Background
The transmission dynamics of malaria are complex. Climatological, hydrological, and biological factors interact non-linearly at various stages of the transmission cycle and shape malaria transmission dynamics. Another key element of malaria transmission dynamics is environmental factors. The large dimension and non-linearity of those factors make it difficult to predict and intervene against malaria.
Malaria can be sustainably prevented through environmental modification approaches. Climatological, hydrological, and biological factors are hardly controllable; malaria treatment interventions require continuous effort to attenuate or avoid the impact of those factors. Environmental factors, on the other hand, can be manipulated; well-designed planning of environmental conditions could work as a long-term malaria prevention approach. Facing the low momentum in the public health arena of malaria control, due to fatigue of donors, spread of drug-resistance, fragile health infrastructures etc., prevention approaches, as opposed to treatment approaches, could be more sustainable and cost-effective in fighting malaria.
Planning of house locations relative to vector breeding sites and removal of pools near houses could be effective malaria prevention techniques. The importance of the relative distributions of houses and pools has been reported both in simulation studies [
1,
2] and in observational studies [
3‐
6], spelling out the large risk of contracting malaria when houses are located near vector breeding pools. The threshold distance for high malaria transmission risk is reported to be some hundreds of meters [
3,
4,
6]. This paper will demonstrate that the threshold distance to prevent malaria is not universal, but significantly influenced by climatology, hydrology, and biology of local vectors, and that those factors interact in a complex manner. Planning of malaria-resistant village, thus, may not be straightforward.
This study seeks both to reduce the dimension of malaria transmission determinants, and to aid environmental manipulation to prevent malaria. The objective of this paper is to provide a tool to analyse malaria transmission potential at various environments, including different house distribution conditions. The analyses are conduct for conditions where mosquito populations are limited primarily by water availability, such as the fringe of Sahel. Based on theoretical studies with a wide range of forcings and parameters, a predictive theory of malaria transmission potential will be presented. The theory will then be tested for West Africa. In testing the theory, the impact of house distribution is emphasized.
Discussion
The malaria transmission potential estimate compared well with contemporary observational data, when X
dist (hypothetical distance between pools and human habitants) was adjusted for population density (Fig.
4c). Even without adjustment for population density (Fig.
4a), the estimate performed as well as other well-known estimates, such as those of the MARA project [
12].
One of the strengths of the estimates is the detailed parametrization of hydrology. Instead of the commonly used parameter of monthly or daily rainfall amount [
12,
20], three hydrological variables were employed in this study: T
wet, T
on, and T
int. The same amount of rainfall, but with different temporal rainfall patterns, results in different malaria transmission potentials [
21]. Having a large amount of rainfall at a time followed by subsequent dry days is different from having continuous but low intensity rainfall for many days. Pool persistence, T
on, and storm inter-arrival time, T
int, account for both rainfall amount and temporal patterns. The information of T
on is rarely available from either ground observations or satellite data sets; however, a previous study [
9] made it possible to estimate T
on/T
int through the association of the annual rainfall and T
wet. In reality, pools persist over a range of period. T
on represents the average behaviour of pools for a given hydrological condition. Some pools disappear quicker, decreasing the total area of breeding pools. The effect of such heterogeneous pool persistence was implicitly modeled through imposing declining probability of mosquitoes laying eggs and persistence-dependent larval mortality.
The length of the rainy season, T
wet, is also an important determinant of malaria transmission, because it takes a certain time for mosquitoes to increase their populations. The effect of the rainy season length, however, is often demonstrated only implicitly, both in statistical models and in computational models. In the MARA project, Craig et al. [
12] argued that malaria transmission requires 3 and 5 months of rain at relatively warm and cold regions of Africa, respectively. The MARA project, however, did not use the rainy season length itself as a model parameter, but used the 3 or 5 months as given “time windows” for calculation. The Malaria Early Warning System (MEWS) is an improved version of MARA [
22], and it outputs the number of months in a year during which climate conditions are suitable for malaria transmission. This notion is similar to T
wet; yet the importance of T
wet is better understood in comparison to T
o. The close description of hydrological conditions provides the predictive theory with an advantage over other malaria transmission models.
The consideration of the spatial effect made the estimate even more accurate. This study employed the hypothetical spatial setup, and the conceptual relationship between the house-to-pool distance and population density. The hypothetical setting is relevant to villages near water-resources reservoirs, having a long shoreline as a vector breeding pool. In reality, the distribution of houses and pools varies significantly from place to place, and hence the hypothetical setup is not valid for many locations. However, the relationship between the house-to-pool distance and population density is based on an implied relationship and should represent the characteristic relationship of regions on a large scale.
The testing of the predictive theory produced a good malaria estimate over West Africa; however, it also has noteworthy shortcomings. First of all, although the inclusion of population density data improved the quality of the estimation of malaria transmission potential, the effect of population density on malaria transmission is not straightforward. This analysis assumed that having a large population density is associated with a denser house network, and so a small distance between houses and pools, resulting in large transmission potential. A large population density, on the other hand, may be linked to economic development and to enhanced malaria controls, especially when an analysis is conducted at a village scale [
23,
24]. The former effect appears to be stronger than the latter at the scale of the analysis, given that the spatial patterns of malaria transmission intensity were more closely reproduced by positively associating the malaria risk and population density. However, the latter effect, the negative association between the malaria risk and population density, could be dominating in some parts of the region.
Second, the estimate did not account for past and current levels of malaria interventions and human immunity, which may explain the overestimated malaria transmission levels west to −12°E and east to 4°E (Fig.
4c, d) in this study. In Senegal, located around −16°E to −12°E, malaria parasite rate dropped significantly (by around 30%) between 2000 and 2015 due to extensive malaria control programmes [
25,
26]. Around 4°E to 12°E and 12°N to 14°N is Southern Niger, where Hausa-Fulani people live. The overestimation around this region may be accounted for by the unique low-susceptibility to malaria of the Hausa-Fulani people [
27]. In this sense, this estimate addressed the climatic and environmental suitability for malaria transmission in the absence of human controls. The estimate of actual malaria transmission intensity is useful; however, the climatic and environmental suitability for malaria transmission is also vital information for malaria control programmes.
To is a biological time scale introduced in this study, which is associated with the time needed to reach \({\hat{\text{R}}}_{\text{o}} = 1\) under the assumption of the hydrologically-saturated condition. The calculation of To depends on temperature and spatial settings of houses and pools but is independent of hydrological conditions, i.e., Twet, Ton, and Tint.
Malaria transmission is complex, requiring many factors to be considered. The introduction of To, together with the two dimension-less variables, D1 = Twet/To and D2 = Ton/Tint disclosed a universality in the conditions for stable malaria transmission. D1 and D2 not only reduce the number of malaria transmission determinants, but are also intuitive. Readers should, however, be aware that the values of To were obtained for relatively dry regions in West Africa. For other regions with more or less competent vectors, or with other limiting factors in play, the values of To should be evaluated accordingly.
The application of T
o and the predictive theory is not limited to the estimation of malaria transmission potential; it also offers guidelines regarding the minimum distances that houses and pools should be apart to prevent malaria, as shown in the following examples. Firstly, T
o helps in defining the house-to-pool distances needed to prevent malaria transmissions around permanent water bodies, such as water-resources reservoirs. To prevent malaria near a permanent water body, where the condition compares with the hydrologically-saturated condition, T
o should be infinite. T
o can be rendered infinite by locating houses away from pools by a certain distance, whose value depends on temperature (Fig.
2). Secondly, malaria-preventive distances between houses and pools can also be inferred for other general conditions from the predictive theory and the T
o–X
dist relationship [from climatological data, T
on/T
int can be estimated as described in this paper’s “
Methods” section. By using the T
on/T
int with the predictive theory (Fig.
3), T
wet/T
o associated with Ro = 1 can be found. As T
wet can be obtained from climatological data, T
o can be calculated. Finally, applying the T
o–X
dist relationship (Fig.
2a) for a given temperature, an X
dist value leading to the Ro = 1 condition can be found]. Malaria-resistant villages would require that houses should be located further than the critical distances, or that pools should be removed within the critical distances from houses.
The critical distances to prevent malaria found in this study also provide guidance for resource allocation. When relocation of settlements or removal of pools is not feasible, conventional interventions, such as distribution of bednets, remain primary malaria control strategy. The critical distances presented in this study shows the distance from pools within which such intervention should be prioritized. This study provides a useful guidance for estimating malaria transmission potential, and for designing malaria resistant villages by controlling house-to-pool distances. R
o values and critical distances suggested in this study should not be taken as absolute values that fit every condition, but they should be adjusted depending on the details of the local environment. In particular, malaria transmission potential and critical malaria-preventive distances depend on the distribution of houses and the initial number of mosquitoes in the beginning of the rainy seasons. The impact of different house distribution could be a future research topic. The sensitivity to the initial mosquito population is not the focus of this study; how and how many mosquitoes emerge after a long dry period are the questions yet to be clarified. At the limit of no mosquitoes surviving after a long dry season, the potential for malaria transmission would not exist even under the wettest hydrologic condition. The appearance of mosquito population after a long dry period can be explained either by aestivation or migration [
28], and imposing the minimum mosquito population in HYDREMARS conceptually agree with the aestivation hypothesis.