Mathematical Modeling, Analysis and Control of Some Infectious Diseases
type: CreativeWork
description: Mathematical models are useful in epidemiological research to describe, explain or predict the development and spread of infectious diseases. In addition they play a critical role in disease control, indicating intervention strategies concerning public health such as vaccinations, isolation, treatments and so on. The underlying theme of this Ph.D. thesis is the mathematical modeling and analysis of some aspects concerning infectious diseases, in the absence and presence of infection. In fact, the control of a possible epidemic can be carried out both by investigating aspects external to the infection, such as vaccination (as was done in chapter 1) or alternative prevention methods, such as controlling the life cycle of carriers of the virus (as presented in chapter 4) and by analyzing and studying models that describe the dynamics of the infection itself (as we will see in chapters 2 and 3). Chapter 1 models epidemiological aspects when the disease is not present in the population. Indeed it focuses mainly on the decision of individuals to be vaccinated or not, in the absence of infection and based on information they receive from the outside on the state of the disease and on the side effects of the vaccine. This information is modeled through the introduction of a spatial kernel that weighs the distance from which the information comes. The proposed new model is based on the theory of the "Imitation Game", in which the exchanges of opinions and contacts between individuals are taken into consideration. The model is parabolic, since the Fickian diffusion is assumed to be valid. In chapters 2 and 3, we investigate on the spread of two infectious diseases, which differ from each other via different transmission vehicles of the virus. In particular, chapter 2 deals with a new model for the transmission of cholera, a water-borne disease that involves host-environment interaction. The model extends works featured in the published literature on the subject, including the…
abstract: Mathematical models are useful in epidemiological research to describe, explain or predict the development and spread of infectious diseases. In addition they play a critical role in disease control, indicating intervention strategies concerning public health such as vaccinations, isolation, treatments and so on. The underlying theme of this Ph.D. thesis is the mathematical modeling and analysis of some aspects concerning infectious diseases, in the absence and presence of infection. In fact, the control of a possible epidemic can be carried out both by investigating aspects external to the infection, such as vaccination (as was done in chapter 1) or alternative prevention methods, such as controlling the life cycle of carriers of the virus (as presented in chapter 4) and by analyzing and studying models that describe the dynamics of the infection itself (as we will see in chapters 2 and 3). Chapter 1 models epidemiological aspects when the disease is not present in the population. Indeed it focuses mainly on the decision of individuals to be vaccinated or not, in the absence of infection and based on information they receive from the outside on the state of the disease and on the side effects of the vaccine. This information is modeled through the introduction of a spatial kernel that weighs the distance from which the information comes. The proposed new model is based on the theory of the "Imitation Game", in which the exchanges of opinions and contacts between individuals are taken into consideration. The model is parabolic, since the Fickian diffusion is assumed to be valid. In chapters 2 and 3, we investigate on the spread of two infectious diseases, which differ from each other via different transmission vehicles of the virus. In particular, chapter 2 deals with a new model for the transmission of cholera, a water-borne disease that involves host-environment interaction. The model extends works featured in the published literature on the subject, including the…
author: LUPICA, ANTONELLA
language: ita
keywords: Mathematical Modeling, Epidemiology, Infectious diseases, Vaccination, Water-borne disease, Vector-borne disease, Slow and fast diffusion process, Stability analysis , Traveling wave solutions, Basic reproductive number
date published: 2020-03-17
date modified: 2026-07-24T01:35:01Z
provider: Università degli Studi di Catania
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Università degli studi di Catania

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property ID: Handle
value: https://hdl.handle.net/20.500.11769/581974