Publication: Modelos matemáticos de propagación de enfermedades
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2018-06
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Abstract
En este trabajo se puede encontrar una aplicación directa de las matemáticas, más exactamente una aplicación de los sistemas de ecuaciones diferenciales o de variaciones. Se les dará el uso de modelar el proceso y evolución de una determinada enfermedad contagiosa según ciertas variables y parámetros de entrada. Para el desarrollo supondremos una población inicial (personas, bacterias, virus…) dividida en varios subgrupos (los consideraremos como variables del sistema), pudiendo cada miembro pasar de un subgrupo a otro según ciertas hipótesis propias de cada modelo. Se hará una simulación utilizando el tiempo como parámetro de derivación con el objetivo de medir la cantidad de población de cada subgrupo y su comportamiento temporal. Utilizaremos R (librería deSolve) para realizar la simulación de diversos modelos: SI, SIS, variantes del SIS, SIR, variantes del SIR, SIRS, variantes del SIRS, SEIR y SEIRS donde cada sigla identifica a un subgrupo (S: susceptibles, I: infectados, R: recuperados, E: individuos incubando la enfermedad).
This projects aims to give a direct application of mathematics, more exactly the application of systems of differential equations or variations. The systems will model the process and evolution of a certain contagious disease according to certain variables and input parameters. For the project development we will assume an initial population (people, bacteria, viruses...) divided into several subgroups (we will consider them as system variables) where each member can move from one subgroup to another according to certain hypotheses of each model. A simulation will be made using time as a derivation parameter in order to measure the amount of population of each subgroup and its temporal behaviour. We will use R (Solvent library) to perform the simulation of several models: SI, SIS, SIS variants, SIR, SIR variants, SIRS, SIRS, SEIR and SEIRS variants where each acronym identifies a subgroup (S: susceptible, I: infected, R: recovered, E: individuals incubating the disease).
This projects aims to give a direct application of mathematics, more exactly the application of systems of differential equations or variations. The systems will model the process and evolution of a certain contagious disease according to certain variables and input parameters. For the project development we will assume an initial population (people, bacteria, viruses...) divided into several subgroups (we will consider them as system variables) where each member can move from one subgroup to another according to certain hypotheses of each model. A simulation will be made using time as a derivation parameter in order to measure the amount of population of each subgroup and its temporal behaviour. We will use R (Solvent library) to perform the simulation of several models: SI, SIS, SIS variants, SIR, SIR variants, SIRS, SIRS, SEIR and SEIRS variants where each acronym identifies a subgroup (S: susceptible, I: infected, R: recovered, E: individuals incubating the disease).
Description
UCM subjects
Matemáticas (Matemáticas), Análisis matemático, Medicina
Unesco subjects
12 Matemáticas, 1202 Análisis y Análisis Funcional, 32 Ciencias Médicas
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Citation
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