Abstract
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.
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Appendix A: Supporting Information
Appendix A: Supporting Information
1.1 Figures
Estimate of S(t) and I(t), SIR model by the C-N algorithm
Estimate of R(t), SIR model by the C-N algorithm, and S(t) SIR model, Gibbs algorithm
Estimate of I(t) and R(t), SIR model, Gibbs Algorithm.
Estimate of S(t) and E(t), model (7), Euler’s method
Estimate of I(t) and A(t), model (7), Euler’s method
Estimate of Sq and Eq, model (7), Euler’s method
Estimate of H(t) and A(t), model (7), Euler’s method
Estimate of S(t) and E(t), model (14), Gibbs algorithm
Estimate of I(t) and A(t), model (14), Gibbs algorithm
Estimate of \(S_{q}(t)\) and \(E_{q}(t)\), model (14), Gibbs algorithm
Estimate of H(t) and R(t), model (14), Gibbs algorithm
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Luis, S., Saba, I. (2022). Epidemic Models and Estimation of the Spread of SARS-CoV-2: Case Study Portoviejo-Ecuador. In: Narváez, F.R., Proaño, J., Morillo, P., Vallejo, D., González Montoya, D., Díaz, G.M. (eds) Smart Technologies, Systems and Applications. SmartTech-IC 2021. Communications in Computer and Information Science, vol 1532. Springer, Cham. https://doi.org/10.1007/978-3-030-99170-8_29
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DOI: https://doi.org/10.1007/978-3-030-99170-8_29
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