Stochastic Epidemic Models
Abstract
Mathematical modeling is a very useful tool to understand,
in a simple way, some real problems from reality that are of our
interest. In the case of the diseases transmission, mathematical
epidemiology has allowed us to understand the mechanics of
propagation among the population. Deterministic models such
as SI, SIS, SIR, SEIR, have been widely studied, and are the
basis for more complex models, which include, for example,
some vaccination policy. Another alternative is stochastic modeling.
In this paper we present two stochastic models, based
on Markov chains. Both models are the stochastic version of
the classic SIS. The first is a discrete time model, while the second
is a continuous time model. From each of them we present
simulations, and overlapping with the simulation performed for
the deterministic model.
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References
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