TITLE:
Epidemic Propagation: An Automaton Model as the Continuous SIR Model
AUTHORS:
Luciano Misici, Filippo Santarelli
KEYWORDS:
Cellular Automaton; SIR Model; Epidemic Spread
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.10C,
October
23,
2013
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.