BRANCHING PROCESSES IN DISEASE EPIDEMICS

Branching processes have served as a model for chemical reactions, biological growth processes and contagion (of disease, information or fads). Through this connection, these seemingly different physical processes share some common universalities that can be elucidated by analyzing the underlying branching process. In this thesis, we focus on branching processes as a model for infectious diseases spreading between individuals belonging to different populations. The distinction between populations can arise from species separation (as in the case of diseases which jump across species) or spatial separation (as in the case of disease spreading between farms, cities, urban centers, etc). A prominent example of the former is zoonoses – infectious diseases that spill from animals to humans – whose specific examples include Nipah virus, monkeypox, HIV and avian influenza. A prominent example of the latter is infectious diseases of animals such as foot and mouth disease and bovine tuberculosis that spread between farms or cattle herds. Another example of the latter is infectious diseases of humans such as H1N1 that spread from one city to another through migration of infectious hosts. This thesis consists of three main chapters, an introduction and an appendix. Th