Statistical Inference on a Stochastic Epidemic Model

Raúl Fierro, Víctor Leiva, N. Balakrishnan

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


In this work, we develop statistical inference for the parameters of a discrete-time stochastic SIR epidemic model. We use a Markov chain for describing the dynamic behavior of the epidemic. Specifically, we propose estimators for the contact and removal rates based on the maximum likelihood and martingale methods, and establish their asymptotic distributions. The obtained results are applied in the statistical analysis of the basic reproduction number, a quantity that is useful in establishing vaccination policies. In order to evaluate the population size for which the results are useful, a numerical study is carried out. Finally, a comparison of the maximum likelihood and martingale estimators is conducted by means of Monte Carlo simulations.

Original languageEnglish
Pages (from-to)2297-2314
Number of pages18
JournalCommunications in Statistics: Simulation and Computation
Issue number9
StatePublished - 21 Oct 2015
Externally publishedYes


  • Asymptotic normality
  • Chi-squared test
  • Markov chains
  • Martingale estimators
  • Maximum likelihood estimators
  • SIR epidemic model


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