The spread of most diseases is strongly affected by the migrations of populations due to wars, natural disasters or prevailing economic circumstances. These migrations also impact the economies of the regions affected by the migrations. To better assess the overall impact of the interplay of diseases and the economic and demographic environment in a region and thus more effectively control the disease, we build and analyse a general meta-population model of the spread of diseases, integrating the cause of migration and also the economic impact to provide decisionmakers with better tools for efficient malaria control. Mathematically, the model consists of a collection of systems of differential equations on the nodes of a network (graph) representing the residence sites of subpopulations and edges representing migration paths. We analyse the model by combining the existing tools for multi-patch systems with novel integration of techniques of asymptotic analysis and monotone systems in applications to epidemiological models.
The project is multidisciplinary, using topics and tools from demography and population dynamics, epidemiology, mathematical modelling and various branches of mathematics ranging from mathematical analysis through dynamical systems and asymptotic analysis to graph theory and linear algebra.
