Statistical Inference on a Stochastic Epidemic Model |
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Authors: | Raúl Fierro Víctor Leiva N Balakrishnan |
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Institution: | 1. Instituto de Matemática, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile;2. Instituto de Estadística, Universidad de Valparaíso, Valparaíso, Chile;3. Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibá?ez, Vi?a del Mar, Chile;4. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada |
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Abstract: | 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. |
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Keywords: | Asymptotic normality Chi-squared test Markov chains Martingale estimators Maximum likelihood estimators SIR epidemic model |
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