A likelihood‐based method for real‐time estimation of the serial interval and reproductive number of an epidemic

We present a method for the simultaneous estimation of the basic reproductive number, R(0), and the serial interval for infectious disease epidemics, using readily available surveillance data. These estimates can be obtained in real time to inform an appropriate public health response to the outbreak. We show how this methodology, in its most simple case, is related to a branching process and describe similarities between the two that allow us to draw parallels which enable us to understand some of the theoretical properties of our estimators. We provide simulation results that illustrate the efficacy of the method for estimating R(0) and the serial interval in real time. Finally, we implement our proposed method with data from three infectious disease outbreaks.

[1]  P. Hall,et al.  Martingale Limit Theory and its Application. , 1984 .

[2]  J. Hyman,et al.  The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. , 2004, Journal of theoretical biology.

[3]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[4]  Peter Donnelly,et al.  Strong approximations for epidemic models , 1995 .

[5]  I. Longini,et al.  A generalized stochastic model for the analysis of infectious disease final size data. , 1991, Biometrics.

[6]  J. Robins,et al.  Transmissibility of 1918 pandemic influenza , 2004, Nature.

[7]  A. Ghani,et al.  The Transmissibility of Highly Pathogenic Avian Influenza in Commercial Poultry in Industrialised Countries , 2007, PloS one.

[8]  T. E. Harris,et al.  The Theory of Branching Processes. , 1963 .

[9]  Peter Guttorp,et al.  Statistical inference for branching processes , 1991 .

[10]  Christl A. Donnelly,et al.  Real-time Estimates in Early Detection of SARS , 2006, Emerging infectious diseases.

[11]  Hans Heesterbeek,et al.  Nonhomogeneous birth and death models for epidemic outbreak data. , 2007, Biostatistics.

[12]  J. Wallinga,et al.  Different Epidemic Curves for Severe Acute Respiratory Syndrome Reveal Similar Impacts of Control Measures , 2004, American journal of epidemiology.

[13]  T. Britton,et al.  Statistical studies of infectious disease incidence , 1999 .

[14]  W. Rida,et al.  Asymptotic Properties of Some Estimators for the Infection Rate in the General Stochastic Epidemic Model , 1991 .

[15]  Stefan Ma,et al.  The estimation of SARS incubation distribution from serial interval data using a convolution likelihood , 2005, Statistics in medicine.

[16]  J. Robins,et al.  Transmission Dynamics and Control of Severe Acute Respiratory Syndrome , 2003, Science.

[17]  J. P. Trapman,et al.  On stochastic models for the spread of infections , 2006 .

[18]  C. Fraser,et al.  Factors that make an infectious disease outbreak controllable. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[20]  S. Cauchemez,et al.  Estimating in real time the efficacy of measures to control emerging communicable diseases. , 2006, American journal of epidemiology.

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

[22]  C. Fraser,et al.  Transmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact of Public Health Interventions , 2003, Science.

[23]  N. Becker,et al.  Estimation for an epidemic model. , 1976, Biometrics.

[24]  F. Ball.  A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models , 1986, Advances in Applied Probability.

[25]  Some properties of an estimator for the basic reproduction number of the general epidemic model. , 1999, Mathematical biosciences.

[26]  James O Lloyd-Smith,et al.  Dynamically Modeling SARS and Other Newly Emerging Respiratory Illnesses: Past, Present, and Future , 2005, Epidemiology.

[27]  A. Nizam,et al.  Containing pandemic influenza with antiviral agents. , 2004, American journal of epidemiology.

[28]  G. Roberts,et al.  Bayesian inference for partially observed stochastic epidemics , 1999 .

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