Dynamic social networks with beneficial and detrimental interactions

The complex social relationships in society can be understood as a network. In recent years, complex networks have given researchers a more accurate picture of social interactions than aggregation models such as compartmental models had hitherto provided. Compartmental models which collect individuals into population classes based on infection state, for instance, had left out local interactions that could be important for understanding social relationships and attendant phenomena such as epidemics, rumors, etc., in the society. Topics of modeling for complex networks have included the dynamics of social relationships and how they affect disease and opinion spread. Different types of relationships, such as friendly or unfriendly, have been considered. In this dissertation we study social network models in which interactions can be beneficial or detrimental to the parties involved. Motivated by HIV, in which a person\u27s infection status is not readily known to others, we implement a model where individual decisions may affect the disease transmission. Individuals in such a situation may use information about each other\u27s behavior such as the number of connections (degree) to form a risk-benefit assessment for whether to engage in a relationship. We study this model for a single benefit case, and then a multiple benefit case. We also investigate the case where offspring may inherit the benefit of their parents to determine how this affects disease transmission. We find that human behavior and individual differences can affect infection transmission and that adaptation in behavior can mitigate the disease prevalence. Further, we study mutual ratings in a growing social network. We use two types of links, positive for favorable ratings between two nodes, and negative otherwise. We model a social network where positive and negative ratings are assigned preferentially based on existing positive and negative links. Extending previous ideas and analytical methods in the growing networks literature, we study the resulting network structure. For one of the preferential attachment mechanisms we consider, we derive an analytical expression for the joint distribution of positive and negative degrees in the limit of large networks. The insights gleaned in these studies will inform potential investigations of the impact of personal decisions on transmission of STIs such as HIV, and empirical studies of the evolution of friend-foe relationships on online social networks that have mechanisms for users to note or express opinions about other users or the contributions they made