Doctor of Philosophy (Ph.D.)
Leah B Shaw
Spread of infectious diseases progresses as a result of contacts between the individuals in a population. Therefore, it is crucial to gain insight into the pattern of connections to better understand and possibly control the spread of infectious diseases. Moreover, people may respond to an epidemic by changing their social behaviors to prevent infection. as a result, the structure of the network of social contacts evolves adaptively as a function of the disease status of the nodes. Recently, the dynamic relationships between different network topologies and adaptation mechanisms have attracted great attention in modeling epidemic spread. However, in most of these models, the original network structure is not preserved due to the adaptation mechanisms involving random changes in the links. In this dissertation, we study more realistic models with network structure constraints to retain aspects of the original network structure.;We study a susceptible-infected-susceptible (SIS) disease model on an adaptive network with two communities. Different levels of heterogeneity in terms of average connectivity and connection strength are considered. We study the effects of a disease avoidance adaptation mechanism based on the rewiring of susceptible-infected links through which the disease could spread. We choose the rewiring rules so that the network structure with two communities would be preserved when the rewiring links occur uniformly. The high dimensional network system is approximated with a lower dimensional mean field description based on a moment closure approximation. Good agreement between the solutions of the mean field equations and the results of the simulations are obtained at the steady state. In contrast to the non-adaptive case, similar infection levels in both of the communities are observed even when they are weakly coupled. We show that the adaptation mechanism tends to bring both the infection level and the average degree of the communities closer to each other.;In this rewiring mechanism, the local neighborhood of a node changes and is never restored to its previous state. However, in real life people tend to preserve their neighborhood of friends. We propose a more realistic adaptation mechanism, where susceptible nodes temporarily deactivate their links to infected neighbors and reactivate the links to those neighbors after they recover. Although the original network is static, the subnetwork of active links is evolving.;We drive mean field equations that predict the behavior of the system at the steady state. Two different regimes are observed. In the slow network dynamics regime, the adaptation simply reduces the effective average degree of the network. However, in the fast network dynamics regime, the adaptation further suppresses the infection level by reducing the dangerous links. In addition, non-monotonic dependence of the active degree on the deactivation rate is observed.;We extend the temporary deactivation adaptation mechanism to a scale-free network, where the degree distribution shows heavy tails. It is observed that the tail of the degree distribution of the active subnetwork has a different exponent than that of the original network. We present a heuristic explanation supporting that observation. We derive improved mean field equations based on a new moment closure approximation which is derived by considering the active degree distribution conditioned on the total degree. These improved mean field equations show better agreement with the simulation results than standard mean field analysis based on homogeneity assumptions.
© The Author
Tunc, Ilker, "Epidemic models on adaptive networks with network structure constraints" (2013). Dissertations, Theses, and Masters Projects. William & Mary. Paper 1539623618.