Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 5: Statistical physics in biological systems (joint session DY/BP)
DY 5.7: Vortrag
Montag, 25. Februar 2008, 16:00–16:15, MA 001
Continuous description of a contact diffusion spread: complete separation of variables and the approximate analytical solution — •Eugene Postnikov1, Uta Naether2, and Igor Sokolov2 — 1Lehrstuhl für Theoretische Physik, Staatliche Universität Kursk, Russland — 2Institut für Physik, Humboldt - Universität zu Berlin, Deutschland
Despite of a century of thorough work, the problem of mathematical description of spread of an epidemic is still an actual question. In the present contribution we present the analytical considerations on the PDE system describing an SIR epidemic spread reproducing the realistic asymmetric Kendall waves of infection as well as to verify the analytical solution by stochastic simulations. The model system as comprises three kinds of individuals (or cells with the perfect mixing of individuals inside) which are the susceptible (S), the infected (I), and the removed (R) ones. The probability for a cell to be infected can only change in case the cell is susceptible and depends on the number of its infected nearest-neighbors.
We show that the corresponding system of PDEs allows for a complete separation of variables. Moreover the solutions for I and R are given in a closed form if the solution for S is known. The autonomous equation for S admits the approximate analytical solutions for a wide range of parameters including the regions of a strong non-linearity.
The results of our analytical treatment are compared with direct Monte-Carlo simulations as well as with real epidemiological data on the epidemic among the harbor seals in Wadden Sea and Baltic Sea.