Modelling the ‘last mile’ of malaria elimination

Malaria remains a serious threat to public health, with an estimated 249 million cases and 608,000 deaths in 2022 (1). However, many countries are making good progress towards eliminating malaria, with some countries, such as those in the World Health Organization (WHO) Greater Mekong Subregion, now entering the so-called ‘last mile’ of malaria elimination (2). This phase of malaria elimination requires a shift from country-based interventions to more targeted, focal approaches.

Lisa White (second from right), of Model Health Ltd, and Pengby Ngor (right), head of Cambodia’s Malaria Information System, meet with some village malaria workers (photo credit: Adam Bodley).

Mathematical modelling has proven to be a valuable tool in malaria elimination efforts, for example being used to predict which combinations of interventions would lead to the elimination of Plasmodium falciparum malaria for a range of starting prevalence and antimalarial drug resistance scenarios (3). Now, as some countries prepare for the malaria elimination certification and maintenance phases, questions remain as to which interventions should be retained during each phase and which additional interventions may need to be included to eliminate malaria, including Plasmodium vivax malaria.

In this post, we outline how a mathematical modelling approach can be used to develop strategies to assist countries as they enter the last mile of malaria elimination.

The model structure is an extension of a structure previously published by Lisa White and colleagues (4). The model is structured at the village level, with each patient being at some stage of the treatment pathway, e.g. untreated asymptomatic, untreated symptomatic, treated by a community health worker, treated at a health centre etc.

Individuals with malaria may or may not have clinical symptoms, with a probability depending on whether they have experienced a recent (in the past year or two) infection. If an individual does not have a clinical infection, then the infection is asymptomatic and assumed not to be treated. This stage is infectious and can last for several months; therefore, an individual under these circumstances is a source of local transmission within a village. However, an asymptomatic infection may be treated later as part of the establishment of a new active focus of malaria control efforts for a subset of the population.

If an individual has a clinical infection, and if a community health worker is present locally, the individual will visit the community health worker with a given probability (this probability may be higher if the village is an active focus, due to weekly fever screening). If the patient will ultimately be treated by a community health worker, they enter a state that includes those individuals who will be treated and those undergoing treatment. All of these individuals are infectious until they have been cured by their antimalarial treatment.

The treatment pathway may also include those individuals who are to be treated or who are being treated at a health centre. In addition, there may be some clinical infections that are not treated and will become asymptomatic, then sub-patent, before ultimately recovering. As both of these asymptomatic stages are infectious and can have a duration of several months, they also represent potential sources of local transmission of malaria in a village.

The treatment pathway outlined above forms the basis of a P. falciparum and P. vivax transmission model for individual villages, with the P. vivax model including a hypnozoite stage. The model is expressed as a set of ordinary differential equations that are replicated for each village and linked via a connectivity matrix.

A village is classified as ‘active’ if local cases were above an elimination threshold within the past 12 months; ‘residual’ if local cases remained below the elimination threshold for a further 24 months; and ‘cleared’ if local cases remained below the elimination threshold beyond this time. Any increase in local cases above the elimination threshold means a return to active status. Villages that have cleared status may be reclassified as non-foci during annual restratifications (illustrated in Figure 1).

Figure 1. An illustration of the categorisation of villages according to their focus status.

The model is a multi-patch model. This means that each village is modelled as a population for which the transmission of malaria is linked to the other villages via imported cases from those other villages. The shape and level of connectivity between villages will define this linkage and will have implications for the predicted impact of any interventions. We assume that each village has a proportion of its population who are mixing with members of other villages at any given point in time. We also assume that this mixing sub-population is distributed evenly across all of the connected villages. An illustrative example is provided in Figure 2.

Figure 2. An illustration of how villages are connected in the model. In this example, village 1 is connected to village 2, village 2 is connected to villages 1 and 3, and village 3 is connected to village 2.

The model is coded to import data for a specific set of villages and then run a simulation that incorporates those villages. The user can adjust some of the model parameters as required, such as the transmission coefficient, to obtain a reasonable reproduction of the observed data. The model can then be run to explore the relative impact of different interventions on a country’s progress during the last-mile phase of malaria elimination and ultimately which interventions will be most effective for helping the country to maintain their malaria-free status.

To find out more about how mathematical modelling approaches can assist with malaria elimination and other global health initiatives, please contact Model Health Ltd.

References

1. World Health Organization. World malaria report 2023. Geneva: World Health Organization; 2023 (https://cdn.who.int/media/docs/default-source/malaria/world-malaria-reports/world-malaria-report-2023-spreadview.pdf?sfvrsn=bb24c9f0_3, accessed 9 January 2024).

2. World Health Organization. Countries of the Greater Mekong ready for the “last mile” of malaria elimination. Geneva: World Health Organization; 2020 (https://iris.who.int/bitstream/handle/10665/337970/WHO-UCN-GMP-MME-2020.05-eng.pdf?sequence=1, accessed 9 January 2024 ).

3. White LJ, Maude RJ, Pongtavornpinyo W, Saralamba S, Aguas R, Van Effelterre T et al. The role of simple mathematical models in malaria elimination strategy design. Malaria Journal. 2009;8:212. doi: 10.1186/1475-2875-8-212.

4.  Tun STT, Parker DM, Aguas R, White LJ. The assembly effect: the connectedness between populations is a double‐edged sword for public health interventions. Malaria Journal. 2021;20:189. doi: 10.1186/s12936-021-03726-x.