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.


35B36 Pattern formations in context of PDEs
92C15 Developmental biology, pattern formation
35K57 Reaction-diffusion equations
35K55 Nonlinear parabolic equations
92D30 Epidemiology
35K51 Initial-boundary value problems for second-order parabolic systems
Full Text: DOI


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