Abstract
Vector-borne diseases remain a major global health challenge. In an increasingly interconnected world, human and vector mobility play a central role in transmission, yet key gaps remain in understanding how different movement patterns interact to shape disease dynamics.
Chapter 1 develops a hierarchical multi-patch model integrating Lagrangian time allocation (commuting without relocation) with Eulerian dispersal (permanent movement). This hybrid framework captures limited mosquito mobility alongside global human connectivity, extending metapopulation models to clarify how these regimes influence transmission thresholds. Uniform persistence is established when the basic reproduction number exceeds one, ensuring an endemic equilibrium. Under partial homogeneity, human dispersal modulates transmission, revealing conditions under which highly endemic regions drive global persistence and identifying thresholds that stabilize the disease-free state.
Chapter 2 focuses on the Lagrangian framework to examine how heterogeneity and mobility shape transmission. Individuals are assigned home patches but distribute time across locations, capturing human-driven connectivity. Analysis shows that interactions between epidemiologically distinct patches make heterogeneity a key structural driver, potentially raising global transmission above local levels. Analytical and numerical results indicate that movement can either increase or reduce transmission, highlighting its dual role in connected systems.
Together, these results show that spatial heterogeneity and mobility interact in structurally significant ways, and that mixing across patches can elevate outbreak risk even when local conditions appear subcritical.