Evolutionary Dynamics on Complex Networks

Many complex systems such as the Internet can be represented as networks, with vertices denoting the constituent components of the systems and edges denoting the patterns of interactions among the components. In this thesis, we are interested in how the structural properties of a network, such as its average degree, degree distribution, clustering, and homophily affect the processes that take place on it. In the first part of the thesis we focus on evolutionary game theory models for studying the evolution of cooperation in a population of predominantly selfish individuals. In the second part we turn our attention to an evolutionary model of disease dynamics and the impact of vaccination on the spread of infection. Throughout the thesis we use a network as an abstraction for a population, with vertices representing individuals in the population and edges specifying who can interact with whom. We analyze our models for a well-mixed population, i.e., an infinite population with random mixing, and compare the theoretical results with those obtained from computer simulations on model and empirical networks