Country selection and data sources

Figure1 illustrates the cumulative number of reported COVID-19 cases and the incidence of malaria infection in Africa. The four countries are located in eastern Africa, western Africa, and central and southern Africa, where the infection risk of both COVID-19 and malaria is relatively high. First, to estimate the epidemiological parameters of COVID-19 in each country, we use the time series of cumulative COVID-19 cases in each country till June 2, 2020. The reported COVID-19 cases in each country are collected from the website of the World Health Organization (Source: https://covid19.who.int/). Then, we characterize the annual pattern of malaria transmission potential in each country based on the historical values of VCAP from January 1, 2004, to December 31, 2019. The values of VCAP are downloaded from the International Research Institute for Climate and Society (Source: http://iridl.ldeo.columbia.edu/maproom/Health/Regional/Africa/Malaria/VCAP/index.html). Finally, to quantify the impact of COVID-19 pandemic on malaria transmission potential, we have also collected the population size, the ITN coverage, and the total number of ITNs available for each country. Based on the Malaria Indicator Survey (MIS) in each country, the ITN coverage rate before 2020 is estimated by the percentage of de facto household population who slept under an ITN the night before the survey. While the total number of ITNs available in 2020 can be obtained from the Malaria Operational Plan (FY 2019) of each country. All data and their sources are summarized in Table1.

An illustration of the cumulative number of reported COVID-19 cases and the incidence of malaria infection in Africa. The left shows the total number of reported COVID-19 cases till June 30, 2020. The right shows the incidence of malaria infection (per 1000 population at risk) in 2018. The figure was generated using the Free Software R with version 3.6.3

To accurately predict the trend of COVID-19 pandemic, we first estimate the epidemiological parameters of COVID-19 by fitting the time series of reported COVID-19 cases in each country. Here, the time series is about the reported date of the COVID-19 infections as of June 2, 2020. Evidence has shown that asymptomatic infections play essential roles in the spread of COVID-19. However, due to limited public health resources in the four countries in Africa, it is difficult to identify asymptomatic infections in the early stages of the epidemic. In this case, following existing studies[26, 27], we resort to the classical susceptibleexposedinfectiousremoved (SEIR) model to simulate the transmission dynamics of COVID-19 in a population of size N:

$$begin{aligned} {left{ begin{array}{ll} frac{dS(t)}{dt} = - frac{R_0}{D_I} cdot frac{ S(t) I(t)}{N}\ frac{dE(t)}{dt} = frac{R_0}{D_I} cdot frac{ S(t) I(t)}{N} - frac{E(t)}{D_E} \ frac{dI(t)}{dt} = frac{E(t)}{D_E} - frac{I(t)}{D_I} \ frac{dR(t)}{dt} = frac{I(t)}{D_I} end{array}right. } end{aligned}$$

(1)

where S(t), E(t), I(t), and R(t) represent the number of susceptible, exposed, infectious, and removed individuals at time t. In this study, we assume that the reported COVID-19 cases are removed or quarantined from the population and can no longer infect others. Along this line, the time series of reported cases we observed is actually the states of R(t) over time.

There are three epidemiological parameters in the SEIR model: (R_0) is the basic reproduction number; (D_E) is the average latent period; and (D_I) is the average contagious period (i.e., the average duration that an infectious individual is confirmed to be infected). Following the study in[26], we assume that the latent period is the same as the incubation period. Further, based on the estimation in[1], the mean incubation period of COVID-19 was 5.2 days. In this case, we set (D_E=5.2). The infectious rate, (beta =R_0/D_I), controls the rate of spread that represents the probability of transmitting disease between a susceptible and an infectious individual. In this study, we adopt the particle Markov Chain Monte Carlo method to estimate epidemiological parameters (R_0) and (D_I) in each country by fitting the time series of the cumulative number of reported COVID-19 cases[16, 20].

We implement the PMCMC method and simulate the COVID-19 epidemic using python programming language version 3.8.5 (source: https://www.python.org/). We assume that the first exposed case [i.e., E(0)] appears d days before the date of the first reported case in each country. According to the Bayesian inference method, uninformative uniform priors are assigned to model parameters to reduce their influence on the posteriors, that is, (R_0 sim U(0,8)), (D_I sim U(1,20)), and (d sim U(0,30)). Since the interval of each prior covers almost all possible values of the corresponding parameter, such settings have little effect on the inference results as long as the number of iterations is enough. With careful pre-testing, we set the proposal distribution of each parameter to be normal distribution: (q(R_0^{*}|R_0)=norm(R_0^{*}|R_0,0.5)), (q(D_I^{*}|D_I)=norm(D_I^{*}|D_I,0.5)), and (q(d^{*}|d)=norm(d^{*}|d,0.5)). After initializing the values of model parameters as (R_0=2.5), (D_I=5), and (d=14), we run the PMCMC algorithm with 200 particles for 100,000 iterations. Finally, the posterior of each parameter is built upon the last (80%) iterations with a discarded burn-in of 20,000 iterations.

Based on the estimated model parameters, we simulate the dynamics of COVID-19 under two groups of NPIs: (1) contact restriction and social distancing (e.g., contact restrictions and personal preventive actions), and (2) early identification and isolation of cases. Generally speaking, contact restrictions can reduce the infectious rate (beta) of COVID-19; while early identification and isolation of potential cases can reduce the average duration of infection (D_I). On the one hand, we assess the effects of social distancing interventions by reducing the estimated infectious rate (beta) to 25% and 10%, while keeping the duration of infection unchanged. This is equivalent to reducing (R_0) to 25% and 10% of its original value. On the other hand, we also evaluate the impact of combined intervention strategies, where both social distancing and early identification and isolation are implemented. Specifically, the epidemic dynamics of COVID-19 are simulated when reducing (R_0) to 25% and (D_I) to 2 (or 4) at the same time. In addition to what types of NPIs are implemented, it is also important when to implement the interventions. Accordingly, we further simulate the epidemic dynamics of COVID-19 under various settings of NPIs that are implemented on May 18 and June 17, 2020, respectively.

We adopt the notion of vectorial capacity to evaluate malaria transmission potential in malaria-endemic countries in Africa. Based on the Macdonald model[21], the VCAP can be formulated as:

$$begin{aligned} V=frac{ma^2e^{-gn}}{g} = frac{-ma^2p^n}{ln p}, end{aligned}$$

(2)

where m is the average mosquito density per person; a is the expected number of bites on humans per mosquito, per day (i.e., human feeding rate); g is the per-capita daily death rate of a mosquito (i.e., the force of mortality); n is the sporogonic cycle length of the Plasmodium; (p=e^{-g}) represents the probability of a mosquito survives through one whole day. Conceptually, the VCAP incorporates all information about mosquito population (e.g., human biting rate, life expectancy), which is defined as the number of potentially infective contacts a person makes, through the mosquito population, per day. Many studies have shown that the value of VCAP can be calculated based on meteorological factors, such as temperature and precipitation[22, 23]. For example, Ceccato et al. have calculated the average vectorial capacity per 8 days for areas where malaria is considered to be an epidemic in Africa[19]. If there is no abnormal climate change, the annual pattern of malaria transmission potential in each country should be relatively stable across different years. On this basis, we download and extract the 8-day average vectorial capacity for each county from January 1, 2004, to December 31, 2019. We then use the means of the 16-year VCAP as a baseline of the annual pattern of malaria transmission potential.

In this study, we focus mainly on assessing the impact of COVID-19 response on the disruption of ITN distribution, and further on the transmission potential of malaria. Launched in 2005, the Presidents Malaria Initiative (PMI) strives to reduce the burden of malaria across 15 high-burden countries in sub-Saharan Africa through a rapid scale-up of four proven and highly effective malaria prevention and treatment measures, including insecticide-treated mosquito nets. In most countries, the PMI has supported ITN distribution through universal mass campaigns and continuous distribution channels. Based on the Malaria Operational Plan (FY 2019) in each country, we can obtain the total ITNs available from different partner contributions in 2020 (see Table1). In this study, we assume that the available ITNs are distributed throughout the year in a way that the number of distributed ITNs is proportional to the annual pattern of malaria transmission potential in each time interval (eight days in this study). In doing so, the newly increased number of ITNs in a specific time interval t in 2020 can be estimated as:

$$begin{aligned} Delta _i(t) = frac{V_i(t)}{sum _t V_i(t)}Delta _i, end{aligned}$$

(3)

where (Delta _i) represents the total number of available ITNs in country i throughout 2020, and (V_i(t)) represents the mean value of 16-year VCAP in time interval t of each year.

As the number of newly reported COVID-19 cases (Delta _{R_i}(t)=R_i(t)-R_i(t-1)) increases, it is assumed that the distribution of ITNs will be disrupted accordingly. Moreover, when the COVID-19 becomes serious (e.g., the number reaches a threshold value (tau)), the distribution of ITNs will be suspended. Mathematically, we assume that the number of distributed ITNs in time interval t, (D_i(t)), is inversely proportional to the number of reported COVID-19 cases. Thus, we have:

$$begin{aligned} D_i(t) = {left{ begin{array}{ll} (1-Delta _{R_i}(t)/tau )Delta _i(t), &{} text {if } Delta _{R_i}(t) < tau , \ 0, &{} text {otherwise}. end{array}right. } end{aligned}$$

(4)

Let (D_i(1:t)= sum _t D_i(t)) represent the cumulative number of distributed ITNs from the first time interval to the tth interval in 2020. Then, the newly increased ITN coverage rate till time interval t becomes (D_i(1:t)/N_i), where (N_i) is the population size of country i. For case studies in each of the four African countries, the threshold value (tau) is set to be the number of reported cases when various NPIs are implemented.

The disruption or cessation of distribution of ITNs may reduce the expected ITN coverage in a country, which may lead to the increase in human feeding rate a, as well as the transmission potential of malaria. Denote (C_i) as the ITN coverage rate in country i before 2020. In this study, we treat (C_i) as a reference value, which corresponds to human feeding rate of the baseline value of VCAP. Then, if all available ITNs are distributed as expected, the relative change of human feeding rate can be estimated as follows:

$$begin{aligned} r_i^{exp}(t) = frac{1-alpha (C_i+Delta _i(1:t)/N_i)}{1-alpha C_i}, end{aligned}$$

(5)

where (alpha) indicates the efficiency of ITNs against mosquito bites. According to the definition of vectorial capacity, the expected transmission potential of malaria at time interval t can be calculated as:

$$begin{aligned} V_i^{exp}(t) = (r_i^{exp}(t))^2cdot V_i(t). end{aligned}$$

(6)

Similarly, if the distribution of ITNs is disrupted, the relative change of human feeding rate is:

$$begin{aligned} r_i^{dis}(t) = frac{1-alpha (C_i+D_i(1:t)/N_i)}{1-alpha C_i}, end{aligned}$$

(7)

and the transmission potential becomes:

$$begin{aligned} V_i^{dis}(t) = (r_i^{dis}(t))^2cdot V_i(t). end{aligned}$$

(8)

In this study, we set (alpha =1). Note that if the ITN distribution is disrupted, we have (V_i^{exp}(t)

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Accessing the syndemic of COVID-19 and malaria intervention in Africa - Infectious Diseases of Poverty - BioMed Central