Malaria Landscapes & Targeting
Population Structure & the Topology of Malaria Transmission
In the Ross-Macdonald model, everything happens everywhere all at once. These simple models are, at best, only generically useful. In designing vector control for real programs, the goal is to suppress transmission well enough to interrupt it. Ideally, this would be done at the lowest possible cost.
In taking on the question of how to target vector control to best effect, the spatial distribution of humans, mosquito habitats, and malaria have real operational consequences. In making any attempt to study real landscapes, we must come to grips with the nature of the problem. In designing malaria control, it matters how the various components are arranged. At the very least, it affects costs through travel times for malaria control teams.
In discussing the arrangement of components, we are talking about the two hosts: humans and mosquitoes. Where do humans live and spend time? For malaria vectors, humans are a source of blood that mosquitoes need to make eggs: blood feeding is the mode of transmission for malaria parasites. Mosquitoes also need aquatic habitats – water where they lay eggs. Other resources include resting sites, sugar sources, mating habitats, and perhaps other limiting resources. Humans move around, and mosquitoes search for resources. The arrangement of these resources affects the structure of mosquito populations. Mosquito population structure and human mobility determine the structure of malaria transmission.
Human mobility, the arrangement of mosquito habitats, and the structure of adult mosquitoes set the stage for transmission. In some places, mosquito habitat and human activities change seasonally. In any place, these features make up a malaria landscape. The study of malaria landscapes partly belongs to a branch of mathematics called topology. Perhaps the most accessible form of topology is graph theory. How much can we learn about malaria landscapes from studying their graphs?
Topological ideas are not exactly new. In mathematical studies of spatial dynamics on resources, an edge is (in some ways) an unwanted mathematical distraction. An easy way to get around having to deal with an edge is to connect the edges, during the surface into a torus (a doughnut). A torus is the simplest object that is topologically different from a sphere. The practice unwittingly exposes an important aspect of spatial dynamics – that topology matters.
This convention is designed to avoid the sort of mess we must confront. There is another bit of advice that acknowledges the underlying complexity: it is the standard advice about when larval source management is likely to work. Habitats should be few, fixed, and findable. Beyond this vague advice, there are no protocols or procedures defined.
To study malaria landscapes, it might be possible to make a graph that to help us understand some of the essential features of the landscapes. We can explore ideas through simulation. If we represented malaria transmission (or mosquito ecology) in a metapopulation model, how much can we understand about malaria transmission by studying the corresponding graph?
A challenge is how to study malaria topologies. Two approaches immediately present themselves:
We can try to imagine an abstract space that has all possible topologies. Unfortunately, this space would almost certainly be too complex and gangly to handle. By analogy, how many ways could you arrange lego blocks? One study identifed 915,103,765 combinations of 6 standard 4 \(\times\) 2 lego blocks.
Alternatively, we could try to study some real landscape. To do this, we would would need to know a lot about mosquitoes. Our current methods for mosquito populations are blunt.
To make a start of it, we will make some points by constructing simple landscapes that illustrate specific points about malaria transmission. We will stick to some familiar concepts, such as thresholds, connectivity, source-sink dynamics, and foci.