2022/02/26 by Rong Wang, Yihong Du, Wang, Rong +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35R09 #35R35 #92D30 #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2202.13068
openalex publication_date 2022/02/26 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this paper, we examine the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators.The spreading front of the disease is represented by the free boundaries in the model. We show that the model is well-posed, its long-time dynamical behaviour is characterised by a spreading-vanishing dichotomy, and we also obtain sharp criteria to determine the dichotomy. Some of the nonlocal effects in the model pose extra difficulties in the mathematical treatment, which are dealt with by introducing new approaches. The model can capture accelerated spreading, and its spreading rate will be discussed in a subsequent work.