Using multitype branching processes to quantify statistics of disease outbreaks in zoonotic 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 work we focus on coupled branching processes as a model of infectious diseases spreading from one population to another. An exceedingly important example of such coupled outbreaks are zoonotic infections that spill over from animal populations to humans. We derive several statistical quantities characterizing the first spillover event from animals to humans, including the probability of spillover, the first passage time distribution for human infection, and disease prevalence in the animal population at spillover. Large stochastic fluctuations in those quantities can make inference of the state of the system at the time of spillover difficult. Focusing on outbreaks in the human population, we then characterize the critical threshold for a large outbreak, the distribution of outbreak sizes, and associated scaling laws. These all show a strong dependence on the basic reproduction number in the animal population and indicate the existence of a novel multicritical point with altered scaling behavior. The coupling of animal and human infection dynamics has crucial implications, most importantly allowing for the possibility of large human outbreaks even when human-to-human transmission is subcritical.