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Open AccessArticle

Evolution Model for Epidemic Diseases Based on the Kaplan-Meier Curve Determination

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Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain
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Universitat de València, Doctor Moliner, 10, 46100 Burjassot (València), Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(8), 1260; https://doi.org/10.3390/math8081260
Received: 27 June 2020 / Revised: 24 July 2020 / Accepted: 27 July 2020 / Published: 1 August 2020
(This article belongs to the Section Mathematics and Computer Science)
We show a simple model of the dynamics of a viral process based, on the determination of the Kaplan-Meier curve P of the virus. Together with the function of the newly infected individuals I, this model allows us to predict the evolution of the resulting epidemic process in terms of the number E of the death patients plus individuals who have overcome the disease. Our model has as a starting point the representation of E as the convolution of I and P. It allows introducing information about latent patients—patients who have already been cured but are still potentially infectious, and re-infected individuals. We also provide three methods for the estimation of P using real data, all of them based on the minimization of the quadratic error: the exact solution using the associated Lagrangian function and Karush-Kuhn-Tucker conditions, a Monte Carlo computational scheme acting on the total set of local minima, and a genetic algorithm for the approximation of the global minima. Although the calculation of the exact solutions of all the linear systems provided by the use of the Lagrangian naturally gives the best optimization result, the huge number of such systems that appear when the time variable increases makes it necessary to use numerical methods. We have chosen the genetic algorithms. Indeed, we show that the results obtained in this way provide good solutions for the model. View Full-Text
Keywords: Kaplan-Meier; survival; quadratic; optimization; epidemic; model Kaplan-Meier; survival; quadratic; optimization; epidemic; model
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Calabuig, J.M.; García-Raffi, L.M.; García-Valiente, A.; Sánchez-Pérez, E.A. Evolution Model for Epidemic Diseases Based on the Kaplan-Meier Curve Determination. Mathematics 2020, 8, 1260.

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