Inference of malaria reproduction numbers in three elimination settings by combining temporal data and distance metrics

Individual-level geographic information about malaria cases, such as the GPS coordinates of residence or health facility, is often collected as part of surveillance in near-elimination settings, but could be more effectively utilised to infer transmission dynamics, in conjunction with additional information such as symptom onset time and genetic distance. However, in the absence of data about the flow of parasites between populations, the spatial scale of malaria transmission is often not clear. As a result, it is important to understand the impact of varying assumptions about the spatial scale of transmission on key metrics of malaria transmission, such as reproduction numbers. We developed a method which allows the flexible integration of distance metrics (such as Euclidian distance, genetic distance or accessibility matrices) with temporal information into a single inference framework to infer malaria reproduction numbers. Twelve scenarios were defined, representing different assumptions about the likelihood of transmission occurring over different geographic distances and likelihood of missing infections (as well as high and low amounts of uncertainty in this estimate). These scenarios were applied to four individual level datasets from malaria eliminating contexts to estimate individual reproduction numbers and how they varied over space and time. Model comparison suggested that including spatial information improved models as measured by second order AIC (ΔAICc), compared to time only results. Across scenarios and across datasets, including spatial information tended to increase the seasonality of temporal patterns in reproduction numbers and reduced noise in the temporal distribution of reproduction numbers. The best performing parameterisations assumed long-range transmission (> 200 km) was possible. Our approach is flexible and provides the potential to incorporate other sources of information which can be converted into distance or adjacency matrices such as travel times or molecular markers.