Host movement, transmission hot spots, and vector-borne disease dynamics on spatial networks

We examine how spatial heterogeneity combines with mobility network structure to influence vector-borne disease dynamics. Specifically, we consider a Ross-Macdonald-type disease model on $n$ spatial locations that are coupled by host movement on a strongly connected, weighted, directed graph. We derive a closed form approximation to the domain reproduction number using a Laurent series expansion, and use this approximation to compute sensitivities of the basic reproduction number to model parameters. To illustrate how these results can be used to help inform mitigation strategies, as a case study we apply these results to malaria dynamics in Namibia, using published cell phone data and estimates for local disease transmission. Our analytical results are particularly useful for understanding drivers of transmission when mobility sinks and transmission hot spots do not coincide. A few minor notation typos. 1) Figure 1, N_{i} corrected to N_{i}^{h}. 2) Typo in vector equations, system 2.1. N_{i} corrected to N_{i}^{h} and I_{i} corrected to I_{i}^{h} 3) On page 10, \mu_{v,i} corrected to \mu{i}^{v}