Paul A. Valle

Tijuana Institute of Technology | ITT · Postgraduate in Engineering Sciences Program

This paper is devoted to exploring personalized applications of cellular immunotherapy as a control strategy for the treatment of chronic myelogenous leukemia described by a dynamical system of three first-order ordinary differential equations. The latter was achieved by applying both the Localization of Compact Invariant Sets and Lyapunov’s stabil...

In this paper, we explore the application of Chimeric Antigen Receptor (CAR) T cell therapy for the treatment of Acute Lymphocytic Leukaemia (ALL) by means of in silico experimentation, mathematical modelling through first-order Ordinary Differential Equations and nonlinear systems theory. By combining the latter with systems biology on cancer evol...

Cancer with all its more than 200 variants continues to be a major health problem around the world with nearly 10 million deaths recorded in 2020, and leukemia accounted for more than 300,000 cases according to the Global Cancer Observatory. Although new treatment strategies are currently being developed in several ongoing clinical trials, the high...

This paper presents results concerning mechanistic modeling to describe the dynamics and interactions between biomass growth, glucose consumption and ethanol production in batch culture fermentation by Kluyveromyces marxianus (K. marxianus). The mathematical model was formulated based on the biological assumptions underlying each variable and is gi...

This paper deals with a recently reported mathematical model formulated by five first-order ordinary differential equations that describe glucoregulatory dynamics. As main contributions, we found a localization domain with all compact invariant sets; we settled on sufficient conditions for the existence of a bounded positively-invariant domain. We...

The authors wish to make the following corrections to this paper [...]

Predictive models may be considered a tool to ensure food quality as they provide insights that support decision making on the design of processes, such as fermentation. Objective: To formulate a mathematical model that describes the growth of lactic acid bacteria (LAB) in batch fermentation. Methodology: Based on real-life experimental data from e...

This work aims to analyze a fifth-order nonlinear ordinary differential equations that describe the glucoregulatory model system based on intravenous injection of glucose via in-vivo experimentation in rats reported previously in the literature. A mathematical analysis shows that existence of an invariant plane condition associated with insulin can...

This work is devoted to construct a mathematical model of first-order ordinary differential equations that may allow us to estimate the number of people infected by SARS-Cov-2 in Tijuana, Baja California, México. Our model is formulated by considering the widely known SIR compartmental model and the infection and mortality rates provided by Mexico'...

Gastric cancer is a leading cause of cancer death worldwide. Most of these malignant tumors are intestinal-type gastric adenocarcinomas linked to chronic bacterial infection by the Helicobacter Pylori (H. Pylori). Long-term survival for advanced gastric cancer is low, and tumor recurrences are common after a gastrectomy. There is a significant inte...

El cáncer gástrico se ha posicionado como una de las principales causas de muerte a nivel mundial. La mayoría de estos tumores son adenocarcinomas desarrollados en los epitelios del estómago y originados por una infección en la mucosa vinculada con la bacteria H. Pylori. La efectividad de los tratamientos tradicionales es limitada, por ello se busc...

El cáncer es una enfermedad genética que se caracteriza por un proceso gradual y progresivo de modificaciones a nivel del genoma de las células, provocando la proliferación de sus clones mutados que perturban el equilibrio del funcionamiento del tejido afectado. En México, esta enfermedad se posiciona como la tercera causa de mortalidad a nivel nac...

We synthesized polymer nanocomposites (PNCs) based on nanostructures of flower-like hierarchical rutile-phase TiO2 nanorod microspheres that were grow on oxide graphene sheets (GO). The synthesis parameters were modified to obtain desired morphologies (flower-like and cauliflower). The two PNC of TiO2/GO were charac- terized by scanning and transmi...

In this article, we aim to apply mathematical modelling by means of eight first-order ordinary differential equations to investigate the response of prostate cancer and the immune system to an allogenic whole-cell cancer vaccine and metronomic chemotherapy. Research to formulate our mathematical model was based on the clinical study developed by Kr...

El mercurio (Hg) es uno de los contaminantes más tóxicos, se ha convertido en una amenaza seria para la salud humana y el ambiente. Su exposición, produce efectos tóxicos graves en seres vivos, afectando los sistemas: nervioso, digestivo e inmunitario, y otras partes del organismo. El impacto ambiental es significativo y requiere la atención de tod...

This research paper studies a type 1 Diabetes Mellitus (DM1) model in which the dynamics of insulin, glucose and beta cells variables in a non-linear system given by ordinary differential equations are described. In order to estimate glucose and insulin from beta cells, a reduced order observer is designed, using Lyapunov's theory of stability and...

This paper is focused on the study of the global dynamics of a chaotic-cancer system. This mathematical model describes the dynamics of cancer cells and its interaction with healthy cells and effector-immune cells, the system considers the influx of effector cells by adding an immunotherapy treatment parameter. By applying the Localization of Compa...

In this paper, we present research focused on the development of algorithms to generate time-series based on a pseudo-random algorithm, to avoiding determinism on the time-series. The 0-1 test for chaos algorithm was used to evaluate the determinism properties of the synthetic signals. Signals from nature were analyzed to compare their behavior wit...

Mathematical models may allow us to improve our knowledge on tumor evolution and to better comprehend the dynamics between cancer, the immune system and the application of treatments such as chemotherapy and immunotherapy in both short and long term. In this paper, we solve the tumor clearance problem for a six-dimensional mathematical model that d...

The complexity of cancer has motivated the development of different approaches to understand the dynamics of this large group of diseases. One that may allow us to better comprehend the behavior of cancer cells, in both short- and long-term, is mathematical modelling through ordinary differential equations. Several ODE mathematical models concernin...

En este trabajo se muestra una metodología para calcular de manera analítica los límites superiores de un modelo matemático de ecuaciones diferenciales ordinarias que describen la interacción entre células cancerosas, células sanas y células efectoras. Lo anterior se realiza mediante integración por separación de variables, el método de Localizació...

It can be expected that adequate immune response should be able to annihilate cancer at a very early stage of its appearance. However, in some cases cancer is able to persist avoiding immune response. One can conject that cancer is able to avoid immune response control due to a succession of mutations leading to the development of immune-resistant...

This book features 15 chapters based on the Numerical and Evolutionary Optimization (NEO 2017) workshop, held from September 27 to 29 in the city of Tijuana, Mexico. The event gathered researchers from two complimentary fields to discuss the theory, development and application of state-of-the-art techniques to address search and optimization proble...

En este documento se estudia la dinámica global de un Sistema de Quimioterapia presentado por de Pillis et al. en 2007. Este modelo matemático describe la interacción entre células cancerosas, células inmuno-efectoras, linfocitos circundantes y el tratamiento de quimioterapia. Mediante la aplicación del método de Localización de Conjuntos Compactos...

En este artículo se estudia la dinámica global de tres modelos que presentan el efecto de latencia tumoral los cuales fueron desarrollados por K.M. Page y J.W. Uhr en 2005. La diferencia entre el primer y segundo modelo se encuentra en la generación de anticuerpos, que se efectúa como consecuencia de su interacción con las células cancerosas y por...

In this paper we study the global dynamics for a Tumor Immune-Evasion model proposed by Arciero, Jackson and Kirschner [1], which describes the interaction between effector cells, cancer cells, and the cytokines IL -2 and TGF - β in the tumor site. This system describes different behaviors such as equilibrium points, periodic orbits, and stable lim...