Epidemic Propagation: An Automaton Model as the Continuous SIR Model

Affiliation(s)

Mathematics Department, School of Science and Technology, University of Camerino, Camerino, Italy.

Mathematics Department, School of Science and Technology, University of Camerino, Camerino, Italy.

ABSTRACT

The use of the SIR model to predict the time evolution of an epidemic is very frequent and has spatial information about its propagation which may be very useful to contrast its spread. In this paper we take a particular cellular automaton model that well reproduces the time evolution of the disease given by the SIR model; setting the automaton is generally an annoying problem because we need to run a lot of simulations, compare them to the solution of the SIR model and, finally, decide the parameters to use. In order to make this procedure easier, we will show a fast method that, in input, requires the parameters of the SIR continuous model that we want to reproduce, whereas, in output, it yields the parameters to use in the cellular automaton model. The problem of computing the most suitable parameters for the reticular model is reduced to the problem of finding the roots of a polynomial Equation.

Cite this paper

L. Misici and F. Santarelli, "Epidemic Propagation: An Automaton Model as the Continuous SIR Model,"*Applied Mathematics*, Vol. 4 No. 10, 2013, pp. 84-89. doi: 10.4236/am.2013.410A3011.

L. Misici and F. Santarelli, "Epidemic Propagation: An Automaton Model as the Continuous SIR Model,"

References

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http://dx.doi.org/10.1098/rspa.1927.0118

[2] C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin and W. M. Liu, “Epidemiological Models with Age Structure, Proportionate Mixing, and Cross-Immunity,” Journal of Mathematical Biology, Vol. 27, No. 3, 1989, pp. 233-258. http://dx.doi.org/10.1007/BF00275810

[3] V. Capasso, “Mathematical Structures of Epidemic Systems,” Lecture Notes in Biomathematics, Vol. 97, 1993.

http://dx.doi.org/10.1007/978-3-540-70514-7

[4] I. Nasell, “Stochastic Models of Some Endemic Infections,” Mathematical Biosciences, Vol. 179, No. 1, 2002, pp. 1-19.

http://dx.doi.org/10.1016/S0025-5564(02)00098-6

[5] N. T. J. Bailey, “The Simulation of Stochastic Epidemics in Two Dimensions,” Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, Vol. 4, 1967, pp. 237-257.

[6] S. Chang, “Cellular Automata Model for Epidemics,” 2008.

http://csc.ucdavis.edu/~chaos/courses/nlp/Projects2008/SharonChang/Report.pdf

[1] W. O. Kermack and A. G. McKendrick, “A Contribution to the Mathematical Theory of Epidemics,” Proceedings of the Royal Society of London A, Vol. 115, No. 772, 1927, pp. 700-721.

http://dx.doi.org/10.1098/rspa.1927.0118

[2] C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin and W. M. Liu, “Epidemiological Models with Age Structure, Proportionate Mixing, and Cross-Immunity,” Journal of Mathematical Biology, Vol. 27, No. 3, 1989, pp. 233-258. http://dx.doi.org/10.1007/BF00275810

[3] V. Capasso, “Mathematical Structures of Epidemic Systems,” Lecture Notes in Biomathematics, Vol. 97, 1993.

http://dx.doi.org/10.1007/978-3-540-70514-7

[4] I. Nasell, “Stochastic Models of Some Endemic Infections,” Mathematical Biosciences, Vol. 179, No. 1, 2002, pp. 1-19.

http://dx.doi.org/10.1016/S0025-5564(02)00098-6

[5] N. T. J. Bailey, “The Simulation of Stochastic Epidemics in Two Dimensions,” Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, Vol. 4, 1967, pp. 237-257.

[6] S. Chang, “Cellular Automata Model for Epidemics,” 2008.

http://csc.ucdavis.edu/~chaos/courses/nlp/Projects2008/SharonChang/Report.pdf