# The basic reproduction number of infectious diseases: Computation and estimation using compartmental epidemic models

Gerardo Chowell, Fred Brauer

Research output: Chapter in Book/Report/Conference proceedingChapter

14 Citations (Scopus)

### Abstract

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.

Original language English (US) Mathematical and Statistical Estimation Approaches in Epidemiology Springer Netherlands 1-30 30 9789048123124 https://doi.org/10.1007/978-90-481-2313-1_1 Published - 2009

### Fingerprint

Compartmental Model
Basic Reproduction number
Infectious Diseases
Epidemic Model
Influenza
Backward Bifurcation
Endemic Equilibrium
Epidemiology
Time Series Data
Ordinary differential equation
Model-based
Uncertainty
Methodology
Model

### Keywords

• Basic reproduction number
• Epidemiology
• Influenza
• Model
• Pandemic

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

Chowell, G., & Brauer, F. (2009). The basic reproduction number of infectious diseases: Computation and estimation using compartmental epidemic models. In Mathematical and Statistical Estimation Approaches in Epidemiology (pp. 1-30). Springer Netherlands. https://doi.org/10.1007/978-90-481-2313-1_1
Mathematical and Statistical Estimation Approaches in Epidemiology. Springer Netherlands, 2009. p. 1-30.

Research output: Chapter in Book/Report/Conference proceedingChapter

Chowell, G & Brauer, F 2009, The basic reproduction number of infectious diseases: Computation and estimation using compartmental epidemic models. in Mathematical and Statistical Estimation Approaches in Epidemiology. Springer Netherlands, pp. 1-30. https://doi.org/10.1007/978-90-481-2313-1_1
Chowell G, Brauer F. The basic reproduction number of infectious diseases: Computation and estimation using compartmental epidemic models. In Mathematical and Statistical Estimation Approaches in Epidemiology. Springer Netherlands. 2009. p. 1-30 https://doi.org/10.1007/978-90-481-2313-1_1
Chowell, Gerardo ; Brauer, Fred. / The basic reproduction number of infectious diseases : Computation and estimation using compartmental epidemic models. Mathematical and Statistical Estimation Approaches in Epidemiology. Springer Netherlands, 2009. pp. 1-30
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