Perspectives on the basic reproductive ratio

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Abstract

The basic reproductive ratio, R ₀ , is defined as the expected number of secondary infections arising from a single individual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of epidemiology and within-host pathogen dynamics. Most importantly, R ₀ often serves as a threshold parameter that predicts whether an infection will spread. Related parameters which share this threshold behaviour, however, may or may not give the true value of R ₀ . In this paper we give a brief overview of common methods of formulating R ₀ and surrogate threshold parameters from deterministic, non-structured models. We also review common means of estimating R ₀ from epidemiological data. Finally, we survey the recent use of R ₀ in assessing emerging diseases, such as severe acute respiratory syndrome and avian influenza, a number of recent livestock diseases, and vector-borne diseases malaria, dengue and West Nile virus.

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Transmissibility of 1918 pandemic influenza

Christina E Mills, James M. Robins, Marc Lipsitch (2004)

The 1918 influenza pandemic killed 20–40 million people worldwide 1 , and is seen as a worst-case scenario for pandemic planning. Like other pandemic influenza strains, the 1918 A/H1N1 strain spread extremely rapidly. A measure of transmissibility and of the stringency of control measures required to stop an epidemic is the reproductive number, which is the number of secondary cases produced by each primary case 2 . Here we obtained an estimate of the reproductive number for 1918 influenza by fitting a deterministic SEIR (susceptible-exposed-infectious-recovered) model to pneumonia and influenza death epidemic curves from 45 US cities: the median value is less than three. The estimated proportion of the population with A/H1N1 immunity before September 1918 implies a median basic reproductive number of less than four. These results strongly suggest that the reproductive number for 1918 pandemic influenza is not large relative to many other infectious diseases 2 . In theory, a similar novel influenza subtype could be controlled. But because influenza is frequently transmitted before a specific diagnosis is possible and there is a dearth of global antiviral and vaccine stores, aggressive transmission reducing measures will probably be required. Supplementary information The online version of this article (doi:10.1038/nature03063) contains supplementary material, which is available to authorized users.

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Containing pandemic influenza with antiviral agents.

I Longini (2004)

For the first wave of pandemic influenza or a bioterrorist influenza attack, antiviral agents would be one of the few options to contain the epidemic in the United States until adequate supplies of vaccine were available. The authors use stochastic epidemic simulations to investigate the effectiveness of targeted antiviral prophylaxis to contain influenza. In this strategy, close contacts of suspected index influenza cases take antiviral agents prophylactically. The authors compare targeted antiviral prophylaxis with vaccination strategies. They model an influenza pandemic or bioterrorist attack for an agent similar to influenza A virus (H2N2) that caused the Asian influenza pandemic of 1957-1958. In the absence of intervention, the model predicts an influenza illness attack rate of 33% of the population (95% confidence interval (CI): 30, 37) and an influenza death rate of 0.58 deaths/1,000 persons (95% Cl: 0.4, 0.8). With the use of targeted antiviral prophylaxis, if 80% of the exposed persons maintained prophylaxis for up to 8 weeks, the epidemic would be contained, and the model predicts a reduction to an illness attack rate of 2% (95% Cl: 0.2, 16) and a death rate of 0.04 deaths/1,000 persons (95% CI: 0.0003, 0.25). Such antiviral prophylaxis is nearly as effective as vaccinating 80% of the population. Vaccinating 80% of the children aged less than 19 years is almost as effective as vaccinating 80% of the population. Targeted antiviral prophylaxis has potential as an effective measure for containing influenza until adequate quantities of vaccine are available.

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Risk of indoor airborne infection transmission estimated from carbon dioxide concentration.

S N Rudnick, D Milton (2003)

The Wells-Riley equation, which is used to model the risk of indoor airborne transmission of infectious diseases such as tuberculosis, is sometimes problematic because it assumes steady-state conditions and requires measurement of outdoor air supply rates, which are frequently difficult to measure and often vary with time. We derive an alternative equation that avoids these problems by determining the fraction of inhaled air that has been exhaled previously by someone in the building (rebreathed fraction) using CO2 concentration as a marker for exhaled-breath exposure. We also derive a non-steady-state version of the Wells-Riley equation which is especially useful in poorly ventilated environments when outdoor air supply rates can be assumed constant. Finally, we derive the relationship between the average number of secondary cases infected by each primary case in a building and exposure to exhaled breath and demonstrate that there is likely to be an achievable critical rebreathed fraction of indoor air below which airborne propagation of common respiratory infections and influenza will not occur.