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$R_0$ Game

Age 11 to 16
  • Project

This classroom activity is part of the Disease Dynamics collection




This short activity leads on from The Standing Disease to show real life examples of $R_0$.

$R_0$ (otherwise known as the reproduction number) is a measure used in epidemiology to indicate the average number of people an infected person infects during the course of the infectious period (in an otherwise unvaccinated population).

This number varies depending on the pathogen (such as bacteria, virus or fungus) and also on the method of transmission (airborne, sexual contact, bodily fluids etc).
If $R_0$ is greater than one - the disease will spread through the population
If $R_0$ is less than one - the cases of the disease will decrease and die out.


Resources: Slides (PowerPoint or PDF )

Curriculum Links

Science:
  • Communicable diseases
  • Bacteria, viruses and fungi as pathogens
  • Reducing and preventing the spread of infectious diseases

Aims

  • To understand that different diseases have different reproduction numbers - that is the number of cases that one case generates on average.
  • To understand that $R_0$ is not necessarily the same as severity of the disease.


Activity (Small Groups)


This task offers 5 different diseases and the students have to order these infectious diseases by the order of reproduction number.

This can be done either on a screen, or by printing out the slide for students individually.


Questions for thought


Is there a connection between severity of symptoms and $R_0$?
Not necessarily. In fact, in the case of ebola, the severe symptoms and high mortality actually limit the pathogen spreading as people die too quickly to be able to infect a large group.

What can you say about the diseases with high $R_0$ (measles, chicken pox) - why are they so high?
The method of transmission used by these diseases (airborne instead of bodily/contact) means on average more people are infected.

Why is the $R_0$ for rabies 0?
There is no known human to human transmission.

Why is ebola cause for concern, when it has a low $R_0$ value?
Outbreak in West Africa is in an area with weak health systems to enforce infection control and has a mobile population. Crucially, Ebola has a high mortality rate, despite having the same $R_0$ as flu. Further, cultural issues of washing the dead for burial lead to increased transmission, as well as a perception of fear which has built up around the disease through the media.

Why can the $R_0$ of the same pathogen vary in different outbreaks?
Population density, vaccination thresholds, number of immune people in population, contact patterns between people etc. can all vary.

If measles has a high $R_0$, why do we not see big outbreaks of it?
MMR vaccination policy in UK since 1980s.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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