Effect of host movement on the prevalence of vector-borne diseases

Human movement plays a key role in spreading vector-borne diseases globally. Various spatial models of vector-borne diseases have been proposed and analyzed, mainly focusing on disease dynamics. In this paper, based on a multi-patch Ross-Macdonald model, we study the impact of host migration on the local and global host disease prevalences. Specifically, we find that the local disease prevalence of any patch is bounded by the minimum and maximum disease prevalences of all disconnected patches and establish a weak order-preserving property. For global disease prevalence, we derive its formula at both zero and infinite dispersal rates and compare them under certain conditions, and calculate the right derivative at no dispersal. In the case of two patches, we give two complete classifications of the model parameter space: one is to compare the host disease prevalences with and without host dispersal, and the other is to determine the monotonicity of host disease prevalence with respect to host dispersal rate. Numerical simulations confirm inconsistence between disease persistence and host disease prevalence, as well as between host prevalence and vector prevalence in response to host movement. In general, a more uneven distribution of hosts and vectors in a homogeneous environment leads to lower host prevalence but higher vector prevalence and stronger disease persistence.