A cellular automata model of epidemics of a heterogeneous susceptibility |
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Authors: | Jin Zhen and Liu Quan-Xing |
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Institution: | School of Science, North University of China, Taiyuan 030051,China |
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Abstract: | In this paper we present a model
with spatial heterogeneity based on cellular automata (CA). In the
model we consider the relevant heterogeneity of host (susceptible)
mixing and the natural birth rate. We divide the susceptible
population into three groups according to the immunity of each
individual based on the classical susceptible--infected--removed
(SIR) epidemic models, and consider the spread of an infectious
disease transmitted by direct contact among humans and vectors
that have not an incubation period to become infectious. We test
the local stability and instability of the disease-free
equilibrium by the spectrum radii of Jacobian. The simulation
shows that the structure of the nearest neighbour size of the cell
(or the degree of the scale-free networks) plays a very important
role in the spread properties of infectious disease. The positive
equilibrium of the infections versus the neighbour size follows
the third power law if an endemic equilibrium point exists.
Finally, we analyse the feature of the infection waves for the
homogeneity and heterogeneous cases respectively. |
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Keywords: | cellular automata epidemic
spreading SIR model spatial heterogeneity model evolution |
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