I have been doing mathematical modelling all my adult life, initially using programming languages such as Simscript and Fortran, to run event-based simulation models for military purposes. Most recently, I have used MATLAB for infectious disease modelling of COVID-19 in the UK. The techniques fall within a generic topic, Queuing Theory.
In the 1970s, I worked at the Ministry of Defence in London’s Whitehall for the Defence Operational Analysis Establishment (RAF), under the MoD Chief Scientist, later to be Prof. Hermann Bondi, who had been one of my Mathematics professors at King’s College, London in the late 1960s. I applied Queuing Theory to some Cold War applications (in preparation for any potential real war) that I can’t tell you about, otherwise they have to shoot me (and you).
Similar statistical mathematics underlies the planning of telephone exchange capacity (Erlang statistical distributions for call arrivals and durations), and I suppose they are now used for planning the size of server farms for Internet applications, including gaming apps such as Zwift.
Zwift online cycle rides are booked in advance for people to use with their Internet-connected exercise bikes, sometimes up to 30,000 people riding at the same time. As Zwift becomes more popular, Zwift must plan and enhance server capacity to cope with increasing demand, especially during busy periods of high arrival rates of Zwift cycling sessions.
The UK Post Office (PO) work on telephone exchange capacity, my own MoD work on how aircraft failure rates influence the number of aircraft required for military operations, and the forecasting of infectious disease transmission we have seen so much about recently are all connected by similar kinds of patterns.
Incidence – telephone call rates, failure rates in aircraft and infection rates in infectious disease models;
Duration – telephone call times, aircraft repair times and infectious periods;
Cessation – ending of telephone calls, repair/replacement completion for aircraft and recovery from infections.
The PO was a leader in applying mathematical modelling for planning the vital physical exchange capacity required for their telephone business.
This was done by a PO group called Trunking and Grading. They took ‘overflow’ figures (the volume of calls that didn’t get through in busy periods) and assessed the need to increase or reduce the number of junctions to individual exchanges. I’m indebted to Arthur Evans, like me an Old Boy of Tottenham Grammar School, who worked for the PO for many years, for outlining how the PO made these calculations.
Here is a description of Erlang distributions used to model call times… https://www.statisticshowto.com/erlang-distribution/.
The 2006 paper below, which I consulted about infectious disease modelling, describes the (negative) Exponential Distribution. It relates R0, the Reproduction Number, the Generation Interval α and the growth rate r of an infectious disease:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1766383/pdf/rspb20063754.pdf
Note that the probability density distributions are very similar. One is about telephone call arrival times, and the other is about infection generation intervals, infection reproductive time and infection rate. The infection generation interval would be analogous to the time between telephone calls arriving.
It suggests that not making a telephone call in a busy period has a direct correlation with avoiding mixing with others who may or may not have a Coronavirus infection. In the telephone context, if you call in a busy period, you get the EET (Equipment Engaged Tone), different from the engaged tone (known as busy tone); in the infectious disease context, if you mix with infected people, you can get Covid-19, and can then pass it on, like passing the parcel.
I had Erlang distributions in the back of my mind in 2020 when I was working through the mathematics behind the infection model charts; I needed a mental “jog” to remind me of these analogies, and it helped with applying the thoughts to my Coronavirus modelling.
Looking back through the infectious diseases literature, as I have many times, I see that many of today’s well-known researchers, such as Prof. Neil Ferguson of Imperial College, have extensive experience in the field. The introduction to the 2006 paper below, published by Neil Ferguson and others, discusses many aspects of infection management.
http://courses.washington.edu/b578a/readings/ferguson2006.pdf
It discusses the kind of public behavioural measures we have all experienced since early 2020 in our new, periodically locked-down lives.
In the intervening years, much more has been published about the need for social distancing and other Non-Pharmaceutical Interventions (NPIs). The recent spread of infectious diseases such as SARS and COVID-19 has led to further recommendations.
You can see more about my own Coronavirus modelling in one of my later papers at https://brianrsutton.com/2023/10/12/my-coronavirus-model-post-pirola/, a paper from late 2023 that happens to describe the structure and many of the parameters of my model, as well as bringing my model up to date with the Pirola variant that had just appeared.
All 66 of my papers on Coronavirus since March 2020 can be seen at https://brianrsutton.com/?s=Coronavirus. The latest (apart from this one) is a review paper looking back over the five years of the pandemic in the UK, at https://brianrsutton.com/2025/03/28/my-model-calculations-for-covid-19-cases-for-an-earlier-uk-lockdown-20250325-review/.
Some of this isn’t new and should not have been a surprise, except, perhaps, the infectiveness – virulence – of Covid-19, and therefore its rapid spread around the world.
I suppose many of those infectious disease scientists might have been regarded by some, just a few years ago, as doom-mongers.
Their clinical, mathematical and vaccine research has proven to be very useful in persuading governments to take notice and take action, offering methods to model and manage different approaches to containing and slowing the transmission of the latest major infectious disease, Covid-19.
As I have suggested in this paper, some of the mathematical principles and methods are shared with many other applications, such as the defence and communications fields.
The potential application of Mathematics to such a wide range of scientific, commercial and industrial disciplines is what encouraged me to choose Mathematics as my degree topic as long ago as 1964, a choice I am glad to have made.
An example of my more academic mathematical work can be seen at https://brianrsutton.com/2024/10/16/the-restricted-three-body-problem/, where I analyse the motion of a satellite under the gravitational influence of two planetary objects.
A rambling mind 