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An age-dependent epidemic model with spatial diffusion. (English) Zbl 0484.92018

MSC:
92D25 Population dynamics (general)
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[1] Capasso, V., Global solution for a diffusive nonlinear deterministic epidemic model. SIAM J. Appl. Math. 35, 274–294 (1978) · Zbl 0415.92018
[2] Capasso, V., & D. Fortunato, Asymptotic behaviour for a class of non-autonomous semilinear evolution systems and application to a deterministic epidemic model, to appear. · Zbl 0447.35046
[3] Conway, E., Hoff, D., & J. Smoller, Large time behavior of solutions of systems of nonlinear reaction-diffusion equations. SIAM J. Appl. Math. 35, 1–16 (1978). · Zbl 0383.35035
[4] Di Blasio, G., & L. Lamberti, An initial-boundary value problem for age-dependent population diffusion. SIAM J. Appl. Math. 35, 593–615 (1978). · Zbl 0394.92019
[5] Elderkin, R., Summary analysis of an age-dependent, nonlinear model of seed dispersal, to appear. · Zbl 0483.92017
[6] Gurtin, M., & R. MacCamy, Non-linear age-dependent population dynamics. Arch. Rational Mech. Anal. 54, 281–300 (1974). · Zbl 0286.92005
[7] Gurtin, M., & R. MacCamy, On the diffusion of biological populations. Math. Biosciences 38, 35–49 (1977). · Zbl 0362.92007
[8] Gurtin, M., & R. MacCamy, Population dynamics with age dependence, Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. III. London: Pitman 1979 (to appear in Math. Biosciences).
[9] Hoppensteadt, F., Mathematical theories of populations: demographics, genetics, and epidemics, SIAM Regional Conference Series in Applied Mathematics, Philadelphia, 1975. · Zbl 0304.92012
[10] JornĂ©, J., & S. Carmi, Lyapunov stability of the diffusive Lotka-Volterra equations. Math. Biosciences 37, 51–61 (1977). · Zbl 0376.92014
[11] Kahane, C., On a system of nonlinear parabolic equations arising in chemical engineering. J. Math. Anal. Appl. 53, 343–358 (1976). · Zbl 0326.35044
[12] Leung, A., Limiting behavior for a prey-predator model with diffusion and crowding effects. J. Math. Biology 6, 87–93 (1978). · Zbl 0386.92011
[13] MacCamy, R., A population model with nonlinear diffusion, to appear. · Zbl 0458.92012
[14] Marcati, P., & M. Pozio, Global asymptotic stability for a vector disease model with spatial spread, to appear. · Zbl 0419.92013
[15] Martin, R., Nonlinear operators and differential equations in Banach space. New York: Wiley-Interscience 1976.
[16] Mimura, M., & J. Murray, On a diffusive prey-predator model which exhibits patchiness. J. Theor. Biol. 75, 249–262 (1978).
[17] de Mottoni, P., Orlandi, E., & A. Tesei, Asymptotic behavior for a system describing epidemics with migration and spatial spread of infection. Nonl. Anal. Theory, Methods, and Appl. 3, 663–675 (1979). · Zbl 0416.35009
[18] Murray, J., Lectures on nonlinear-differential-equation models in biology. Oxford: Claredon Press, 1977. · Zbl 0379.92001
[19] Pozio, M., Behaviour of solutions of some abstract functional differential equations and application to predator-prey dynamics, to appear. · Zbl 0444.34063
[20] Waltman, P., Deterministic threshold models in the theory of epidemics. Berlin Heidelberg New York: Springer 1974. · Zbl 0293.92015
[21] Webb, G., A reaction-diffusion model for a deterministic diffusive epidemic, to appear. · Zbl 0484.92019
[22] Webb, G., A deterministic diffusive epidemic model with an incubation period, to appear in the Proceedings of the Functional Differential Equations and Integral Equations Conference at the University of West Virginia, 1979. · Zbl 0479.92017
[23] Williams, S., & P.-L. Chow, Nonlinear reaction-diffusion models for interacting populations. J. Math. Anal. Appl. 62, 157–169 (1978). · Zbl 0372.35047
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