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.

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 ...

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.

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 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...

Estudia 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.

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 trabajo se hace una evaluación de las técnicas de aprendizaje automáticos: Arboles de decisión, Bosques aleatorios, Redes Neuronales y Máquinas de soporte vectorial para predecir el rendimiento académico de alumnos. Encontramos que el algoritmo de bosques aleatorios presenta una mayor precisión en la predicción del rendimiento académico. Esta investigación es relevante en las instituciones educativas, especialmente para la definición de políticas de seguimiento y apoyo a los alumnos principalmente en riesgo académico. Adicionalmente se hace una estimación del potencial de la aplicación de estos algoritmos de aprendizaje automático en las diferentes carreras de la facultad de Ciencias Empresariales y Económicas de la Universidad de Lima.

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 ...