Abstract
Our motivation is a mathematical model describing the spatial propagation of an epidemic disease through a population. In this model, the pathogen diversity is structured into two clusters and then the population is divided into eight classes which permits to distinguish between the infected/uninfected population with respect to clusters. In this paper, we prove the weak and the global existence results of the solutions for the considered reaction-diffusion system with Neumann boundary. Next, mathematical Turing formulation and numerical simulations are introduced to show the pattern formation for such systems.
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Bendahmane, M., Saad, M. Mathematical Analysis and Pattern Formation for a Partial Immune System Modeling the Spread of an Epidemic Disease. Acta Appl Math 115, 17–42 (2011). https://doi.org/10.1007/s10440-010-9569-3
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DOI: https://doi.org/10.1007/s10440-010-9569-3