Avian influenza strains have been proven to be highly virulent in human populations, killing approximately 70 percent of infected individuals. Although the virus is able to spread across species from birds-to-humans, some strains, such as H5N1, have not been observed to spread from human-to-human. Pigs are capable of infection by both avian and human strains and seem to be likely candidates as intermediate hosts for co-infection of the inter-species strains. A co-infected pig potentially acts as a mixing vessel and could produce a new strain as a result of a recombination process. Humans could be immunologically naive to these new strains, hence making them super-strains. We propose an interacting host system (IHS) for such a process that considers three host species that interact by sharing strains; that is, a primary and secondary host species can both infect an intermediate host. When an intermediate host is co-infected with the strains from both the other hosts, co-infected individuals may become carriers of a super-strain back into the primary host population. The model is formulated as a classical susceptible-infectious-susceptible (SIS) model, where the primary and intermediate host species have a super-infection and co-infection with recombination structure, respectively. The intermediate host is coupled to the other host species at compartments of given infectious subclasses of the primary and secondary hosts. We use the model to give a new perspective for the trade-off hypothesis for disease virulence, by analyzing the behavior of a highly virulent super-strain. We give permanence conditions for a number of the subsystems of the IHS in terms of basic reproductive numbers of independent strains. We also simulate several relevant scenarios showing complicated dynamics and connections with epidemic forecasting.

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The present work is divided in two parts. The first is concerned with the dynamics on the Grassmann manifold of k-dimensional subvector spaces of an n dimensional real or complex vector space induced by a linear invertible transformation A of the vector space into itself. The Grassmann map GA sends p to Ap, and one asks, what are the dynamics of GA? In the second part, I consider dynamics induced by a linear cocycle covering a diffeomorphism of a compact manifold, acting on the Grassmann bundle of k-dimensional linear subspaces of TN. I prove a Kupka-Smale theorem for the space of cocycles covering diffeomorphisms of a compact manifold. The proof of this theorem implies the same type of results for derived cocycles parametrized in the space of diffeomorphisms. The results of the second part can be generalized without effort to cocycles covering endomorphisms of N.

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Output regulation problems are a class of problems that has high importance in systems control engineering. The solutions of such problems generally involve the design of an internal model based controller with error feedback structure that can also provide stability to the closed-loop system. Most of previous studies of such problems, however, are based on dynamical systems described by di erential equations for continuous-time and by di erence equations for discrete-time on the space of Rn. Few results have been obtained for dynamical systems with more abstract descriptions on sets with more general topologies. In this thesis, we use a set-theoretic approach with commutative diagrams to describe a dynamical system and its properties. Output regulation problems will also be de ned based on such dynamical systems. We will present su cient conditions for output regulation problems on complete metric spaces and Banach spaces.

Output regulation problems are a class of problems that has high importance in systems control engineering. The solutions of such problems generally involve the design of an internal model based controller with error feedback structure that can also provide stability to the closed-loop system. Most of previous studies of such problems, however, are based on dynamical systems described by di erential equations for continuous-time and by di erence equations for discrete-time on the space of Rn. Few results have been obtained for dynamical systems with more abstract descriptions on sets with more general topologies. In this thesis, we use a set-theoretic approach with commutative diagrams to describe a dynamical system and its properties. Output regulation problems will also be de ned based on such dynamical systems. We will present su cient conditions for output regulation problems on complete metric spaces and Banach spaces.

No description available.

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No description available.