Mathematical models of emergent and re-emergent infectious diseases: Assessing the effects of public health interventions on disease spread
Communicable diseases have long been recognized as a continuous threat to humans. Hence, understanding the underlying mechanisms by which diseases spread and cause epidemics is key for their control. This dissertation is concerned with the development of new mathematical models for the spread of infectious diseases and the effects of Public Health interventions.
In Chapter I, a mathematical model for the 2003 Severe Acute Respiratory Syndrome outbreaks in Toronto, Hong Kong and Singapore is developed. In Toronto, our model predicted control in late April by the identification of the nonexponential dynamics in the rate of increase of the number of cases. The reproductive number is estimated to be approximately 1.2. Our model predicts that 20% of the population in Toronto could have been infected without control interventions. In Chapter II, an uncertainty and sensitivity analysis is performed on the basic reproductive number.
In Chapter III, a novel mathematical model for Ebola spread is developed. Ebola outbreaks have been observed in African regions since 1976. Our model includes a smooth transition in the transmission rate at the time when interventions are put in place. We evaluate the effects of interventions and estimate the reproductive number.
In Chapter IV, Foot-and-Mouth disease (FMD) epidemics are modeled using spatial deterministic epidemic model. FMD is a highly infectious illness of livestock. Our model is compared to its non-spatial counterpart. We assess the effectiveness of the contingency plan implemented during the epidemic and explore the expected impact of a mass vaccination policy depending on when it is implemented.
In Chapter V, we analyzed from a network point of view the cumulative and aggregated data generated from the simulated movements of 1600,000 individuals generated by TRANSIMS (Transportation Analysis and Simulation System developed at Los Alamos National Laboratories) during a typical day in Portland, Oregon. The node out-degree, the out-traffic, and the total out-traffic follow power law behavior. The resulting weighted graph is a “small world” and has scaling laws consistent with an underlying hierarchical structure. We also explore the time evolution of the largest connected component and the distribution of the component sizes.
0573: Public health