Bayesian computational methods for state-space models with application to SIR model

The state-space model is a powerful statistical tool to estimate linear or non-linear discrete-time dynamic systems. This model naturally leads to the estimation problem of the time-varying parameters of the discovery-time demographic version of the susceptible-infected-recovered (SIR) model that we consider. In this paper, we consider computational methods to perform Bayesian inference on state-space models for analysing time-series data. We compare the three popular Bayesian computational methods for state-space models: the adaptive Metropolis-within-Gibbs algorithm, Liu and West's algorithm and variational approximation method based on Gaussian distributions. The performances of the three methods are compared based on synthetic datasets. Furthermore, we analyse the trend of the spread of COVID-19 in South Korea to point out the limitations of existing methods and derive meaningful results. [ FROM AUTHOR] Copyright of Journal of Statistical Computation & Simulation is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Epidemic Models and Estimation of the Spread of SARS-CoV-2: Case Study Portoviejo-Ecuador

The mathematical models can help to characterize, quantify, summarize, and determine the severity of the outbreak of the Coronavirus, the estimation of the dynamics of the pandemic helps to identify the type of measures and interventions that can be taken to minimize the impact by classified information. In this work, we propose four epidemiological models to study the spread of SARS-CoV-2. Specifically, two versions of the SIR model (Susceptible, Infectious, and Recovered) are considered, the classical Crank-Nicolson method is used with a stochastic version of the Beta-Dirichlet state-space models. Subsequently, the SEIR model (Susceptible, Exposed, Infectious, and Recovered) is fitted, the Euler method and a stochastic version of the Beta-Dirichlet state-space model are used. In the results of this study (Portoviejo-Ecuador), the SIR model with the Beta-Dirichlet state-space form determines the maximum point of infection in less time than the SIR model with the Crank-Nicolson method. Furthermore, the maximum point of infection is shown by the SEIR model, that is reached during the first two weeks where the virus begins to spread, more efficient is shown by this model. To measure the quality of the estimation of the algorithms, we use three measures of goodness of fit. The estimated errors are negligible for the analyzed data. Finally, the evolution of the spread is predicted, that can be helpful to prevent the capacity of the country’s health system. © 2022, Springer Nature Switzerland AG.