Introducing the Outbreak Threshold in Epidemiology

When a pathogen is rare in a host population, there is a chance that it will die out because of stochastic effects instead of causing a major epidemic. Yet no criteria exist to determine when the pathogen increases to a risky level, from which it has a large chance of dying out, to when a major outbreak is almost certain. We introduce such an outbreak threshold (T0), and find that for large and homogeneous host populations, in which the pathogen has a reproductive ratio R0, on the order of 1/Log(R0) infected individuals are needed to prevent stochastic fade-out during the early stages of an epidemic. We also show how this threshold scales with higher heterogeneity and R0 in the host population. These results have implications for controlling emerging and re-emerging pathogens.

[1]  A. Danchin,et al.  The Severe Acute Respiratory Syndrome , 2003 .

[2]  M. Woolhouse,et al.  Human viruses: discovery and emergence , 2012, Philosophical Transactions of the Royal Society B: Biological Sciences.

[3]  P. E. Kopp,et al.  Superspreading and the effect of individual variation on disease emergence , 2005, Nature.

[4]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[5]  N L Kaplan,et al.  The "hitchhiking effect" revisited. , 1989, Genetics.

[6]  N. Barton,et al.  Genetic hitchhiking. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[7]  C. Fraser,et al.  Public Health Risk from the Avian H5N1 Influenza Epidemic , 2004, Science.

[8]  D. Fleming,et al.  Severe acute respiratory syndrome--Singapore, 2003. , 2003, Releve epidemiologique hebdomadaire.

[9]  Y. Guan,et al.  The severe acute respiratory syndrome. , 2003, The New England journal of medicine.

[10]  A. J. Hall.  Infectious diseases of humans: R. M. Anderson & R. M. May. Oxford etc.: Oxford University Press, 1991. viii + 757 pp. Price £50. ISBN 0-19-854599-1 , 1992 .

[11]  A. Fauci,et al.  The challenge of emerging and re-emerging infectious diseases , 2004, Nature.

[12]  R. Antia,et al.  How do pathogen evolution and host heterogeneity interact in disease emergence? , 2006, Proceedings of the Royal Society B: Biological Sciences.

[13]  T. Day,et al.  Risk factors for the evolutionary emergence of pathogens , 2010, Journal of The Royal Society Interface.

[14]  Mark Bartlett,et al.  The Critical Community Size for Measles in the United States , 1960 .

[15]  L. Allen.  An Introduction to Stochastic Epidemic Models , 2008 .

[16]  Sally Blower,et al.  Modelling infectious diseases in humans and animals , 2008 .

[17]  D. Fargette,et al.  Molecular ecology and emergence of tropical plant viruses. , 2006, Annual review of phytopathology.

[18]  Michael M. Desai,et al.  Beneficial Mutation–Selection Balance and the Effect of Linkage on Positive Selection , 2006, Genetics.

[19]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[20]  M. Keeling,et al.  Modeling Infectious Diseases in Humans and Animals , 2007 .

[21]  O. Chay,et al.  Severe acute respiratory syndrome in Singapore , 2004, Archives of Disease in Childhood.

[22]  Angela R. McLean,et al.  Insights into the Evolution and Emergence of a Novel Infectious Disease , 2010, PLoS Comput. Biol..

[23]  Rustom Antia,et al.  The role of evolution in the emergence of infectious diseases , 2003, Nature.