Transmission dynamics for vector-borne diseases in a patchy environment

摘要

In this paper, a mathematical model is derived to describe the transmission and spread of vector-borne diseases over a patchy environment. The model incorporates into the classic Ross–MacDonald model two factors: disease latencies in both hosts and vectors, and dispersal of hosts between patches. The basic reproduction number R_0 is identified by the theory of the next generation operator for structured disease models. The dynamics of the model is investigated in terms of R_0. It is shown that the disease free equilibrium is asymptotically stable if R_0 < 1, and it is unstable if R_0 > 1; in the latter case, the disease is endemic in the sense that the variables for the infected compartments are uniformly persistent. For the case of two patches, more explicit formulas for R_0 are derived by which, impacts of the dispersal rates on disease dynamics are also explored. Some numerical computations for R_0 in terms of dispersal rates are performed which show visually that the impacts could be very complicated: in certain range of the parameters, R_0 is increasing with respect to a dispersal rate while in some other range, it can be decreasing with respect to the same dispersal rate. The results can be useful to health organizations at various levels for setting guidelines or making policies for travels, as far as malaria epidemics is concerned.