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Diffusion epidemic models with incubation and crisscross dynamics. (English) Zbl 0836.92018
Summary: A diffusion age-structured epidemic model is analyzed. The model describes an epidemic in a host-vector two-population system. Each population is diffusing in a spatial region. Each population is divided into susceptible, incubating, and infectious subclasses. The incubating and infectious subclasses in each population are determined by a structure variable corresponding to age since infection. The model consists of a system of nonlinear partial differential equations with crisscross dynamics. The existence, uniqueness, and asymptotic behavior of solutions are analyzed.

MSC:
92D30Epidemiology
35Q80Applications of PDE in areas other than physics (MSC2000)
35B40Asymptotic behavior of solutions of PDE
35K99Parabolic equations and systems
65M25Method of characteristics (IVP of PDE, numerical methods)
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