Controlling infectious disease outbreaks: Lessons from mathematical modelling

Abstract

Epidemiological analysis and mathematical models are now essential tools in understanding the dynamics of infectious diseases and in designing public health strategies to contain them. They have provided fundamental concepts, such as the basic and effective reproduction number, generation times, epidemic growth rates, and the role of pre-symptomatic infectiousness, which are crucial in characterising infectious diseases. These concepts are outlined and their relevance in designing control policies for outbreaks is discussed. They are illustrated using examples from the 2003 severe acute respiratory syndrome outbreak, which was brought under control within a year, and from pandemic influenza planning, where mathematical models have been used extensively.

Figure 1

Probable SARS cases with onset between 1 November 2002 and 31 July 2003 by country, as reported by the WHO on 26 September 2003.⁵ The five countries with the largest number of probable cases are labelled.

Figure 2

The basic reproduction number and the characteristics of epidemics. (a) Illustration of an epidemic with discrete generations. If the basic reproduction number, R₀ is greater than 1 (here R₀=1.75) then the epidemic expands exponentially. The effective reproduction number, R, is calculated as the number of new infections divided by the number of infected individuals in the previous generation. (b) The characteristic shape of an uncontrolled outbreak where R₀>1. Initially the epidemic may die out because of stochastic factors, but once it is established it grows exponentially until susceptibles are exhausted at which point the epidemic slows until the disease either becomes endemic or extinct. (c) Estimating R₀ from the first month of cases in Hong Kong, shown by date of onset, as published by the WHO⁵ R₀ may be estimated from the exponential growth rate, here the slope of the log-linear fitted line, r=0.15. See text for estimation of R₀.