangle asymptomatic and symptomatic disease. Underreporting can introduce artifacts in the autocorrelation structure and may confound the estimation of lag weights of the underlying serial interval distribution (52).

Additionally, we assumed that model coefficients were constant over time. This represents a trade-off of sufficient data required for stable model fitting versus the need to embrace the nonstationarity of the evolving pandemic. The empirical model approach we employed depends only on case data and therefore does not change as infectivity changes with viral variants, reinfection, and vaccination. We further ignored seasonal variation, implying that the interaction with weather is the same in summer and winter, or rainy and dry seasons closer to the equator. As the pandemic extends beyond the first year, introducing additional covariates to the endemic term, such as seasonal oscillations or animal reservoirs, may improve model fit.

This modeling strategy is limited by the quality of the data and the lack of nonlinear dynamics in the model. As effective vaccines become more widely available within Africa, modification of this model framework, and validation against observations and predictions, will become important to consider. Our modeling strategy enables us to focus on any window of time during an epidemic to examine the contributing properties. As the African pandemic and policies evolve, and as the variants of the virus introduce changes in infectivity, this model should be refit for later time periods to establish the changing relationships that best account for the epidemic dynamics within and between countries. Our archived open-source code enables others to refit for any past or future time window of interest.

We present a pan-African COVID-19 surveillance tool to track and perform short-term forecast of COVID-19 cases and to quantify between- and within-country sources. Our analyses give insight into the sociodemographic, geodemographic, testing, mitigation/containment, and meteorological factors that influence the spread of the SARS-CoV-2 infection at the national scale. Although our strategy can be used for short-term predictions of cases, its accuracy is dependent upon the quality of testing and reported data. In settings with fragile health systems, coupled with the vulnerability of lower-HDI economies, the capacity to effectively track the pandemic is especially challenging. Such challenges point to the potential advantages in regional efforts to coordinate resources to test and report cases. Seeking equitable behavioral and social interventions, balanced with coordinated country-specific strategies in infection suppression, should be a continental priority to control the COVID-19 pandemic in Africa.

Our analyses included 46 countries of mainland Africa. We do not provide estimates for Equatorial Guinea, Guinea-Bissau, and Western Sahara, due to the missing data on stringency index, or the six island nations (Madagascar, Comoros, Mauritius, Seychelles, Cape Verde, São Tomé, and Príncipe), due to the lack of spatial connectivity. Modeling the spread of COVID-19 over the African continent poses challenges, given the extensive cultural, political, and environmental heterogeneity between countries. Indeed, this heterogeneity results in substantial variability of reported case counts across countries. It is this variability in case counts that motivates our choice of a relatively simple data-driven autoregressive modeling approach. Such a modeling approach focuses on the interaction of cases reported in time and space without hidden variables to be estimated.

The seasonality of influenza transmission has been associated with cycles of temperature, rainfall, and specific humidity, although, in different regions of the world, transmission may peak during the “cold-dry” season (temperate climates) or during “humid-rainy” season (tropical climates) (53).

We estimated the influence of meteorological factors on the transmission dynamics of COVID-19 in Africa. Real-time, daily, in situ synoptic weather observations are sparse across much of Africa. Therefore, daily, 10-km spatial resolution mean temperature, rainfall, and specific humidity data were obtained from UK Met-Office numerical weather prediction model output (54, 55). These data are extracted from the early time steps of the model following data assimilation, to more closely approximate an observational dataset. This approach also has the advantage that future studies have access to the same coherent dataset at a global scale for applications outside of continental Africa. The weather product that generates these data closely approximates an observational dataset at locations that have dense observation coverage, whereas, in observation-sparse areas, the dataset relies more heavily upon the numerical weather prediction model (a physics-based rather than statistical model). The meteorological dataset contained no missing data.

A population density-weighted spatial average (SI Appendix, Figs. S7–S9) was then applied for each day and country using the R package “exactextractr” (56). Population density was obtained from the Gridded Population of the World version 4 (GPWv4) from the Centre for International Earth Science Information Network (57). Weighting climate variables by population gives a closer approximation to the weather conditions faced by humans living in that country compared to an unweighted average over total land area. For example, the country of Algeria, in which much of the population resides along the coast, demonstrates a cooler, wetter, and more humid climate when weighting by population (SI Appendix, Figs. S7E, S8E, and S9E).

To include an aggregate measure of countries’ social policies, the stringency index sourced from the OxCGRT dataset was used. This composite measure reflects government policies related to school and workplace closures, restrictions on public gatherings, events, public transportation, limitations of local and global travel, stay-at-home orders, and public education campaigns (23). A full description of these variables is provided in SI Appendix, Table S2. The stringency index is calculated from these categorical variables using a weighted average, with a range of 0 to 100 indicating weak to strict stringency measures, respectively. A time-dependent metric of testing policy was also extracted from this dataset. Ranging from zero to four, this categorical metric increases with more open and comprehensive testing policy.

In our modeling strategy, we incorporate key socioeconomic and sociodemographic epidemiological data, including HDI, population, United Nations geographic regions, and coastline access (SI Appendix, Fig. S15). HDI represents the national data on key aspects of development, namely, education, economy, and health (58). The HDI is the geometric mean of normalized indices for each of the three dimensions. The education dimension is measured by average years of schooling for adults aged 25 y and more and expected years of schooling for children of school-entering age. The economy dimension is measured by gross national income per capita, and the health dimension is assessed by life expectancy at birth. In Africa, the majority of the countries fall in the low-HDI category (SI Appendix, Fig. S15). The northern part of Africa and South Africa have a considerably higher HDI compared to the rest of the continent. Country-specific median age was correlated with HDI (Pearson’s correlation coefficient R = 0.71, P $<$ 0.0001; SI Appendix, Fig. S16); therefore, we excluded this covariate from the model. We include in the model the 2020 population obtained from the Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat (59). The categorization of sub-Saharan and northern Africa was based on the United Nations geoscheme for Africa (60). This regional factor captures the human genetics (61), environment and climate (62), and sociocultural and sociodemographic variations of the African population (63). Finally, lack of direct access to the coastline may influence the flow of infections from neighboring countries, as border trade remains an essential operation. For example, Uganda introduced border closures and tighter preventive measures on truck drivers’ movements during the epidemic; despite this, a substantial number of new infections have been imported from truck drivers crossing the border for trade (64). Such cross-border commerce remains a crucial part of the supply chain for landlocked African countries such as Uganda and Rwanda.

We chose a class of multivariate time series models for case count data introduced by Held et al. (65), and further extended by Bracher and Held (51) with the addition of higher-order distributed lags.

Conditional on past observations $Y_{i,t-d}$, $i=1,\dots ,N$, and $d=1,\dots ,D$, new COVID-19 cases $Y_{it}$ from country $i$ at time $t$ are assumed to follow a negative binomial distribution with mean ${\mu }_{it}$ and overdispersion parameter $\psi$ asThe conditional variance is ${\mu }_{it}+\psi {\mu }_{it}^2$, which demonstrates the role of the overdispersion parameter to capture variability greater than the mean. The conditional mean ${\mu }_{it}$ is decomposed into three additive components,where ${ϵ}_i$, ${\lambda }_{it}$, and ${\varphi }_{it}$ represent three contributions to case incidence. The first term, ${ϵ}_{it}$, is the so-called endemic component and captures infections arising from sources other than past observed cases (e.g., contributions from areas that are not included in the neighbor set). The two other terms in [1], ${\lambda }_{it}$ and ${\varphi }_{it}$, constitute the epidemic part of the model and modulate how infective individuals reported in the past $d$ days both locally and from neighboring countries will contribute to the average future number of reported cases. The strength of connection between countries is described by spatial weights $w_{ji}$. This intercountry transmission susceptibility is defined using a power-law formulation proposed by Meyer and Held (66),where $o_{ji}$ is the path distance between countries $j$ and $i$ (with $o_{ii}=0$, $o_{ji}=1$ for direct neighbors $i$ and $j$ and so on), and $\rho$ is a decay parameter to be estimated from the data. The path distance $o_{ji}$ is on an ordinal scale based upon the adjacency index. The spatial weights are normalized such that ${\sum }_k{w}_{jk}=1$ for all rows $j$ of the weight matrix (SI Appendix, Fig. S17).

The normalized autoregressive weights $u_d$ are shared between the local and global epidemic components, and represent the probability for a serial interval of up to $D$ days—which is the average time in days between symptom onset in an infectious individual (or primary case) and symptoms appearing in a newly infected individual (or secondary case) when both are in close contact (67).

The parameters ${ϵ}_{it}$, ${\lambda }_{it}$, and ${\varphi }_{it}$ are constrained to be nonnegative and modeled as the natural log-transformed linear combination of different country-specific covariates. The endemic component,is decomposed as a constant ${\alpha }^{\left(ϵ\right)}$ specific to the baseline endemic and a term proportional to the country-level population $N_i$. In the epidemic part of the model, we expect new cases to also be driven by country-specific factors: Population ($N_i$), HDI classifications of low, medium, or high ($HD{I}_i=\left\{\mathrm{0,1,2}\right\}$), and land-locked ($L{L}_i$) status for each country are assumed constant over the time scale of analysis. Other forces driving new cases vary over time, as a response to either policy changes or natural fluctuation in environmental or societal patterns. Time-dependent covariates include mean daily temperature ($T_{i,t-\tau }$), rainfall ($R_{i,t-\tau }$), specific humidity ($H_{i,t-\tau }$), testing policy ($X_{i,t-\tau }$), and government stringency index ($S_{i,t-\tau }$), lagged at $\tau$ days. The full set of explanatory variables that contribute to the model from both internal and external epidemic components are formalized in [4] and [5] asandwhere ${\alpha }_i^{\left(\lambda \right)}\approx N\left({\alpha }_0^{\left(\lambda \right)},{\sigma }_{\lambda }^2\right)$ and ${\alpha }_i^{\left(\varphi \right)}\approx N\left({\alpha }_0^{\left(\varphi \right)},{\sigma }_{\varphi }^2\right)$ are a set of independent country-level random effects. This modeling framework is implemented in the R package “surveillance” (68). A complete table of data sources for model input is found in SI Appendix, Table S3.

We selected models based on AIC (69) if random effects were not present (SI Appendix, Table S1). To compare models that included random effects, we used proper scoring rules for count data (70). Scoring rules are functions $S\left(P,y\right)$ that evaluate the accuracy of a predictive distribution $P$ against an outcome $y$ that was observed. We chose the model with the lowest AIC or with the lowest logarithmic score computed as minus the logarithm of the predictive distribution evaluated at the observed count. We began with the first-order autoregressive modeling ($D=1$ in [1]) of daily COVID-19 incidence using intercept-only model population offset and country connectivity. In a mechanistic interpretation of such a first-order model, the time between the appearance of symptoms in successive generations is assumed to be fixed to the observation interval at which the data are collected, here as 1 d (52).

After the estimation and illustration of this basic model, we expand the model by sequentially adding the following additional covariates: country-specific HDI, population both within country and in neighboring countries, meteorology factors, stringency index, testing policy, landlocked status, and random effects to more fully account for unobserved heterogeneity of the cases. Social policies and meteorological data were included in the model, testing for fit at different lags (for example, $T_{i,t-\tau },\tau \in \mathrm{0,7,14}$ d).

As in previous work by Held and Meyer (71), we use plug-in forecasts: forecast from the fitted model without carrying forward the uncertainty in the parameter estimates. We assess both the model fit and 1-wk-ahead forecast of the higher-order autoregressive model with the logarithmic score. The smaller the score, the better the predictive quality (72, 73). Mean scores were generated for each country’s forecast, by averaging the log-score obtained for each day of the validation week.