Analysis of a two patch model for disease vector-animal dynamics with non-linear anthropization-driven migration
Landscape dynamics are key drivers of the movement and distribution of sylvatic hematophagous disease vectors and their (wild) animal hosts. Their habitats are undergoing increasing change, particularly fragmentation, through anthropogenic activity. In this article, we present and analyse a novel mathematical model that explicitly combines anthropization-induced landscape dynamics with the population dynamics of hematophagous vectors and (wild) animals dynamics. We develop a phenomenological and analytically tractable two-patch model in which the migration terms between the patches nonlinearly depend on the anthropization level of the patches. Our model analysis comprising analytical stability analysis and numerical bifurcation analysis provides information on how changes in model parameters, especially anthropization levels, shape the long-term dynamics in the model. Precisely, we find that low anthropogenic activity allows for a vector-animal coexistence state, while high anthropization leads to a vector extinction state. However, we establish that for intermediate anthropization levels, the transition between the two states is not necessarily monotonic, but may instead occur via a sequence of concurrent bifurcations along the anthropization axis.