| Abstract: |
| We conduct a detailed analysis of the asymptotic spatial profiles of positive steady states for a reaction-diffusion system modeling infectious diseases with vaccinated individuals. This allows us to systematically examine how restricted population movement influences disease dynamics, revealing several novel mathematical and biological phenomena. In particular, when the diffusion rates of both susceptible and infected populations tend to zero, disease eradication is possible provided the environment contains a nonempty low risk region. However, if only the diffusion rate of the infected population approaches zero, the disease becomes spatially localized in high-risk areas. Moreover, vaccination substantially reduces the region of infection persistence as the diffusion rate of infected individuals becomes sufficiently small. |
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