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The Basic Reproduction Number of Infectious Diseases: Computation and Estimation Using Compartmental Epidemic Models

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Mathematical and Statistical Estimation Approaches in Epidemiology

The basic reproduction number (R0) is a central quantity in epidemiology as it measures the transmission potential of infectious diseases. In this chapter we review the basic theory of the spread of infectious diseases using simple compartmental models based on ordinary differential equations including the simple Kermack-McKendrick epidemic model, SIR (susceptible-infectious-removed) models with demographics, the SIS (susceptible-infectious-susceptible) model, backward bifurcations, endemic equilibria, and the analytical derivation of R0 using the next-generation approach. This theory is followed by simple methodology for the estimation of R0 with its corresponding uncertainty from epidemic time series data. The 1918–1919 influenza pandemic in Winnipeg, Canada, and the 1968 influenza pandemic in US cities are used for illustration.

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Authors and Affiliations

  1. Arizona State University School of Human Evolution&Social Change, Tempe, AZ 85287-2402, USA

    Gerardo Chowell

  2. Department of Mathematics, The University of British Columbia, Vancouver, B.C., Canada V6T 1Z2

    Fred Brauer

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Editors and Affiliations

  1. Arizona State University School of Human Evolution & Social Change, Tempe, AZ 85287-2402, USA

    Gerardo Chowell

  2. Los Alamos National Laboratory, Mail Stop B284, Los Alamos, NM 87545, USA

    James M. Hyman  & Luís M. A. Bettencourt  & 

  3. Dept. Mathematics & Statistics, Arizona State University, P.O.Box 871804, Tempe, AZ 85287, USA

    Carlos Castillo-Chavez

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Chowell, G., Brauer, F. (2009). The Basic Reproduction Number of Infectious Diseases: Computation and Estimation Using Compartmental Epidemic Models. In: Chowell, G., Hyman, J.M., Bettencourt, L.M.A., Castillo-Chavez, C. (eds) Mathematical and Statistical Estimation Approaches in Epidemiology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2313-1_1

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