As anticipated, Prime Minister Boris Johnson announced, on 12 March 2020, a transition from the “contain” phase to the “delay” phase of the UK’s coronavirus action plan. Guided by “the science” available to the government’s advisers, the magnitude of the British response appeared distinctly muted, when compared with the more robust decisions taken at the same time by the UK’s closest neighbours-the Republics of Ireland and France. The British public have merely been recommended self-isolation at home for seven days in the presence of “mild” symptoms, likely to be due to coronavirus infection, and told not to ring 111 for advice under these circumstances. Mass gatherings have not been prohibited, schools and universities have not been closed, and any foreign travel bans are of a rather targeted nature, such as trips to Italy, school trips, and cruises over those aged over 70. The concern for many is why the scientific advice in the UK appears to differ so substantially from that which is available to so many other countries around the world.
The rationale for the advice given to the British public appears to be based upon mathematical modelling of the current pandemic, coupled with predictions of the expected behaviour of the public in the face of restrictions that are enforced too early and thereby lead to “fatigue” when it comes to persevering with the same. Thereby any decisions taken are ostensibly deemed to be “scientific”, untainted by any political coercion or financial interests.
Epidemics and pandemics have been with us for a long time. although the overall impacts of such events appear not to have changed significantly since the earliest outbreaks of infectious diseases. Biblical pestilences, the Black Death of 1347-51, the Great Plague of 1665-66, and the Spanish flu pandemic of 1918 are all known to have caused severe disruption through the significant loss of life and and an overwhelming economic impact. Indeed, many mighty empires of the past came to an untimely end, solely as the result of uncontrollable epidemics.
The study of infectious disease outbreaks has, in recent times, been facilitated by various forms of mathematical analysis. In an earlier era, weekly counts of deaths during the Great Plague, including more detailed records of plague victims in the quarantined village of Eyam in Derbyshire, provided numerical data about outbreaks. This information was then used to map the progression of plague among the affected populations. Since then, sophisticated mathematical methods have been developed to help us better understand the transmission of infectious diseases. The knowledge thus acquired can then be harnessed to develop methods to control the further spread of disease.
Mathematical models can be used to predict the potential scale and severity of a particular epidemic, based on observations of those already infected within a given population. As Covid-19 is a newly recognised infection, there is no past reservoir of surveillance information to draw upon. Modelling has thus to depend on information gleaned from the current pandemic as it continues to evolve. Epidemics and pandemics may vary in the way they start, how they spread between people, how long it takes for infection to become established following exposure (incubation period), the duration of illness, period of infectivity and severity of disease in affected individuals or “cases”, the proportion of infected people without symptoms, the special characteristics of the population involved, not to mention the likelihood of death from infection (case mortality rate). All of these factors add to the difficulty of constructing models that are suitable for the study of individual outbreaks
Mathematical models can be thought of as abstract and simplified depictions of what is actually a complex disease process, and are at best only approximations to the bigger picture. The behaviour of an epidemic can be described in terms of a series of mathematical equations, which, however, cannot be expected to account for all aspects of the epidemic. Once created, a model can be used to predict the trajectory of an epidemic, including recognising when it is likely to peak, when the largest numbers of people are infected. The British response seems to be based around an enhanced and targeted response at the time of the anticipated peak. Furthermore, a model can then be used to determine the efficacy of any measures taken to control the epidemic at the chosen time.
To create a model of an epidemic, the host population is typically subdivided into three mutually exclusive groups or compartments, consisting of Susceptible hosts, Infectious hosts and Recovered hosts. This is the so-called SIR model. The numbers of people in each of these groups is then tracked, creating a model of disease transmission between the different groups. Certain assumptions are required to be made, which may unfortunately reduce the validity of the model when applied to what is actually happening.
Different models involve making different assumptions about the host population as well as the nature of the epidemic under study. Deterministic models are based on differential equations, which describe the dynamic relationships between variables that are changing continuously. These models assume that the behaviour of an epidemic is largely predictable, with the sizes of the susceptible and infectious populations varying as continuous functions of time . In reality, epidemics frequently comprise several events that vary randomly, thus requiring stochastic models for analysis. These models make use of a larger number of variables, or parameters, and use probabilities to define a range of possible outcomes. In other words, a precise prediction is actually not possible, giving rise to some uncertainty about the outcome.
The coronavirus epidemic is particularly difficult to model. The host population is global in dimension and continues to increase with time as waves of travellers continue to spread the infection in different directions. The infected host population is difficult to quantify, as mass testing is generally unavailable and yet many of those infected may be relatively well or only display mild and self-limiting symptoms.
Whatever the ultimate outcome of this pandemic, control of the spread of Covid-19 will have to rely for the time, at least in part, on the old-fashioned measures of isolation and quarantine (lockdown, curfew), given the lack of both naturally-acquired herd immunity and a protective vaccine. What is notable is that, although the pandemic is very much a global concern, different methods of control continue to reflect the differing approaches of various nation-states, frequently focused on restricting the movement of people across national borders. At times of global crisis, it seems that collaborative thinking is being subsumed by narrower national interests and a certain lack of “joined-up ” thinking.
Ashis Banerjee (retired consultant in emergency medicine, with an interest in both inanimate numbers and animate behaviour)