A mathematical model of spatial transmission of vector-borne disease

A mathematical model of the propagation of vector-borne diseases in a two-species population of a carrier and reservoir of the disease is proposed and studied. The model is based on the mechanism of dirofilariosis propagation.  The model is formulated as a system of four partial differential equations. As variables of the model, densities of two population divided by the number of healthy and infected ones were chosen. The simplest case of a spatially homogeneous distribution of populations was studied, stationary regimes were found, and their stability conditions were obtained. It is shown that a sufficiently intensive application of all possible preventive arrangements (extermination of the vectors of the disease, treatment of infected individuals, prevention of contact with the vector of the disease) leads to the stability of a stationary regime with no disease. A scheme for numerical analysis of a full mathematical model that takes into account the spatial inhomogeneity of population distribution is proposed. In the computational experiment, various strategies for the application of insecticides in space have been studied. As a result, the following recommendations on the use of insecticides for the prevention of vector-borne diseases are formulated: the most effective is the localized use of insecticides; treatment should be carried out near the source of reproduction of the vectors of the disease, creating a barrier between the source and reservoir of the pathogen; for each amount of insecticide there is an optimal size of the processing area.