Estimating finite-population reproductive numbers in heterogeneous populations

Hotspots and super-spreaders: Modelling fine-scale malaria parasite transmission using mosquito flight behaviour

Malaria hotspots have been the focus of public health managers for several years due to the potential elimination gains that can be obtained from targeting them. The identification of hotspots must be accompanied by the description of the overall network of stable and unstable hotspots of malaria, especially in medium and low transmission settings where malaria elimination is targeted. Targeting hotspots with malaria control interventions has, so far, not produced expected benefits. In this work we have employed a mechanistic-stochastic algorithm to identify clusters of super-spreader houses and their related stable hotspots by accounting for mosquito flight capabilities and the spatial configuration of malaria infections at the house level. Our results show that the number of super-spreading houses and hotspots is dependent on the spatial configuration of the villages. In addition, super-spreaders are also associated to house characteristics such as livestock and family composition. We found that most of the transmission is associated with winds between 6pm and 10pm although later hours are also important. Mixed mosquito flight (downwind and upwind both with random components) were the most likely movements causing the spread of malaria in two out of the three study areas. Finally, our algorithm (named MALSWOTS) provided an estimate of the speed of malaria infection progression from house to house which was around 200-400 meters per day, a figure coherent with mark-release-recapture studies of Anopheles dispersion. Cross validation using an out-of-sample procedure showed accurate identification of hotspots. Our findings provide a significant contribution towards the identification and development of optimal tools for efficient and effective spatio-temporal targeted malaria interventions over potential hotspot areas.

Assessing intervention strategies for non-homogeneous populations using a closed form formula for R0

A general stochastic model for susceptible → infective → recovered (SIR) epidemics in non-homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex models. The basic reproduction number R₀, an indication of the probability of an outbreak for homogeneous populations does not indicate the probability of an outbreak for non-homogeneous models anymore, because it changes with the initially infected case. Therefore, we use "individual R₀" that is the expected number of secondary cases for a unique given initially infected individual. Thus, the effectiveness of intervention strategies can be assessed by their capability to reduce individual R₀ values. Also a vaccination plan based on individual R₀ values for fully heterogeneous populations is proposed. It is based on the recursive calculation of individual R₀ values.