Human life and diseases are inseparable. For millions of years, humans and their ancestors suffered from diseases, caused by infectious pathogens (e.g., bacteria, viruses, parasites) and caused by our own bodies as they age and degenerate. Within the last century, with the advent of public health measures, improved nutrition and medicine, such as antibiotics, some of the infectious diseases have been controlled. However, infectious diseases still lead to most of the non-age related deaths in the world, especially in nations with insufficient health support. My research has taken the complex and dynamic contact networks as well as heterogeneity in disease transmission and recovery into account. Real social networks among individuals were used to generate an adjacency matrix in my formulas. Both, transition and recovery rates have been used as unique variables for each individual. I have used the forward Kolmogorov equation to solve the system. To control and prevent the infectious diseases such as influenza, sexually transmitted diseases, we have to model the dynamics of a particular disease, estimate the parameters, and forecast the behavior of the disease over time. The estimated parameters help us to design and implement interventions, such as vaccination, closure of public places, to limit the spread of diseases. R0, the reproduction number is an important parameter in epidemiology. R0 is the average number of secondary infections produced by a primary infection. If R0 is larger than one an epidemic will most likely happen, an R0 smaller than one suggests that the disease outbreak is local and will die out. In this study I have shown that R0 estimators that only use the the number of contacts and some network features such as covariance of coefficient are not enough to estimate the epidemic threshold. I have formulated R0 to consider both node degree distribution as well as the spectral gap in the eigenvalue of a weighted adjacency matrix of contact network. Only recently, researchers have developed theoretical approaches that can take into account dynamic networks and, independently, that can use genomic data of the pathogen, sampled from infected persons, to reconstruct the path of an epidemic. By considering the location and time of the sampled pathogen sequence data we can combine the sampled infection network and the mutational history of the pathogen to reconstruct a more accurate contact network. We can reconstruct this dynamic contact network using genetic data and epidemic parameters via a Hidden Markov Model. Sampled genome sequenced data of the pathogen are the observation and a set of dynamic networks are the hidden states in our HMM framework. The system switches between the set of dynamic contact networks to fit the best pattern to observation data. The outcome of such an analysis is the accurate dynamic network among samples of the pathogen. These set of dynamic networks capture the dynamics of the social contact network of the infected people. My model will most likely enable earlier detection of infectious disease spread in dynamic social networks than currently available methods.
