Global dynamics of a partially degenerate nonlocal model for mosquito-borne disease transmission

Abstract

Host mobility and environmental heterogeneity in vector populations are critical determinants of spatial patterns in mosquito-borne disease transmission. To investigate the impact of spatial heterogeneity and host dispersal on transmission dynamics, this manuscript proposes a partially degenerate nonlocal dispersal Ross–Macdonald model. The basic reproduction number (Formula presented.) is identified as a critical threshold that determines the global dynamics of the model. The analytical challenge of noncompact solution map of this partially degenerate nonlocal model is addressed using comparison arguments for the phase space of Lebesgue measurable and bounded functions. Furthermore, we characterize the asymptotic behavior of (Formula presented.) under small and large diffusion regimes, linking dispersal rates to transmission potential. Numerical simulations reveal how host mobility and spatially varying environment modulate disease persistence and transmission risks. Simulations also indicate that the model assuming local dispersal may underestimate transmission risks, and the epidemic size does not monotonically increase with (Formula presented.).