  This study presents a comprehensive analysis of a two-patch, two-life stage
SI model without recovery from infection, focusing on the dynamics of disease
spread and host population viability in natural populations. The model,
inspired by real-world ecological crises like the decline of amphibian
populations due to chytridiomycosis and sea star populations due to Sea Star
Wasting Disease, aims to understand the conditions under which a sink host
population can present ecological rescue from a healthier, source population.
Mathematical and numerical analyses reveal the critical roles of the basic
reproductive numbers of the source and sink populations, the maturation rate,
and the dispersal rate of juveniles in determining population outcomes. The
study identifies conditions for disease-free, endemic, and extinction
equilibria in sink populations, emphasizing the potential for ecological and
evolutionary mechanisms to facilitate coexistence or recovery. These findings
provide insights into managing natural populations affected by disease, with
implications for conservation strategies, such as the importance of maintaining
reproductively viable refuge populations and considering the effects of
dispersal and maturation rates on population recovery. The research underscores
the complexity of host-pathogen dynamics in spatially structured environments
and highlights the need for multi-faceted approaches to biodiversity
conservation in the face of emerging diseases.
