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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/717| MATHEMATICAL MODELING AND COMPUTATIONAL ANALYSIS OF ACUTE RESPIRATORY DISEASES | |
| YURY ELENA GARCIA PUERTA | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| MATEMÁTICAS APLICADAS Densidad espectral | |
| Respiratory infections represent a public health problem worldwide. They are responsible for a substantial morbidity and mortality, mainly affecting children under five years of age and people above 65 years old. Factors such as weather, pathogen diversity, vaccination programs, and virus fitness can affect the behavior of these infections at the population level. In temperate regions like San Luis Potosí México; the main viruses during the annual outbreak are influenza and Respiratory Syncytial Virus. We propose a stochastic multi-pathogen model to study the dynamic of these two viruses. Understanding the dynamics of these pathogens is important because nowadays there exists vaccine against influenza only. To carry out our analysis, we use two sets of data from the state of San Luis Potosí provided by Dr. Daniel Noyola. The first set corresponds to the medical consultation of people with symptoms of ARI; the second corresponds to laboratory samples taken randomly from children under five years of age to sample the virus circulating in the outbreak period. As a result of this research, we get three results. First, using a Bayesian hierarchical model and techniques of Bayesian analysis, we identify the dynamics of influenza and RSV in San Luis Potosí using the aggregate data and the laboratory samples. We also quantify the uncertainty in the parameters involved in the model. Second, we present a mathematical and computational analysis to determine the role of the effective vaccination, the cross-immunity/enhancement, and the fitness of the viruses in the early pathogen replacement in the annual outbreaks of influenza and RSV. We compute the power spectral density of the fluctuation in a two-pathogens model for both, with and without seasonality. We present different scenarios where the vaccine can, indirectly, affect the behavior of RSV. We also give conditions where influenza or RSV can be the first infection during the annual outbreak. Finally, we describe a Bayesian method to detect outbreaks using surveillance data. We argue that, during the early phase of the outbreak, surveillance data changes from autoregressive dynamics to a regime of exponential growth. Thus, we use Bayes factors to compare a linear and an exponential model to identify the breakpoint. The method detects the onset of an epidemic successfully with simulated and real data. | |
| 14-12-2017 | |
| Tesis de doctorado | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
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| TE 647.pdf | 9.72 MB | Adobe PDF | Visualizar/Abrir |