Papers by Jesús López-Estrada
Mathematics, 2022
There are a great many epidemiological models that have been implemented to describe COVID-19 dat... more There are a great many epidemiological models that have been implemented to describe COVID-19 data; however, few attempted to reproduce the entire phenomenon due to the complexity of modeling recurrent outbreaks. In this work a fractional growth model with delay is developed that implements the Caputo fractional derivative with 00.9995 in all cases. Lastly, as a result of the implementation of the delay effect, the global phenomenon was decomposed into its local parts, allowing for directly comparing each outbreak and its different characteristics.
RESUMEN El polémico problema de la selección de variables ha dado lugar a diferentes procedimient... more RESUMEN El polémico problema de la selección de variables ha dado lugar a diferentes procedimientos que tratan de buscar la ecuación de regresión que mejor ajusta los datos con el menor número de parámetros. En este trabajo se presenta un nuevo procedimiento que utiliza la descomposición RRQR con pivoteo restringido combinada con un criterio empírico de selección de modelos como es el Cp de Mallows. Dos aplicaciones ilustran las ventajas de este procedimiento. MSc: 62G05 ABSTRACT The polemical problem of variable selection has originated different procedures when seeking for the regression equation that best fits the data with minimun number of parameters. In this paper a new procedure for variable selection is proposed, which combines the restricted RRQR algorithm with the statistical criterium of Mallows for model selection. Two applications illustrate the advantages of this procedure. 1. INTRODUCCION El problema de la selección de variables en la regresión lineal continúa siendo ...
Mathematical Medicine and Biology, 2006
Mathematical models for the population dynamics of de novo resistant Mycobacterium tuberculosis w... more Mathematical models for the population dynamics of de novo resistant Mycobacterium tuberculosis within individuals are studied. The models address the use of one or two antimicrobial drugs for treating latent tuberculosis (TB). They consider the effect of varying individual immune response strength on the dynamics for the appearance of resistant bacteria. From the analysis of the models, equilibria and local stabilities are determined. For assessing temporal dynamics and global stability for sensitive and drug-resistant bacteria, numerical simulations are used. Results indicate that for a low bacteria load that is characteristic of latent TB and for small reduction in an immune response, the use of a single drug is capable of curing the infection before the appearance of drug resistance. However, for severe immune deficiency, the use of two drugs will provide a larger time period before the emergence of resistance. Therefore, in this case, two-drugs treatment will be more efficient in controlling the infection.
INTERMATHS Revista de Matemática Aplicada e Interdisciplinar, Jun 30, 2021
A new methodology is introduced to measure school performance based on a mathematical model of Or... more A new methodology is introduced to measure school performance based on a mathematical model of Ordinary Differential Equations (ODEs). Three indexes are proposed that describe long-term school performance. The ODEs model is applied to students of a generation of basic-level, the values of the model's parameters are estimated using the numerical scores of the considered students obtained at the time of their training. This describes the dynamics of long-term school performance, which allows to give a measure of the impact of some educational policy.
Computational and Mathematical Methods in Medicine, 2011
The mathematical model for the dynamics of the hepatitis C proposed in Avendaño et al. (2002), wi... more The mathematical model for the dynamics of the hepatitis C proposed in Avendaño et al. (2002), with four populations (healthy and unhealthy hepatocytes, the viral load of the hepatitis C virus, and T killer cells), is revised. Showing that the reduced model obtained by considering only the first three of these populations, known as basic model, has two possible equilibrium states: the uninfected one where viruses are not present in the individual, and the endemic one where viruses and infected cells are present. A threshold parameter (the basic reproductive virus number) is introduced, and in terms of it, the global stability of both two possible equilibrium states is established. Other central result consists in showing, by model numerical simulations, the feasibility of monitoring liver damage caused by HCV, avoiding unnecessary biopsies and the undesirable related inconveniences/imponderables to the patient; another result gives a mathematical modelling basis to recently develope...
Se revisa el modelo para la dinamica de la hepatitis C propuesto en Avendano et al. (2002), pero ... more Se revisa el modelo para la dinamica de la hepatitis C propuesto en Avendano et al. (2002), pero considerando solamente tres poblaciones: hepatocitos sanos y enfermos, y carga viral. Introduciendo transformaciones adecuadas resulta un modelo adimensionalizado, el cual tiene dos posibles estados de equilibrio: el estzado del individuo sano y el estado del enfermo endemico. Se introduce ademas un parametro umbral que se usa para determinar la existencia y estabilidad del estado de equilibrio endemico, y se establece la estabilidad global del estado de equilibrio del individuo sano. Por otro lado, se presenta un estudio experimental que muestra que es posible realizar el monitoreo del dano hepatico sin biopsias, mediante la estimacion numerica de los parametros del modelo adimensionalizado, considerando solamente mediciones de la carga viral y una valoracion razonable del dano hepatico pretratamiento.
Ingeniería y Ciencia, 2006
Se compara el modelo estandar reducido de tres poblaciones (hepatocitos sanos y enfermos, y carga... more Se compara el modelo estandar reducido de tres poblaciones (hepatocitos sanos y enfermos, y carga viral) para el estudio de la dinamica del virus de la hepatitis C (VHC), con el modelo de la dinamica viral con alanina aminotransferasa (ALT). En terminos del parametro umbral que es el mismo para ambos modelos, se determina la existencia y estabilidad del estado de equilibrio endemico, asi como la estabilidad global del estado de equilibrio del individuo sano. Por otro lado, se presenta un estudio experimental que muestra que es posible monitorear el dano hepatico sin biopsias, mediante la estimacion numerica de los parametros de los modelos, considerando solamente mediciones de la carga viral, de los niveles de ALT y una valoracion razonable del dano hepatico pretratamiento.
A norm minimization problem posed in K-dimensional finite arrays without non-negativity constrain... more A norm minimization problem posed in K-dimensional finite arrays without non-negativity constraints was efficiently solved by Romero Romero [11]. Going beyond we provide here an explicit, exact solution in case the arrays are replaced by L2-Hilbert spaces. Furthermore, we propose a polynomial procedure yielding an approximate optimal solution when non-negativity constraints must be taken into account for K = 2.
Se revisa el modelo para la dinamica del VIH/SIDA propuesto por Perelson y Nelson (1999), pero c... more Se revisa el modelo para la dinamica del VIH/SIDA propuesto por Perelson y Nelson (1999), pero considerando solamente tres poblaciones. El cual tiene dos posibles esta dos de equilibrio: el estado del individuo sano y el estado del enfermo endemico. Se introduce ademas un parametro umbral R 0 que se usa para determinar la existencia y la estabilidad asintotica global de los estados de equilibrio. Esto es, se describe completamente la dinamica de la enfermedad en base al valor del parametro umbral R 0 . Lo que dice que si R 0 ≤ 1 para cierto individuo, sin importar el nivel de la carga viral de infeccion V 0 > 0, el individuo eventualmente se cura.
Mathematical & Computational Applications, 2020
The present work proposes a new model to capture high heterogeneity of single phase flow in natur... more The present work proposes a new model to capture high heterogeneity of single phase flow in naturally fractured vuggy reservoirs. The model considers a three porous media reservoir; namely, fractured system, vugular system and matrix; the case of an infinite reservoir is considered in a full-penetrating wellbore. Furthermore, the model relaxes classic hypotheses considering that matrix permeability has a significant impact on the pressure deficit from the wellbore, reaching the triple permeability and triple porosity model wich allows the wellbore to be fed by all the porous media and not exclusively by the fractured system; where it is considered a pseudostable interporous flow. In addition, it is considered the anomalous flow phenomenon from the pressure of each independent porous medium and as a whole, through the temporal fractional derivative of Caputo type; the resulting phenomenon is studied for orders in the fractional derivatives in (0, 2), known as superdiffusive and subdi...
Scientific Reports
To propose a new test to evaluate the autonomic nervous system in patients with syncope: Multimod... more To propose a new test to evaluate the autonomic nervous system in patients with syncope: Multimodal Monitoring for Diagnosis of Dysautonomia (MMDD). We included 21 patients with syncope (16 female, 6 male, mean age 43.5 years) and 21 with no-syncope subjects (15 female, 7 male, mean age 45.1 years) to perform a test of nine 2-min stages: four while resting and four during active testing of autonomic response. Transcranial-Doppler, electrocardiogram, and photoplethysmography blood pressure pulse-to-pulse monitoring, allow registering six variables from the Middle Cerebral Artery and four from the Cardiovascular System. We analyze each variable's mean differences in each stage and its change when they pass from one stage to another with the T and Z tests. To understand the significance of the change, we use a logistic regression model for a certain subgroup of variables. Since we have a small dataset, we use the bootstrap technique to infer the general behavior that characterizes ...
ABSTRACT It is shown that the problem of finding the Moore-Penrose generalized inverse matrix is ... more ABSTRACT It is shown that the problem of finding the Moore-Penrose generalized inverse matrix is an ill-posed problem in Hadamard’s sense; this is a particularly interesting point because it is a finite dimensional problem. A first study to its stable approximate calculation by Tikhonov’s regularization method is presented. A new criterion is introduced, the appropriate choice principle. It is proved, by this criterion, that the problem in question is well-behaved in F. John’s sense.
It is shown that the problem of finding the Moore-Penrose generalized inverse matrix is an ill-po... more It is shown that the problem of finding the Moore-Penrose generalized inverse matrix is an ill-posed problem in Hadamard’s sense; this is a particularly interesting point because it is a finite dimensional problem. A first study to its stable approximate calculation by Tikhonov’s regularization method is presented. A new criterion is introduced, the appropriate choice principle. It is proved, by this criterion, that the problem in question is well-behaved in F. John’s sense.
Basic concepts and statements of the method of minimal pseudoinverse matrix developed by A. S. Le... more Basic concepts and statements of the method of minimal pseudoinverse matrix developed by A. S. Leonov [Zh. Vychisl. Mat. Mat. Fiz. 27, No. 8, 1123-1138 (1987; Zbl 0663.65037)] are considered. We prove that the minimal pseudoinverse matrix is a numerical ε-pseudoinverse and a comparative analysis with the method based on the singular value decomposition is presented. We also present a computational implementation coded using the MATLAB language for the minimal method and we discuss the results of the numerical experimentation, too.
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Papers by Jesús López-Estrada