Resumo

REYES-ROMERO, A.; FERNANDEZ, J. E.  e  REYES, J. Adrian. Stochastic dynamics for epidemics based on a compartmental scheme: An application to the AH1N1 influenza. Rev. mex. fis. [online]. 2020, vol.66, n.6, pp.863-873.  Epub 31-Jan-2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.66.863.

In this paper a stochastic formulation for describing the dynamics of an epidemic is established. We state our model in the language of a compartmental scheme of three population groups susceptible, infected, and removed, for which the model parameters are extended to be statistical distributions of time. A master equation is established for the dynamics of the probability density P of finding the system in the state characterized by the values of the aleatory variables susceptible, infected, removed, and time t. Our stochastic formalism allows us to recover the associated deterministic model in terms of the expected values of susceptible, infected, and removed; whereas the second momenta of P provides us with statistical standard deviations for these three variables which delimit the region in which most of the particular realizations are to be expected. We have applied the analysis developed here, for studying the specific case of the influenza AH1N1 that took place in Mexico in 2009. The reported data by the main Mexican Health institution are in good agreement with the predictions of our model for the standard deviation of the aleatory variables.

Palavras-chave : Master equation; epidemics; IMSS; AH1N1 influenza virus; SIR model; stochastic modelling.

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