Papers by Patricio Cumsille
arXiv (Cornell University), Dec 28, 2020
The COVID-19 disease has forced countries to make a considerable collaborative effort between sci... more The COVID-19 disease has forced countries to make a considerable collaborative effort between scientists and governments to provide indicators to suitable follow-up the pandemic's consequences. Mathematical modeling plays a crucial role in quantifying indicators describing diverse aspects of the pandemic. Consequently, this work aims to develop a clear, efficient, and reproducible methodology for parameter optimization, whose implementation is illustrated using data from three representative regions from Chile and a suitable generalized SIR model together with a fitted positivity rate. Our results reproduce the general trend of the infected's curve, distinguishing the reported and real cases. Finally, our methodology is robust, and it allows us to forecast a second outbreak of COVID-19 and the infection fatality rate of COVID-19 qualitatively according to the reported dead cases. Highlights • We developed a clear, efficient, and reproducible methodology for parameter optimization to calibrate real data. • We also provided a suitable generalized SIR model, including a fitted positivity rate. • Our methodology reproduces the general trend of the infected' curve for both the reported and the real cases. • It can also forecast different scenarios of the spreading and the infection fatality rate of COVID-19 qualitatively.
Frontiers in Public Health
BackgroundOne of the main lessons of the COVID-19 pandemic is that we must prepare to face anothe... more BackgroundOne of the main lessons of the COVID-19 pandemic is that we must prepare to face another pandemic like it. Consequently, this article aims to develop a general framework consisting of epidemiological modeling and a practical identifiability approach to assess combined vaccination and non-pharmaceutical intervention (NPI) strategies for the dynamics of any transmissible disease.Materials and methodsEpidemiological modeling of the present work relies on delay differential equations describing time variation and transitions between suitable compartments. The practical identifiability approach relies on parameter optimization, a parametric bootstrap technique, and data processing. We implemented a careful parameter optimization algorithm by searching for suitable initialization according to each processed dataset. In addition, we implemented a parametric bootstrap technique to accurately predict the ICU curve trend in the medium term and assess vaccination.ResultsWe show the f...
International Journal of Educational and Pedagogical Sciences, Aug 3, 2021
We analyze a first-class on the convergence of real number sequences, named hereafter sequences, ... more We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of Mathematical Working Spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.
Mathematics and Computers in Simulation, 2021
The COVID-19 disease has forced countries to make a considerable collaborative effort between sci... more The COVID-19 disease has forced countries to make a considerable collaborative effort between scientists and governments to provide indicators to suitable follow-up the pandemic's consequences. Mathematical modeling plays a crucial role in quantifying indicators describing diverse aspects of the pandemic. Consequently, this work aims to develop a clear, efficient, and reproducible methodology for parameter optimization, whose implementation is illustrated using data from three representative regions from Chile and a suitable generalized SIR model together with a fitted positivity rate. Our results reproduce the general trend of the infected's curve, distinguishing the reported and real cases. Finally, our methodology is robust, and it allows us to forecast a second outbreak of COVID-19 and the infection fatality rate of COVID-19 qualitatively according to the reported dead cases. Highlights • We developed a clear, efficient, and reproducible methodology for parameter optimization to calibrate real data. • We also provided a suitable generalized SIR model, including a fitted positivity rate. • Our methodology reproduces the general trend of the infected' curve for both the reported and the real cases. • It can also forecast different scenarios of the spreading and the infection fatality rate of COVID-19 qualitatively.
Considerando la importancia del cáncer en Chile y en el mundo, es necesario planear estrategias p... more Considerando la importancia del cáncer en Chile y en el mundo, es necesario planear estrategias para estudiar y controlar esta enfermedad. Sin embargo, es difícil tener un pronóstico y tratamiento precisos del cáncer, debido a la complejidad del crecimiento de tumores y a la respuesta altamente variable de paciente en paciente. Por esta razón, es necesaria la identificación de biomarcadores del cáncer y su simulación numérica en un modelo apropiado para este sistema biológico. El objetivo del presente trabajo es proponer un nuevo modelo matemático multiescala, lo suficientemente estable con respecto a los valores de los parámetros, y lo suficientemente robusto para predecir el crecimiento de tumores acoplado con angiogénesis tumoral y con el uso de terapias antineoplásicas. A partir de trabajos anteriores del tema se obtienen las hipótesis esenciales que describen la evolución de la enfermedad y con esto se propone un sistema de ecuaciones en derivadas parciales que incorpora las nociones de quimiotaxis de manera de describir la competencia entre el déficit de nutrientes y la aparición de nuevos vasos sanguíneos. Los efectos de una terapia mixta son también uno de los ejes centrales de la modelación, lo cual se hace basado en protocolos aprobados por la U.S. Food and Drug Administration. Desde el punto de vista de la calibración del modelo se puede establecer que dos de tres estimadores se ajustan a la literatura actual (tiempo de explosión de la neoplasia y distribución de capas celulares), mientras que las diferencias en el tercero de ellos (total de células en la neoplasia) se puede justificar por la inclusión de las densidades de células que forman los vasos sanguíneos en el balance de masas. Respecto a los resultados se establece que efectivamente el tratamiento retrasa la vascularización de la enfermedad, pero, que los efectos de químicos antiproliferación no se ajustan a la realidad dejando un margen de mejora de las ecuaciones. Se deja explícito que mediante la experimentación real con cantidades celulares el modelo puede ser contrastado y evaluado de mejor manera, sin embargo, los resultados permiten decir que se va por un camino correcto para entender desde un prisma matemático la enfermedad
Diagnostic and Interventional Imaging, 2013
Modelamiento matemático de crecimiento de tumores, acoplado con angiogénesis tumoral y su uso en ... more Modelamiento matemático de crecimiento de tumores, acoplado con angiogénesis tumoral y su uso en la investigación de nuevas estrategias de tratamiento del cáncer
matematicas.uclm.es
comunicación se propone un nuevo modelo para la formación de una biopelícula y se estudian los as... more comunicación se propone un nuevo modelo para la formación de una biopelícula y se estudian los aspectos numéricos de su simulación computacional. Nuestro modelo está basado en tres aspectos fundamentales: primero, se incorpora un mecanismo de transporte de nutrientes hacia la biopelícula; segundo, se incorpora un mecanismo de consumo y de crecimiento de la biopelícula; y tercero, se incorpora un mecanismo de necrosis y de decaimiento de la biopelícula. Para el modelamiento del transporte de
Comptes Rendus Mathematique, 2008
[5]H. Heck, G. Uhlmann and J.-N. Wang, Reconstruction of obstacles immersed in an incompressible ... more [5]H. Heck, G. Uhlmann and J.-N. Wang, Reconstruction of obstacles immersed in an incompressible fluid, Inverse Probl. Imaging 1 (1) (2007), pp. 6376. ... [6]P. Henrici, Applied and Computational Complex Analysis, Volume 1: Power SeriesIntegrationConformal MappingLocation ...
Computers & Mathematics with Applications, 2014
International Journal of Modern Physics A, 2016
The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a n... more The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais–Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.
Revista Integracion, 2010
Revista Integracion, 2010
Springer Proceedings in Physics, 2015
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Papers by Patricio Cumsille