Dinámica del control biológico basado en un modelo de cadena alimenticia con tres niveles tróficos

En esta tesis se estudia la dinámica del control biológico mediante un modelo matemático de cadena alimenticia simple de tres niveles tróficos. Este modelo matemático esta basado en un modelo depredador presa con respuesta funcional Holling tipo II razón dependiente, incluyendo un depredador superior para obtener un sistema de tres ecuaciones diferenciales ordinarias. Para el cual se estudia la existencia y unicidad, invarianza y acotación de las soluciones. La dinámica del control biológico es estudiada de forma local y asintótica, analizando las condiciones para la coexistencia de las tres especies así como también los escenarios de extinción total y parcial del sistema, de donde vemos cuando tiene o no tiene éxito el control biológico. Los resultados obtenidos fueron contrastados con sus respectivas simulaciones realizadas en un programa desarrollado en la tesis el cual aproxima las soluciones utilizando el método de Runge - Kutta de cuarto orden. PALABRAS CLAVE: DEPREDADOR - PRESA, CADENA ALIMENTICIA, CONTROL BIOLÓGICO, ESCENARIOS DE EXTINCIÓN, ESTABILIDAD ASINTÓTICA, RUNGE-KUTTA.--- In this work, the dynamic of biological control is studied using a mathematical model of simple food chain of three trophic levels. This mathematical model is based on a predator prey model with holling type II functional response rate dependent. including a top predator described by a system of three ordinary differential equations. We study the existence and uniqueness, invariance and boundednees of solutions.Tesi

Análisis y simulación de un modelo matemático glucosa-insulina en personas con diabetes tipo I

Publicación a texto completo no autorizada por el autorEstudia el modelo matemático para la interacción glucosa - insulina desarrollado originalmente por Bergman con la información tomada de la historia clínica de personas con diabetes tipo I, para luego extender el modelo considerando la ingesta de alimentos y el tratamiento de la diabetes. Las perturbaciones producidas por la ingesta de alimentos y el tratamiento de la diabetes son actividades cuasi periódicas es decir se repiten con una frecuencia casi regular, la cual nos sugiere utilizar la ecuación del oscilador armónico amortiguado. Se presentan simulaciones computacionales en Matlab de los modelos construido que verifican los resultados obtenidos.Tesi

Modelo Huésped-Vector: Análisis de estabilidad y simulaciones

In epidemiological mathematics, the SIR model is well known, as well as the diseases that can be simulated with this model. In the present work starting from a SIR model with vital dynamics, a host-vector model is elaborated, where the transmission of the disease is no longer given by interaction of individuals of the same species, but is carried out by interaction of the susceptible individuals with the infected individuals, of both populations. Two host-vector models (MVH) with vital dynamics are also developed, initially maintaining the population constant, then with variable population and death due to disease

Modelo Huésped-Vector: Análisis de estabilidad y simulaciones

In epidemiological mathematics, the SIR model is well known, as well as the diseases that can be simulated with this model. In the present work starting from a SIR model with vital dynamics, a host-vector model is elaborated, where the transmission of the disease is no longer given by interaction of individuals of the same species, but is carried out by interaction of the susceptible individuals with the infected individuals, of both populations. Two host-vector models (MVH) with vital dynamics are also developed, initially maintaining the population constant, then with variable population and death due to disease.En la matemática epidemiológica, el modelo Suceptible - Infectado - Recuperado (SIR) es bastante conocido, así mismo las enfermedades que se pueden simular con dicho modelo. En el presente trabajo, partiendo de un modelo (SIR) con dinámica vital, se elabora un modelo huésped - vector, donde la transmisión de la enfermedad ya no se da por interacción de individuos de una misma especie, sino es realizada por interacción de los individuos susceptibles con los individuos infectados, de ambas poblaciones. También se desarrollan dos modelos huésped - vector (MVH) con dinámica vital, inicialmente manteniendo la población constante, después con población variable y muerte por enfermedad

A mathematical model of the transmission dynamics of tuberculosis with exogenous reinfection in the infection-free state

In the present work, a perturbation of the model presented by Feng, Castillo-Chávez and Capurro (2000) will be carried out, where the dynamics of tuberculosis transmission will be described, where recovery from the disease will be incorporated. The model will include four epidemiological populations: Susceptible (S), Exposed (E), Infected (I) and Infected with treatment (T). This will allow to know how the interaction that exists with the infected can cause the permanence of the individuals with the disease. For which, its qualitative behavior will be analyzed as its evolution in time of the epidemiological populations for the model by the ordinary differential equations (ODE) and its perturbation to the dalay differential equations (DDE). In this way, it will allow us to know how the parameters influence the spread of the disease at the point free of infection and with a computational extension to evaluate an endemic situation.Campus Lima Nort

Computational modeling of HIV-TB coinfection by cellular automata (CELL-DEVS)

In the present study, the computational modeling that describes the evolution and propagation of people susceptible to HIV-AIDS infection as well as Tuberculosis will be carried out. This additionally generates a coinfection in those infected that further complicates the epidemiological situation. Therefore, the presence of sanitary-epidemiological support personnel is important to consolidate prevention and control strategies. This epidemiological phenomenon could be modeled by differential equations, but we will focus on modeling by cellular automata to obtain computational simulations in time-space, and obtain possible scenarios and opt for the appropriate scenario to implement the most effective epidemiological strategies to obtain the results. better results and preserve the quality of life of society.Revisión por pare

Análisis y simulación de un modelo matemático SEIR extendido con vacunación para la propagación del SARS-COV-2

This article analyzes the dynamic of an extended SEIR model for the spread of COVID-19 considering a system of 7 differential equations whose stages are susceptible, exposed, infected, quarantined, recovered, dead and vaccinated. The necessary and sufficient conditions are determined for non-negativity, delimitation, existence and uniqueness of the solution of the model, local stability of the equilibrium points and the next generation matrix method. The simulations made in Python complement the qualitative analysis of the mathematical model to conclude the behavior of the virus spread over time; the information shown in this work could also be useful for the development of new prevention measures.En el presente artículo se analiza la dinámica de un modelo SEIR extendido para la propagación del COVID-19 considerando un sistema de 7 ecuaciones diferenciales cuyas etapas son susceptibles, expuestos, infectados, en cuarentena, recuperados, muertos y vacunados. Se determinan las condiciones necesarias y suficientes para la no negatividad, acotación, existencia y unicidad de la solución del modelo, estabilidad local de los puntos de equilibrio y el método de la matriz de próxima generación. Las simulaciones hechas en Python complementan el análisis cualitativo del modelo matemático para concluir el comportamiento de la propagación del virus en el tiempo; la información que nos brinda este trabajo también podría ser útil para la elaboración de nuevas medidas de prevención

Modelo Huésped-Vector: Análisis de estabilidad y simulaciones

In epidemiological mathematics, the SIR model is well known, as well as the diseases that can be simulated with this model. In the present work starting from a SIR model with vital dynamics, a host-vector model is elaborated, where the transmission of the disease is no longer given by interaction of individuals of the same species, but is carried out by interaction of the susceptible individuals with the infected individuals, of both populations. Two host-vector models (MVH) with vital dynamics are also developed, initially maintaining the population constant, then with variable population and death due to disease.En la matemática epidemiológica, el modelo Suceptible - Infectado - Recuperado (SIR) es bastante conocido, así mismo las enfermedades que se pueden simular con dicho modelo. En el presente trabajo, partiendo de un modelo (SIR) con dinámica vital, se elabora un modelo huésped - vector, donde la transmisión de la enfermedad ya no se da por interacción de individuos de una misma especie, sino es realizada por interacción de los individuos susceptibles con los individuos infectados, de ambas poblaciones. También se desarrollan dos modelos huésped - vector (MVH) con dinámica vital, inicialmente manteniendo la población constante, después con población variable y muerte por enfermedad

A Mathematical Model of the Transmission Dynamics of Tuberculosis with Exogenous Reinfection in the Infection-Free State

In the present work, a perturbation of the model presented by Feng, Castillo-Chávez and Capurro (2000) will be carried out, where the dynamics of tuberculosis transmission will be described, where recovery from the disease will be incorporated. The model will include four epidemiological populations: Susceptible (S), Exposed (E), Infected (I) and Infected with treatment (T). This will allow to know how the interaction that exists with the infected can cause the permanence of the individuals with the disease. For which, its qualitative behavior will be analyzed as its evolution in time of the epidemiological populations for the model by the ordinary differential equations (ODE) and its perturbation to the dalay differential equations (DDE). In this way, it will allow us to know how the parameters influence the spread of the disease at the point free of infection and with a computational extension to evaluate an endemic situation

Computational modeling of HIV-TB coinfection by cellular automata (CELL-DEVS)

In the present study, the computational modeling that describes the evolution and propagation of people susceptible to HIV-AIDS infection as well as Tuberculosis will be carried out. This additionally generates a coinfection in those infected that further complicates the epidemiological situation. Therefore, the presence of sanitary-epidemiological support personnel is important to consolidate prevention and control strategies. This epidemiological phenomenon could be modeled by differential equations, but we will focus on modeling by cellular automata to obtain computational simulations in time-space, and obtain possible scenarios and opt for the appropriate scenario to implement the most effective epidemiological strategies to obtain the results. better results and preserve the quality of life of society