Characterizing the disease diffusion in networks and its empirical application

Infectious diseases remain a major cause of morbidity and mortality worldwide, trigger- ing immeasurable loss in many societies. Their management and control is one of the most challenging problems that humans face. Epidemiological models are fundamental tools for understanding the dynamics of how infectious diseases spread, predicting out- break severity, evaluating the efficacy of interventions, and optimizing the deployment of new control policies. At present, one feasible means of detecting outbreaks is to im- plement surveillance systems in regional or national health and medical centers. The accumulated surveillance data, including temporal, spatial, clinical, and demographic information, can provide valuable information with which to infer the underlying spatial patterns of infectious disease spread.

This project aims to study how infectious diseases spread in networks using surveil- lance data from real-world cases. To the best of our knowledge, there are no comprehen- sive studies using surveillance data for analyzing spatial dynamics of infectious disease spread in networks during an outbreak. Specifically, we will focus on the open issues of (i) how to model the patterns of the geographical interactions in both space and time, (ii) how to discover the epidemic network of infectious disease spread, and (iii) how to estimate the speed of global and local disease spread in epidemic networks. Evidence has indicated that the spread of infectious diseases relies strongly on the structure of the underlying epidemic network, the specifics of which shape the epidemiology of various diseases. We use the network model based approach to develop computational algo- rithms for inferring epidemic network topology and to estimate key parameters in the control of disease spread. In our proposed model, the dynamics modeled in the classical epidemiological model are described by an inhomogeneous Poisson process characterized by a piecewise rate function. The spatial relationships are characterized by interac- tions between multiple in-homogeneous Poisson processes in a network, which allows inferences to be made both qualitatively (structure) and quantitatively (parameters).

We have acquired two real-world data sets to evaluate the performance of the model. Empirical studies and in-depth simulation studies will be carried out. Mathematically inferred patterns of infectious disease spread are useful to public health authorities for predicting the influence of future prevalence and the implications of control polices. The developed model can also be extended to study related dynamic patterns, such as that of a virus spreading through the Internet or information propagation between social networks.