Spatial Dynamics For A Periodic Ross-Macdonald Model On Lattice

Malaria, a vector-borne infectious disease caused by the Plasmodium par-asite, still threatens to human beings in many places in the world. As is well-known, mathematical models have been extensively used to study the dynamics of infectious diseases. As the earliest malaria model, Ross-Macdonald model cap-tures the essential features of malaria transmission process. However, from the ecological and epidemiological view, the immigration of human and mosquitoes, and seasonal change may impact the spread dynamics of malaria. In this thesis, We first take the movement of human and vector, and seasonality into account for malaria transmission, and generalize the classical Ross-Macdonald model on the discrete habitat region. Then we devote to study the spatial dynamics of the model on both the infinite lattice and the finite lattice. The body of this thesis is divided into three parts.In the first chapter, we introduce the research states of malaria model. After presenting the significant factors for malaria transmission, we build a new model by incorporating the human population and vector dispersal between patches, and seasonality into the classical Ross-Macdonald model.In the second chapter, we prove the existence of the spreading speed for the derived model on the infinite lattice. By using the comparison principle, we obtain that the spreading speed coincides with the minimal wave speed of monotone periodic travelling waves.In the third chapter, we study the global dynamics of the Ross-Macdonald model on the finite lattice. Under the assumption that the diffusion has on inflows and outflows on the finite lattice, we first introduce the basic reproduction number R0 via the next generation operator. Applying the monotone dynamical system theory and persistence theory, we then establish the threshold dynamics in terms of R0.