A simple two-patch epidemiological model with Allee effects and disease-modified fitness

In this article, we study population dynamics of a simple two-patch SI model with three features: i) strong Allee effects built in the net reproduction rates; ii) the disease-modified fitness such as the reproduction ability and the competitive ability in different population levels; and iii) dispersal whose rate is proportional to the difference of population between two patches. We derive sufficient conditions on the persistence of disease and explore how different intensities of dispersals combined with spatial heterogeneity affect disease dynamics where spatial heterogeneity can be generated from i)Initial conditions; ii)Different dynamical patterns and iii) Different life history parameters of species such as the reproduction rate, competitive parameters, critical thresholds. Our analysis indicates that dispersal can promote the endemic and save the patch from disease-driven extinction under certain conditions. In addition, our analytical results and numerical simulations suggest that different intensities of dispersals combined spatial heterogeneity can have dramatic impacts on population dynamics: a) Proper intensities of dispersal can save species from disease-driven dynamics; b) Weak intensities of dispersal can generate source-sink dynamics that cannot stop the spreading of disease; c) Intermediate intensities of dispersals may stabilize the population dynamics while strong intensities of dispersals can lead to the synchronization of the system. However, dispersal has no effects on the local stability of the endemic state for the symmetric system, i.e., identical two patches. These results may provide useful insights to understand, identify, test, develop, and improve management practices that are essential to the survival of natural populations, including rare and officially endangered species or communities.