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United States Department of Agriculture

Agricultural Research Service

Research Project: FRAMEWORKS FOR INFECTIOUS DISEASE DYNAMICS

Location: Plant-Microbe Interactions Research

Title: Using multitype branching processes to quantify statistics of disease outbreaks in zoonotic epidemics

Authors
item Singh, Sarabjeet -
item Schneider, David
item Myers, Christopher -

Submitted to: Physical Review E (PRE) - Statistical, Nonlinear, and Soft Matter Physics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: November 22, 2013
Publication Date: March 4, 2014
Citation: Singh, S., Schneider, D.J., Myers, C.R. 2014. Using multitype branching processes to quantify statistics of disease outbreaks in zoonotic epidemics. Physical Review E (PRE) - Statistical, Nonlinear, and Soft Matter Physics. 89:1-14.

Interpretive Summary: Many of the most devastating human diseases are believed to have originated in livestock (e.g., smallpox) or wild animals (e.g., AIDS, rabies, plague). Despite the enormous relevance of such diseases to agriculture and public health, and much effort in modeling individual diseases, we lack a fundamental understanding of how disease outbreaks in animal populations drive cross-species transmission events and subsequent outbreaks in human populations. We introduce a simple model of disease outbreaks that takes into account disease progression in each subpopulation, cross-species transmission, and certain kinds of random effects. We are able to solve analytically for several important properties that are relevant at early stages of outbreaks – the probability and timing of transmission into the human population, the disease prevalence in the animal population when the first human case is identified – as a function of model parameters. We also investigate the distribution of outbreak sizes and identify critical parameter thresholds that imply the possibility of large outbreaks in the human population. All of these quantities show a strong dependence on the structure of the outbreak in the animal population. We find that the coupling of animal and human infection processes allows for the possibility of large human outbreaks even when human-to-human transmission is sub-critical, a result which is relevant for some of the historically important diseases such as rabies, as well as some of the newly emerging ones such as Nipah and novel strains of influenza.

Technical Abstract: Despite the enormous relevance of zoonotic infections to world-wide public health, and despite much effort in modeling individual zoonoses, a fundamental understanding of the disease dynamics and the nature of outbreaks emanating from such a complex system is still lacking. We introduce a simple stochastic model of susceptible-infected-recovered dynamics in a coupled animal-human metapopulation, and solve analytically for several important properties of the coupled outbreaks that are relevant at early timescales -- including the probability of spillover, first passage time, the disease prevalence in the animal population at spillover -- as a function of model parameters. Additionally, in the long time limit, we investigate the distribution of outbreak sizes and the critical threshold for a large human outbreak, all of which show a strong dependence on the basic reproduction number of the animal population. We find that the coupling of animal and human infection processes allows for the possibility of large human outbreaks even when human-to-human transmission is sub-critical, a result which is relevant for some of the historically existing zoonoses, such as rabies as well as some of the newly emerging ones such as Nipah.

Last Modified: 10/20/2014
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