Spatial Dynamics of Malaria Transmission

The Ross-Macdonald model has exerted enormous influence over the study of malaria transmission dynamics and control, but it lacked features to describe parasite dispersal, travel, and other important aspects of heterogeneous transmission. Here, we present a patch-based differential equation modeling framework that extends the Ross-Macdonald model with sufficient skill and complexity to support planning, monitoring and evaluation for Plasmodium falciparum malaria control. We designed a generic interface for building structured, spatial models of malaria transmission based on a new algorithm for mosquito blood feeding. We developed new algorithms to simulate adult mosquito demography, dispersal, and egg laying in response to resource availability. The core dynamical components describing mosquito ecology and malaria transmission were decomposed, redesigned and reassembled into a modular framework. Structural elements in the framework – human population strata, patches, and aquatic habitats – interact through a flexible design that facilitates construction of ensembles of models with scalable complexity to support robust analytics for malaria policy and adaptive malaria control. We propose updated definitions for the human biting rate and entomological inoculation rates. We present new formulas to describe parasite dispersal and spatial dynamics under steady state conditions, including the human biting rates, parasite dispersal, the “vectorial capacity matrix,” a human transmitting capacity distribution matrix, and threshold conditions. An R package that implements the framework, solves the differential equations, and computes spatial metrics for models developed in this framework has been developed. Development of the model and metrics have focused on malaria, but since the framework is modular, the same ideas and software can be applied to other mosquito-borne pathogen systems. Author summary The Ross-Macdonald model, a simple mathematical model of malaria transmission based on the parasite life-cycle, established basic theory and a set of metrics to describe and measure transmission. Here, we extend the Ross-Macdonald model so it has the skill to study, simulate, and analyze parasite dispersal and heterogeneous malaria spatial transmission dynamics in a defined geographical area with malaria importation. This extended framework was designed to build models with complexity that scales to suit the needs of a study, including models with enough realism to support monitoring, evaluation, and national strategic planning. Heterogeneity in human epidemiology or behaviors – differences in age, immunity, travel, mobility, care seeking, vaccine status, bed net use, or any trait affecting transmission – can be handled by stratifying populations. Mosquito spatial ecology and behaviors are responding to heterogeneous resource availability and weather, which affects adult mosquito dispersal, blood feeding, and egg laying in a structured set of aquatic habitats. We propose new formulas for human biting rates and entomological inoculation rates that integrate exposure as humans move around. We rigorously define parasite dispersal, and we develop matrices describing the spatial dimensions of vectorial capacity and parasite dispersal in mobile humans. We relate these to the parasite’s overall reproductive success, local reproductive numbers and thresholds for endemic transmission. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement DLS and SLW were supported by a grant from the National Science Foundation, Directorate for Technology, Innovation, and Partnerships (TIP) as part of the Convergence Accelerator Program (NSF 2040688). DLS was partly funded by the National Institutes of Health 2U19AI089674. DLS, JMH, and AC were supported by a grant from the National Institute of Allergies and Infectious Dseases (R01 AI163398). DLS, DMS, and JNN, were supported by a grant from the Bill and Melinda Gates Foundation (INV 030600). This project is partly a product of discussions with the mosquito working groups of working groups over several years RAPIDD (Research and Policy for Infectious Disease Dynamics). Over that time, many of us benefitted from the unwavering support and inspiration of F. Ellis McKenzie. OJB was supported by a UK Medical Research Council Career Development Award (MR/V031112/1). ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. 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