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

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.