Letters

# Health professionals do not understand mathematical models

BMJ 2000; 320 doi: https://doi.org/10.1136/bmj.320.7234.581/a (Published 26 February 2000) Cite this as: BMJ 2000;320:581
1. W J Edmunds, health economist (jedmunds{at}phls.nhs.uk),
2. N J Gay, mathematical modeller
1. PHLS Communicable Disease Surveillance Centre, London NW9 5EQ

EDITOR—The science commentary on herd immunity that accompanied the article by Panagiotopoulos et al on an increase in the occurrence of congenital rubella after immunisation seemed irrelevant.1 In this letter we attempt to explain the relevant issues.

Immunising a proportion of the population reduces the risk of infection (not necessarily disease) among those who are not immunised. This indirect protection from infection is termed herd immunity. It can be manifested in two different ways.

Firstly, if the level of vaccine coverage is high enough (the proportion of those who are susceptible is low enough) then transmission cannot be sustained, leading to elimination of the infection from the population. This threshold of coverage (occasionally termed the herd immunity threshold) is what Berger was attempting to explain in her commentary.

Secondly, if coverage is below the threshold then the infection will remain endemic. Individuals who have not been immunised will have a lower risk of infection because there will be fewer infectious people in the population. Thus, on average, if they become infected it will be at an older age. It is this which is critical to understanding the paper of Panagiotopoulos et al. Many infections that can be prevented by vaccination cause more severe clinical consequences in adults than in children2; examples include mumps, chickenpox, hepatitis A, and rubella. After mass infant immunisations against such diseases the number of infections will decrease but those who become infected will, on average, be older and therefore have more serious disease. At low or intermediate levels of coverage it may be that the decrease in the incidence of infection is outweighed by the increase in the average seriousness of each case, resulting in more harm than good being done to public health. At higher levels of coverage the decrease in the incidence outweighs the increase in the average seriousness of each case and the programme is beneficial to public health.

The work of Panagiotopoulos et al is important because it is the first to show conclusively that an increase in the average age at infection occurring as a result of low levels of infant immunisation actually leads to more cases of severe disease than occurred before vaccinations were introduced. It is a shame that this had to be so. The warnings from mathematical models have been clear for many years. 34 Perhaps a lack of understanding of the models among health professionals has contributed to their reluctance to adopt the recommendations generated by the models. Education of decision makers is clearly important.

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