The influence of assumptions on generation time distributions in epidemic models.

A simple class of stochastic models for epidemic spread in finite, but large, populations is studied. The purpose is to investigate how assumptions about the times between primary and secondary infections influences the outcome of the epidemic. Of particular interest is how assumptions of individual variability in infectiousness relates to variability of the epidemic curve. The main concern is the final size of the epidemic and the time scale at which it evolves. The theoretical results are illustrated by simulations.

[1]  A. Lambert Branching Processes: Variation, Growth and Extinction of Populations , 2006 .

[2]  P. Grambsch Survival and Event History Analysis: A Process Point of View by AALEN, O. O., BORGAN, O., and GJESSING, H. K. , 2009 .

[3]  Anders Martin-Löf,et al.  Threshold limit theorems for some epidemic processes , 1980, Advances in Applied Probability.

[4]  Marek Kimmel,et al.  Branching processes in biology , 2002 .

[5]  H. Andersson,et al.  Stochastic Epidemic Models and Their Statistical Analysis , 2000 .

[6]  J. Robins,et al.  Generation interval contraction and epidemic data analysis. , 2007, Mathematical biosciences.

[7]  J. Giesecke,et al.  Some model based considerations on observing generation times for communicable diseases. , 2010, Mathematical biosciences.

[8]  M. Lipsitch,et al.  How generation intervals shape the relationship between growth rates and reproductive numbers , 2007, Proceedings of the Royal Society B: Biological Sciences.

[9]  N G Becker,et al.  Martingale methods for the analysis of epidemic data , 1993, Statistical methods in medical research.

[10]  P. Fine The interval between successive cases of an infectious disease. , 2003, American journal of epidemiology.

[11]  Pejman Rohani,et al.  Appropriate Models for the Management of Infectious Diseases , 2005, PLoS medicine.

[12]  I︠u︡. V. Linnik,et al.  Decomposition of Random Variables and Vectors , 1977 .

[13]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[14]  Ả. Svensson A note on generation times in epidemic models. , 2007, Mathematical Biosciences.