Using Mathematics to Help Eliminate Malaria

Malaria continues to impose devastating effects across the globe, despite the fact that it is preventable, treatable, and curable. The World Health Organization (WHO) estimates that there are more than 200 million malaria cases and 400,000 malaria-based deaths worldwide every year [6, 7]. Children less than five years old are especially vulnerable to the disease.

WHO has set ambitious targets to mostly eliminate malaria by 2030. However, this goal rests precariously on our ability to appropriately treat the disease, which is complicated by the emergence and spread of resistance to antimalarial drugs. When not addressed promptly, drug resistance puts lives at risk; the ability to reliably predict a drug’s usefulness at a given point in space and time is therefore crucial.

The use of model-based geostatistics to generate predictive maps of drug resistance requires data from a large number of studies across unique spatiotemporal locations [2]. However, one cannot feasibly obtain the required data with clinical measures of resistance because of the expensive, time-consuming nature of clinical studies [1, 4]. Employment of genetic molecular markers of resistance in Plasmodium falciparum—the malaria parasite that is responsible for the most deaths—is one possible solution. Researchers can utilize genetic P. falciparum mutations that are associated with drug resistance to monitor spatiotemporal trends in antimalarial drug resistance as a proxy of clinical efficacy. Genetic studies are easier to conduct than clinical studies—and incur a fraction of the cost—thus facilitating the collection of larger numbers of samples across more spatiotemporal locations [4]. Moreover, data from genetic studies are readily amenable to model-based geostatistics.

The majority of malaria cases and deaths occur in Africa, where the antimalarial drug sulfadoxine/pyrimethamine (SP) is a common intermittent preventive treatment during infancy (IPTi) and pregnancy (IPTp). It is also used for seasonal malaria chemoprevention in children. However, measurements of genetic mutations in the dihydropteroate synthase gene (e.g., pfdhps540E)—which determines the drug’s efficacy for protecting infants, children, and pregnant women—indicate that SP resistance is spreading. This scenario could have dire consequences; for example, without the protection of SP during pregnancy, babies face an increased risk of premature birth and low birth weight [5]. As such, there is an urgent need to quantify genetic resistance to SP.

We worked with the WorldWide Antimalarial Resistance Network (WWARN), which is based at the University of Oxford, to develop statistical models that can reliably predict genetic resistance to SP in Africa across space and time [3]. Using pfdhps mutation prevalence data from the open-access WWARN repository (see Figure 1a) and a hierarchical Bayesian geostatistical model (see Figure 1b), we generated continuous spatiotemporal surface maps of the estimated prevalence of the SP resistance markers in Africa from 1990 to 2020. These maps fill in the gaps where no information is otherwise available, providing much-needed insight about areas that would benefit from the inclusion of SP in preventive treatments. Health agencies could then utilize these maps to guide new polices about the “where” and “when” of SP prescription. The model output thus elucidates the spatiotemporal spread of resistance in a way that the discrete data points alone cannot.

Our statistical methodology consists of two stages that enable spatiotemporal prediction of the molecular marker’s prevalence. First, we used the observed data to estimate the posterior distribution of model parameters via a Bayesian inference framework. Based on the model parameters from the first stage, we next predicted marker prevalence on a \(5 × 5\) kilometer (km) grid within the P. falciparum spatial limits of Africa for each year between 1990 and 2020. For each location, we drew a distribution of prevalences from the posterior predictive distribution and summarized it with the median statistic to create a single continuous surface. Figure 1 presents the posterior predictive distribution’s standard deviation surface alongside the median maps, which summarizes the associated uncertainty in the predictions at each location and time. We present the posterior predictive median (see Figure 1c) as an estimate of marker prevalence and the posterior predictive standard deviation (see Figure 1d) as a measure of uncertainty for the prevalence in each \(5 × 5\) km pixel within the P. falciparum spatial limits of Africa.

Figure 2 clearly indicates the way in which our model predicts the change in resistance levels across the continent at different relevant thresholds (90 percent for IPTp, 50 percent for IPTi, and five percent to reveal sentinel sites at which resistance is emerging). Figures 2b-2d also illustrate the changing spatial distribution over the areas of Africa where resistance is predicted to fall above the three thresholds.

These maps can directly impact public health. SP for IPTi is only recommended in areas where the prevalence of the pfdhps540E mutation is less than 50 percent; in contrast, research has suggested that SP for IPTp does not have a protective effect in areas where the pfdhps581G mutation exceeds 10 percent. However, data on pfdhps mutation prevalence in Africa are extremely heterogenous and scattered, and hence unavailable for many areas. The outputs of our mathematical model can help address this issue.

Our predictive spatiotemporal maps indicate that the high prevalence of pfdhps540E mutation is restricted to East and Southeast Africa, which is reassuring for the continued use of SP for infants in West Africa. But analysis indicates that the pfdhps540E distribution is expanding, thus necessitating continuous monitoring efforts.

This study emphasizes the utility of data sharing and predictive modeling to highlight areas of concern for SP resistance that extend beyond national borders. The WWARN SP Molecular Surveyor database serves as a standardized, up-to-date source of information on resistance marker distribution — a model that can be expanded to all validated markers associated with antimalarial resistance. Given the emergence of resistance to artemisinin—the first-line drug against malaria in Rwanda, Uganda, Eritrea, and Ghana—one could easily expand our approach to better understand the evolution of this new and significant threat.

Jennifer Flegg presented this research during an invited presentation at the 2022 SIAM Conference on the Life Sciences, which took place concurrently with the 2022 SIAM Annual Meeting in Pittsburgh, Pa., this July.

References

[1] Ashley, E.A., Dhorda, M., Fairhurst, R.M., Amaratunga, C., Lim, P., Suon, S., … White, N.J. (2014). Spread of artemisinin resistance in Plasmodium falciparum malaria. N. Engl. J. Med., 371(5), 411-423.
[2] Diggle, P.J., Tawn, J.A., & Moyeed, R.A. (1998). Model‐based geostatistics. J. R. Stat. Soc. Ser. C Appl. Stat., 47(3), 299-350.
[3] Flegg, J.A., Humphreys, G.S., Montanez, B., Strickland, T., Jacome-Meza, Z.J., Barnes, K.I., … Otienoburu, S.D. (2022). Spatiotemporal spread of Plasmodium falciparum mutations for resistance to sulfadoxine-pyrimethamine across Africa, 1990-2020. PLOS Comput. Biol., 18(8), e1010317. 
[4] Nsanzabana, C., Djalle, D., Guérin, P.J., Ménard, D., & González, I.J. (2018). Tools for surveillance of anti-malarial drug resistance: An assessment of the current landscape. Malar. J., 17, 75.
[5] Van Eijk, A.M., Larsen, D.A., Kayentao, K., Koshy, G., Slaughter, D.E.C., Roper, C., … Ter Kuile, F.O. (2019). Effect of Plasmodium falciparum sulfadoxine-pyrimethamine resistance on the effectiveness of intermittent preventive therapy for malaria in pregnancy in Africa: A systematic review and meta-analysis. Lancet Infect. Dis., 19(5), 546-556.
[6] WHO Global Malaria Programme. (2019). World Malaria Report 2019. Geneva, Switzerland: World Health Organization. Retrieved from https://www.who.int/publications/i/item/9789241565721.
[7] WHO Global Malaria Programme. (2020). World Malaria Report 2020: 20 years of global progress and challenges. Geneva, Switzerland: World Health Organization. Retrieved from https://www.who.int/publications/i/item/9789240015791.