Analysis of a mixed fractional--classical reaction--diffusion epidemic model with nonlocal asymptomatic transmission

<title>Abstract</title> <p> We study a mixed fractional--classical reaction--diffusion epidemic model with susceptible, asymptomatic infected, symptomatic infected, and recovered populations. The model combines regional fractional diffusion of the susceptible and asymptomatic infected populations, each with its own fractional exponent, with classical diffusion of the remaining populations, and incorporates spatial heterogeneity, asymptomatic transmission, and periodic intermittent treatment. Using semigroup theory and L ^p energy estimates, we prove the global well-posedness and uniform boundedness of solutions and establish sufficient conditions for convergence to the disease-free state. Numerical simulations complement the theoretical analysis by illustrating the spatiotemporal dynamics of the model and revealing the combined effects of regional fractional diffusion, spatial heterogeneity, nonlocal asymptomatic transmission, and intermittent treatment on disease propagation and persistence. </p>