Global dynamics and threshold behavior of an SEIR epidemic model with nonlocal diffusion

This paper studies the global dynamics of an SEIR (Susceptible-Exposed-Infectious-Recovered) model with nonlocal diffusion. We show the model's well-posedness, proving the solutions' existence, uniqueness, and positivity, along with a disease-free equilibrium. Next, we prove that the model admits the global threshold dynamics in terms of the basic reproduction number R-0 , defined as the spectral radius of the next-generation operator. We show that the solution map has a global compact attractor, offering insights into long-term dynamics. In particular, the analysis shows that for R-0 < 1 , the disease-free equilibrium is globally stable. Using the persistence theory, we show that there is an endemic equilibrium point for R-0 > 1 . Moreover, by constructing an appropriate Lyapunov function, we establish the global stability of the unique endemic equilibrium in two distinct scenarios.