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Mathematical analysis and pattern formation for a partial immune system modeling the spread of an epidemic disease. (English) Zbl 1252.35053
The paper concerns a mathematical model describing the spatial propagation of an epidemic disease through a population. The pathogen diversity is structured here 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. Some weak and the global existence results of the solutions for the considered reaction-diffusion system with Neumann boundary condition are proved. Next, a mathematical Turing formulation and numerical simulations are introduced to show the pattern formation for such systems.
35B36Pattern formation in solutions of PDE
92C15Developmental biology, pattern formation
35K57Reaction-diffusion equations
35K55Nonlinear parabolic equations
35K51Second-order parabolic systems, initial bondary value problems
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