Assessing the role of spatial heterogeneity and human movement in malaria dynamics and control.

Mathematical models developed for studying malaria dynamics often focus on a single, homogeneous population. However, human movement connects environments with potentially different malaria transmission characteristics. To address the role of human movement and spatial heterogeneity in malaria transmission and malaria control, we consider a simple malaria metapopulation model incorporating two regions, or patches, connected by human movement, with different degrees of malaria transmission in each patch. Using our two-patch model, we calculate and analyze the basic reproduction number, R(0), an epidemiologically important threshold quantity that indicates whether malaria will persist or go extinct in a population. Although R(0) depends on the rates of human movement, we show that R(0) is always bounded between the two quantities R(01) and R(02)-the reproduction numbers for the two patches if isolated. If without migration, the disease is endemic in one patch but not in the other, then the addition of human migration can cause the disease to persist in both patches. This result indicates that regions with low malaria transmission should have an interest in helping to control or eliminate malaria in regions with higher malaria endemicity if human movement connects them. Performing a sensitivity analysis of R(0) and the endemic equilibrium to various parameters in the two-patch model allowed us to determine, under different parameterizations of the model, which patch will be the better target for control measures, and within that patch, what type of control measure should be implemented. In the analysis of R(0), we found that if the extrinsic incubation period is shorter than the average mosquito lifespan, the control measures should be targeted towards reducing the mosquito biting rate. On the other hand, if the extrinsic incubation period is longer than the average mosquito lifespan, control measures targeting the mosquito death rate will be more effective. Intuitively, one might think that resources for malaria control should be allocated to the region with higher malaria transmission. However, our sensitivity analyses indicated that this is not always the case. In fact, if migration into the lower transmission patch is much faster than migration into the higher transmission patch, the lower transmission patch is potentially the better target for malaria control efforts. While human movement between regions poses challenges to malaria control and elimination, if estimates of relevant parameters in the model are known, including migration rates, our results can help inform which region to target and what type of control measure to implement for the greatest success.