| The main objective of this dissertation is to study mathematical models of immunological and epidemiological aspects of influenza infection.; This dissertation is divided into two main parts. The first part investigates the mechanisms involved in the clearance of the infection by the influenza virus at the epithelium level by analyzing the interaction of the influenza virus-specific cytotoxic T Lymphocytes (CTL) and the epithelial cells. In fact, the understanding of this interaction would provide us with interesting tools for the evaluation of the potential protective cell-mediated immunity. By presenting different scenarios of the interaction of CTL-cells and epithelial cells, we construct ordinary and delay differential models of CTL response to influenza infection. Our ultimate goal is to use these models to provide insight into the pathology and possible treatment of this disease.; The aim of the second part is to explore, via ordinary and delay differential compartmental models, the impact of treatment by antiviral agents with partially effective drugs on the transmission dynamics of the influenza. By considering SEIRS models where E is a compartment that represents the exposed population that has contact with the infected one and which is under treatment, this study tries to answer the question of as to whether such a drug could ever reduce the virulence of infection in case of the delay or the absence of vaccination and determine the minimal antiviral treatment rate required to eradicate the infection in the population. |
