For citation:
Melnikova E. V. Nonlinear dynamics of an epidemic spreading. Izvestiya VUZ. Applied Nonlinear Dynamics, 1998, vol. 6, iss. 2, pp. 110-116.
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Russian
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Article
UDC:
616.036.22.001.573
Nonlinear dynamics of an epidemic spreading
Autors:
Melnikova Ekaterina Vladislavna, Saratov State University
Abstract:
А spatiotemporal model of an epidemic spreading in the human society is introduced. It is based on a reaction-diffusion equation with local and nonlocal modes of growth. The system behavior on the phase surface and limitation of the wave velocity are analysed. The immunization and density of population as the function of spatial coordinate are taken into account.
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Acknowledgments:
In conclusion, I would like to thank my supervisors D.I. Trubetskov and A.A. Koronovsky.
Reference:
- Неdе В. Epidemic model with immunization. J. Phys. А.: Math. Gen. 1989;22(10):L439-L443. DOI: 10.1088/0305-4470/22/10/004.
- Razzhevaikin VN, Svirezhev YuM. Diffusion models in epidemiology. In: "Mathematical Modelling in Immunology and Medicine" Proc. of the IFIP international Conference. 5-11 July 1982, Moscow, USSR. Amsterdam: North Holland Press; 1983. P. 387-394.
- Svirezhev YuM. Nonlinear Waves, Dissipative Structures and Catastrophes in Ecology. М.:Nauka; 1987. 366 p.
- Koronovskii AA, Trubetskov DI. Nonlinear Dynamics in Action: How Ideas of Nonlinear Dynamics Penetrate the Environment, Economics and Social Sciences. Saratov: College; 1995. 129 p. (in Russian).
- Koronovskii AA. About one model of epidemic spread. Izvestiya VUZ. Applied Nonlinear Dynamics. 1996;4(1):40-48. (in Russian).
- Grimson MJ, Barker GС. Continuum model for the spatiotemporal grouth оf bacterial colonies. Phys. Rev. E. 1994;49(2):1680-1684. DOI: 10.1103/PhysRevE.49.1680.
- Baizhanova KS. Questions of studying the speed of epidemic waves. In: Modeling of Environmental Development Processes. Vol. 8. М.: USIISI Publishing; 1984. P. 48-55.
Received:
27.11.1997
Accepted:
29.05.1998
Published:
08.07.1998
Journal issue:
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