An application of homogenization techniques to population dynamics models
B. E. Ainseba W. E. Fitzgibbon M. Langlais J. J. Morgan
Communications on Pure & Applied Analysis 2002, 1(1): 19-33 doi: 10.3934/cpaa.2002.1.19
We are interested in partial differential equations and systems of partial differential equations arising in some population dynamics models, for populations living in heterogeneous spatial domains. Discontinuities appear in the coefficients of divergence form operators and in reaction terms as well. Global posedness results are given. For models offering a great a degree of heterogeneity we derive simpler models with constant coefficients by applying homogenization method. Long term behavior is then analyzed.
keywords: predator-prey. Spatial heterogeneities homogenized model cat retrovirus and persistence reaction advection diffusion equations
Diffusive epidemic models with spatial and age dependent heterogeneity
W. E. Fitzgibbon M.E. Parrott Glenn Webb
Discrete & Continuous Dynamical Systems - A 1995, 1(1): 35-57 doi: 10.3934/dcds.1995.1.35
An epidemic model is analyzed which allows for the spatial spread of individuals within a geographical region and the incubation of the disease within infected individuals. The spatial spread of the disease is modelled by diffusion processes. The incubation period of infectives is modelled by infection-age structure. Results are established which provide qualitative prediction of the development of the epidemic in terms of spatially dependent and age dependent parameters.
keywords: semilinear parabolic systems. diffusion processes disease within infected individuals infection-age structure
A reaction-diffusion system modeling direct and indirect transmission of diseases
W. E. Fitzgibbon M. Langlais J.J. Morgan
Discrete & Continuous Dynamical Systems - B 2004, 4(4): 893-910 doi: 10.3934/dcdsb.2004.4.893
We study the global existence and approximation of the solutions to a reaction diffusion system coupled with an ordinary differential equation modeling direct transmission between individuals and indirect transmission via a contaminated environment of an epidemic disease.
keywords: Reaction diffusion equations global existence.

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