Impact of Varying Community Networks on Disease Invasion
Stephen Kirkland, Zhisheng Shuai, P. van den Driessche, Xueying Wang
Abstract
We consider the spread of an infectious disease in a heterogeneous environment modeled as a network of patches. We focus on the invasibility of the disease, as quantified by the corresponding value of an approximation to the network basic reproduction number, $\mathcal{R}_0$, and study how changes in the network structure affect the value of $\mathcal{R}_0$. We provide a detailed analysis for two model networks, a star and a path, and discuss the changes to the corresponding network structure that yield the largest decrease in $\mathcal{R}_0$. We develop both combinatorial and matrix analytic techniques, and we illustrate our theoretical results by simulations with the exact $\mathcal{R}_0$.