Rozan, Eric A. (2022) Formulación de modelos epidemiológicos avanzados / Formulation of advanced epidemiological models. Maestría en Ciencias Físicas, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En esta tesis se desarrollaron modelos epidemiológicos matemáticos de campo medio en poblaciones heterogéneas. A diferencia de los modelos compartimentales tradicionales, en los que se considera una población homogénea y que todos los individuos están mezclados, en estos modelos se usan conceptos elementales de la teoría de redes complejas para incluir la estructura social de la población, condensada en la distribución de grado de los individuos. De esta forma, el modelo cuenta con las ventajas analíticas de los modelos de campo medio, e incorpora la capacidad de tener en cuenta los patrones de contactos en una sociedad. El modelo admite tratar con redes arbitrarias (mientras se cumplan ciertas propiedades), y en este trabajo se analizaron dos casos: redes regulares, en las que todos los individuos tienen la misma cantidad de contactos, y redes libres de escala, en la que la distribución de grado sigue una ley de potencia. Tras caracterizar el modelo exhaustivamente en cada caso por separado, se implementaron medidas de aislamiento que consisten en cambiar la distribución de grado de manera tal que esté más concentrada sobre grados menores. Se observó cómo se modifican los principales observables epidemiológicos ante distintas estrategias de aislamiento. Se encontró que no hay una única estrategia que sea más efectiva que el resto con la que se mejoren todos los observables analizados. En particular, se encontró que si el aislamiento es demasiado restrictivo durante una primera ola de contagios, entonces si no se repite el aislamiento se da lugar a una segunda ola más severa que la primera, y si se repite puede que el número acumulado de individuos que se infectaron crezca.
Resumen en inglés
In this work we developed mean-field mathematical epidemiology models for heterogeneous populations. As opposed to traditional compartmental models, in which the population is considered to be homogeneous and its individuals to be completely mixed, basic concepts from complex networks theory are used in these models in order to take into account the social structure of the population, reflected in their degree distribution. Thus, the model has the analytical advantages of mean-fields models, and it also gains the capability to consider the social contact patterns of the population. The model works with arbitrary networks (as long as they have certain properties), and in this work two cases were analyzed: regular networks in which all individuals have the same amount of contacts, and scale-free networks that have a power law degree distribution. We characterized each case separately in detail, and after that we modeled preventive isolation measures that consist in changing the degree distribution so that it is more concentrated over lower degrees. We observed the dependency of some key epidemiological observable quantities on the different containment strategies. We found that there is no one strategy that is more effective than the rest in improving all of the analyzed observables at once. In particular, we found that when the isolation measure is too restrictive during the first wave of infections, then if the measure is not repeated the second wave can be worse than the first one, and on the other hand if it is repeated then the final total number of infected individuals can increase.
| Tipo de objeto: | Tesis (Maestría en Ciencias Físicas) |
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| Palabras Clave: | Epidemiology; Epidemiología; Mathematical models; Modelos matemáticos; Dynamical systems; Sistemas dinámicos; Statistical mechanics; Mecánica estadísticas; [Epidemiological dynamics; Dinámica epidemiológica; Complex networks; Redes complejas; Interdiscisciplinary physics; Física interdisciplinaria] |
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| Materias: | Física > Sistemas complejos |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Sistemas complejos y altas energías > Física estadística interdisciplinaria |
| Código ID: | 1164 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 04 Aug 2023 11:47 |
| Última Modificación: | 04 Aug 2023 11:47 |
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