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Convergence of a Continuous-Time Epidemic Model

Hakim El Boustani, Abdellah Ould khal

Abstract



This paper proposes a model for the spread of an epidemic in an unconstrained population. It is a naturalextension of the discrete-time model given by Pierre Loti Viaud. The extended model is more general than the previous probabilistic models of epidemics. It allows for the evolution of the population size, and the simple stochastic epidemic can be obtained as a particular case. We drive conditions in order to establish a law of large numbers and a central limit theorem for such a model.

Keywords


Epidemic models, Markov process, strong convergence.

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