Members of CMMID are actively involved in various outreach and public engagement activities.
Flusurvey is an internet-based project to track the spread of influenza in the UK (and further afield).
Social networks in schools
During 2014-15 Adam Kucharski and Clare Wenham are running a research project with four British secondary schools to measure social contact patterns over the course of an academic year. The project is in collaboration with Andrew Conlan and the Millennium Mathematics Project at the University of Cambridge, and funded by a Wellcome Trust People Award. Through a series of videoconferences and visits, the research team will help students design and run a survey of social interactions in their school. This will improve our understanding of how school-age children mix over a period of time, and what it could mean for disease outbreaks. The research has been featured in +plus magazine.
As well as the core project, the team are developing teaching resources to show how maths can be used to understand epidemics, social interactions and vaccination. They are also running workshops at several schools and science festivals to bring these ideas to a wider audience.
Cheltenham Science Festival Pegademic
We had two Pegademics in the Discover Zone of the Cheltenham Science Festival – one that ran on the Friday night at the adult only event and another that ran all day Saturday that was open to all. We’ve italicised some interesting questions throughout this post that you may want to think about.
Comparing Friday and Saturday Pegademics
The adult-only Friday Pegademic ran for two hours and had 97 cases, whilst the all day event ran for five hours and had 308 cases.
Definition: Case = A person infected with a peg who came to the treatment centre
You can see in the figure below that they were very different Pegademics. Here red is the Friday, and blue the Saturday Pegademic:
On the Friday we had one quick epidemic, whilst on the Saturday we seemed to have three peaks. Interestingly, we can’t find any links between the timings of these peaks and the other events going on at Cheltenham. If you have an idea for what caused them please get in touch!
During the Friday Pegademic, the average speed at which new cases were created was 7 minutes and 41 seconds. On the Saturday Pegademic it was slower at 9 minutes and 24 seconds. The maximum time for Friday was 73 minutes but for Saturday it was 202 minutes! Can you work out why it makes sense that the maximum time was longer for Saturday?
In both Pegademics, the minimum time for a new case was less than a minute – does that make sense with what you saw happening at the Treatment Centre? Do you think this would happen for a real diseases?
Who got infected?
The Pegademics not only spread differently, but they infected male and females differently. On the Saturday 53% of the cases were male and 46% were children, so we had a pretty even split across the ages and genders. On the Friday 53% were female. Do you think there were roughly even numbers of males and females at the Science festival?
If we now look at who gave pegs to whom we find some interesting patterns. In the figure below you can see that on the Friday females tended to preferentially infect males (top image), whilst on the Saturday males tended to preferentially infect females (bottom image). What does this tell us about how an infection might spread in an adult only versus a family environment?
The network of spread through the Discover Zone can be seen below, with each spot representing a person and the different colours the different genders. Here pink is female and blue is male. Can you see that some people spread more pegs to more people than others?
We also considered the Reproduction number (R0) of our Pegademics or the number of infections (pegs given out) that a single infected individual would be expected to infect in a totally susceptible population. The distribution we set for our Pegademic disease had an average R0 of 1.5 and a upper and lower limit of 1 and 5. This means that when we gave out pegs to cases on average we gave each person 1.5 pegs, but could give them anywhere between 1 and 5 pegs to pass on.
When we do our analysis using the above networks we found that the estimates for the R0 using only the data from the Pegademics was very close to this: for Friday it was 1.47 and for Saturday it was 1.43. This suggests that on Friday on average most pegs were passed on, whilst on Saturday there were slightly lower numbers of infections than expected. Can you remember what the R0 of any particular diseases is? What does our Pegademic compare to?
If you want more information on the Cheltenham Pegademics you can see our blog, hear a podcast from Erin and Albert about our talk or for a copy of our more detailed report please email Erin Lafferty. All of the above analysis was done using R (Gwen Knight) or Gephi (Erin Lafferty & Andrea Apolloni).
Talks on Tap Pegademic
The cmmid was also involved in a “Talks on Tap” event at LSHTM on 29th January. This trialled our “PEGADEMIC”, which we are developing as an activity for use in schools and at festivals.
Using pegs to represent infectious disease agents we collected data on the effect of social contact patterns on disease spread in the Pumphandle bar.
The results can be seen below. We set up our Pegademic, so we knew some things before starting. This is similar to when we model diseases such as measles where we now know something about levels of immunity and disease spread. For the Pegademic, we knew that there was no conferred immunity and we set the R0, or reproduction number, to be 1.6. This R0, or reproduction number, is equal to the average number of secondary infections caused by a single infectious individual. This meant that, on average, every pegged (=infected) person who came to the treatment centre received 1.6 pegs. In our Pegademic this means that they went on to cause ~1.6 new infections. Knowing these two things meant that we could try to model or predict the spread of the Pegademic with an SIS (susceptible-infected-susceptible) model with an R0 of 1.6.
However, we didn’t know the recovery time: how long would it take for an infected individual to become susceptible again? This would depend on how long it took people to come to see us at the treatment centre and how people mixed in the bar, spreading the disease. So, we put several different values for the recovery time into our model and plotted the model output (coloured lines on graph) alongside the Pegademic data (red crosses on graph). Can you see that the data lies most closely to the model output that used a recovery time of 3 minutes?
This suggests that each individual who is infected, and hence infectious, takes about 3 minutes to recover and become susceptible again. Using this information we can predict what would happen if the Pegademic had been allowed to continue. We could also use the SIS model to investigate ways to control future Pegademics. For example, what vaccine coverage would we need to stop the Pegademic in 10 minutes? This modelling approach is very similar to work that we do on real infectious diseases. We try to infer, by matching model output to epidemic data, missing parameters. This allows us to build better models that we can use to predict future burden, helping public health practitioners to plan ahead, but also to investigate interventions and their potential impact.
Members of CMMID have given interviews about modelling and epidemiology to several national and international media outlets, including AFP, Associated Press, BBC Radio, BBC World News, Channel 4 News, Dallas Morning News, Evening Standard, FHM, Kristeligt Dagblad and Lateline.
Adam Kucharski has also contributed articles about influenza modelling to Scientific American and the history of R0 to Aeon Magazine, and explained drinking games and social contagion for BBC More or Less.