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Analysis of a spatially extended nonlinear SEIS epidemic model with distinct incidence for exposed and infectives. (English) Zbl 1145.35390

Summary: We present a nonlinear SEIS epidemic model which incorporates distinct incidence rates for the exposed and the infected populations. The model is analyzed for stability and bifurcation behavior. To account for the realistic phenomenon of non-homogeneous mixing, the effect of diffusion on different population subclasses is considered. The diffusive model is analyzed using matrix stability theory and conditions for Turing bifurcation derived. Numerical simulations are performed to justify analytical findings.

MSC:

35K50 Systems of parabolic equations, boundary value problems (MSC2000)
34D20 Stability of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
92D30 Epidemiology
35B32 Bifurcations in context of PDEs
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