Nonlinear Differential Equations,
Electron. J. Diff. Eqns., Conf. 05, 2000, pp.121--133.

Bifurcation of reaction-diffusion systems related to epidemics

Anthony W. Leung & Beatriz R. Villa

The article considers the reaction-diffusion equations modeling the infection of several interacting kinds of species by many types of bacteria. When the infected species compete significantly among themselves, it is shown by bifurcation method that the infected species will coexist with bacterial populations. The time stability of the postitive steady-states are also considered by semigroup method. If the infected species do not interact, it is shown that positive coexistence states with bacterial populations are still possible.

Published October 25, 2000.
Math Subject Classifications: 35B32, 35J60, 35K57, 92D30.
Key Words: Reaction-diffusions; Elliptic systems; Parabolic systems; Bifurcations; Epidemiology; Asymptotic stability.

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Anthony W. Leung
Department of Mathematical Sciences
University of Cincinnati
Cincinnati OH 45221-0025, USA
Beatriz R. Villa
Department of Mathematics
Universidad Nacional de Colombia
Bogota, Colombia

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