This thesis first investigates within-host HIV models for the acute stage. These models incorporate the immune responses and helper T cells produced from the activation of naive CD4 T cells. Because both naive CD4 T cells and helper T cells are susceptible classes, backward bifurcation and bistability may occur. We start with a simple model that ignores the CD8 T cell dynamics, then extend it to include this dynamics. We also extend our model to consider the latent infection of naive CD4 T cells. Backward bifurcation occurs in all these models. We numerically investigate the stability of viral equilibria, and show the bistability caused by backward bifurcation. Increasing the inflow of CTLs prevents the backward bifurcation. With a large homeostatic source of healthy naive CD4 T cells, the disease is easier to establish when the basic reproduction number is less than one. Reducing the reproduction number below one is not sufficient to control the infection of HIV. Secondly, this thesis investigates the development of AIDS caused by viral diversity, as proposed by Wodarz et al. using a model that does not include the details of immune responses. We extend their model to include density dependence, and show that the viral load increases with viral diversity. To study if this result still holds with more realistic HIV dynamics, we incorporate viral diversity into our first model. We conclude theoretically that the total viral load is positively correlated with the number of viral strains, and viral diversity can drive the development of AIDS. We also find that the total CD4 T cell count does not always decrease with viral diversity. Thus further investigation is needed to fully understand the development of AIDS. / Graduate

Le SDRPv est responsable de pertes économiques mondiales et son contrôle est un enjeu majeur pour la production porcine. La vaccination, principale mesure de contrôle, ne permet pas d'éradiquer l'infection et confère seulement une protection partielle de l'hôte. Ce manque d'efficacité est principalement due à grande variabilité de virulence des souches du SDRPv, induisant des dynamiques intra-hôte très variables. L'objectif de cette thèse est de mieux comprendre les interactions entre le virus et la réponse immunitaire, dans l'optique d'améliorer le contrôle de cette maladie. Pour cela, une approche de modélisation dynamique et déterministe a été choisie. Nous avons développé un modèle immunitaire original qui consiste en une représentation intégrative de la dynamique intra-hôte. Il décrit les mécanismes immunitaires à l'échelle inter-cellulaire, incluant la réponse innée, l'activation et l'orientation de la réponse adaptative, ainsi que leurs régulations complexes par les principales cytokines. Nos premiers résultats montrent que des durées d'infection similaires mais associées à des dynamiques immunitaires contrastées s'expliquent par la prise en compte des mécanismes immunitaires impactés par la virulence. Cela apporte de nouvelles pistes pour expliquer les incohérences apparentes entre résultats expérimentaux. Nous avons ensuite montré que l'exposition, dont l'effet est souvent négligé, a un impact sur la dynamique intra-hôte qui varie en fonction de la virulence. Finalement, nous avons exploré la dynamique intra-hôte induite par l'infection d'animaux vaccinés, ouvrant des pistes pour améliorer l'efficacité des vaccins. Cette thèse apporte également de nouvelles pistes pour guider les approches futures, aussi bien expérimentales que par modélisation, ainsi que des perspectives prometteuses pour le contrôle du SDRPv à l'échelle du troupeau. / PRRSv is responsible for significant worldwide production losses and its control is a major challenge for the swine industry. Vaccination, the main control measure, does not allow to eradicate the infection and only confers a partial protection to the host. This lack of efficiency is mainly due to the strong variability in PRRSv strain virulence, which induces highly variable within-host dynamics. This thesis aims at better understanding the interactions between the virus and the immune response in order to improve PRRSv control. To tackle this issue, a dynamic and deterministic modelling approach was chosen. We developed an original immunological model consisting in an integrative representation of the within-host dynamics. It describes the immune mechanisms at the between-cell scale, including the innate response, the activation and orientation of the adaptive response and their complex regulations by the major cytokines. Our first results show that similar infection durations associated with contrasted immune dynamics are explained by the consideration of the immune mechanisms affected by the strain virulence. They provide new insights to explain apparent inconsistencies between experimental data. We then showed that the exposure, whose effect is often neglected, has an impact on the within-host dynamics, which varies depending on the virulence level. Finally, the within-host dynamics induced by the infection of a vaccinated pig was explored, providing new insights to improve vaccine efficiency. This thesis also provides new insights to guide further experimental and modelling approaches and promising prospects for PRRSv control at the herd level.