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

Abstract

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.

Keywords: Disease persistence; Disease prevalence; Dispersal rate; Host reproduction number; Human movement; Monotonicity.

Fig. 1

The global host disease prevalence (blue solid line) and the basic reproduction number (red dashed line) versus host dispersal rate under four scenarios. The x-axis denotes while the left and right y-axes are and , respectively. Refer to Table 1 for parameter settings.

Fig. 2

The global host disease prevalence (blue solid line) versus host dispersal rate under parameter settings a             b            c             and d             and for in all four scenarios. The red dot on the left y-axis corresponds to the point

Fig. 3

The global host and vector disease prevalences, (blue solid line) and (red dashed line), versus host dispersal rate under parameter settings a  b c and d and and in all four scenarios. The x-axis is for while the left and right y-axes represent and respectively.

Fig. 4

The contour plots of the basic reproduction number (first column), the global host disease prevalence (second column), and the global vector disease prevalence (third column) versus and under small vector abundance (first row) and large vector abundance (second row). The x and y-axes are for and , respectively. See text for parameter settings.