How mathematical epidemiology informs public health decision making


Public health is the role government and organisations play in maintaining the general health of a populace. This includes protecting and improving people’s health, as well as improving healthcare services.

Public health measures are all around us. Many of them feature in our everyday lives without us noticing them. For example, fluoride is added to water supplies in many areas of England to help reduce tooth decay, improve dental health and quality of life.

In the wake of the COVID-19 pandemic, the role of public health has become more pronounced. Here public health measures have been introduced to combat the spread of the virus, by limiting contact between infectious and susceptible individuals. These have included:

  • Closing all non-essential shops and services
  • Requiring individuals work from home where possible
  • Restricting outdoor activity
  • Having those with possible symptoms self-isolate

These measures have significantly impacted everybody’s daily lives but are aimed at protecting those most at risk from the virus and reducing the peak of the outbreak, to prevent patient numbers overwhelming the NHS. As it is believed that most of the population remains susceptible to the virus, it is important that whilst lockdown is eased, people continue to follow many of the public health measures, to prevent a second wave of infection. This means that our day-to-day behaviour will need to change long-term.

Mathematical epidemiology is the foundation that has steered the UK’s approach to slowing the spread of the virus. It has underpinned government decisions, from social distancing to the quarantining of those with symptoms.

Something that the majority of people would rarely think about is now one of the most influential factors in their daily lives. It is important that the general population have some understanding of why the public health measures are required and how they were determined, so that they understand and have confidence in their role in the pandemic. Without this, there is a risk that the public health measures will be largely ignored. Here we explore the role of mathematical epidemiology in determining public health measures.

What is epidemiology?

Epidemiology is one of the core pillars that makes up the UK’s public health approach. It studies the general health and levels of disease, both infectious and non-infectious, within a population. Its aim is to determine who, why and where people are affected by various illnesses.

In the case of each disease, the number and demographics of those affected are studied. For infectious diseases, how the disease is spread and the rate of infection are a key focus. Non-infectious diseases are investigated to identify factors that affect their prevalence within a population, including facets linked to the environment and social and economic status.

These analyses paint a picture of the population’s health and important contributing factors. This information can then be used to predict the future prevalence of diseases and the resulting impact on healthcare provision.

In some instances, the results indicate clear mitigation strategies. For instance, if people are being poisoned by nearby water contamination, then the source of the contamination should be addressed, and people treated for its effects. However, when socio-economic factors are involved, resolving issues can be complex, with no clear solution, and can take intervention over generations to resolve.

In the case of infectious diseases, mathematical models simulating the transmission of the disease through a population can be considered. These are not only used to predict the spread of the disease but used to determine the most effective intervention strategies and the level of implementation needed.

For example, in order to attain herd immunity and protect those in the population that cannot be vaccinated, a critical number of the population must be vaccinated to prevent transmission of the disease.

What is the relationship between epidemiology and public health?

Responsibility for public health in the UK has been devolved to each of its constituent countries. Each country has its own public health agency which determines the need and scope of public health measures there. In England, this agency is called Public Health England, sometimes better known by its acronym PHE.

PHE’s mission is “to protect and improve the nation’s health and to address inequalities”. This is achieved by working closely with other scientists and healthcare professionals to research, collect and analyse extensive amounts of epidemiological related data. The results and tools developed, such as mathematical models, enable them to advise the government, the NHS, and the population on public health issues.

This is done in several ways. Public health agencies may identify ways to improve public health or identify the source of healthcare disparities. They also protect public health by identifying potential threats and creating mitigation strategies to combat epidemiological events.

For example, monitoring obesity in the population revealed levels were rising which could ultimately strain healthcare services. So in response, the NHS developed  the Change4Life campaign, aiming to educate people on how to maintain a healthy lifestyle.

Pandemics in particular have always been a threat to public health. And, as demonstrated by, the Spanish flu in 1918, can be extremely deadly.  As a result, epidemiologists have been working with public health agencies long before COVID-19, to prepare mitigation strategies for such an eventuality.

Mathematical epidemiology allows the construction of mathematical models that represent the impact of biological events on a population, including any associated human behaviours, e.g. healthcare seeking behaviours. Such events include biological attacks and outbreaks of infectious diseases.

The models can be used to predict the rate at which the population becomes afflicted and the number at each stage of infection over time, including those in hospital and the number of deaths. This allows the impact on healthcare provision and the population to be assessed. Using mathematical epidemiology, it can therefore be determined if and what intervention may be required to most effectively protect people’s health. Response strategies can be pre-planned based on the model predictions of what’s likely to happen, and authorities can be prepared for such an event.

How do mathematical epidemiology models work?

Mathematical models abstract reality into equations that can be solved to produce values for a desired output, based on available knowledge. In epidemiological models, the equations aim to simulate how biological events evolve over time. This includes the spread of the contaminant or contagion, such as through airborne or direct contact transmission, the number exposed, and their associated behaviour.

Once a set of equations have been defined, different scenarios can be explored for each biological event. Each scenario will differ according to its parameters and initial conditions. If the contaminant or contagion is one that scientists are already aware of, then some parameters will not need to be estimated, as they are directly associated with the substance itself.

When a real biological event occurs, multiple types of data, from multiple sources are fused together to provide best estimates for the parameters and initial conditions. The models can then be used to produce predictions that represent the most likely outcomes of the situation, helping authorities plan the most appropriate response.

In the case of an infectious disease, like COVID-19, a compartmental model is one form of mathematical model that can be utilised. It aims to model the spread of the infection through the population over time, calculating the average number of people at each stage of the disease, and the number that will need hospitalisation.

Parameters used in the model may include:

  • The probability of catching it, given contact with an infected individual (pairwise infectious contact rate)
  • The average number of people infected by an infected individual (basic reproductive number, R0)
  • The average duration of each stage of infection
  • The proportion of people who will need hospital treatment.

If the disease is unknown, these factors will need to be estimated. Initial conditions for the model can include the initial number infected and their locations.

The spread of an airborne contaminant can be modelled utilising weather forecasts. Epidemiologists can use this information to determine the dose that individuals in different regions have received and the effect it will have on them. This could then be fed into compartmental models, similar to those used for infectious diseases, to determine how many people are experiencing different symptoms and will require treatment, over time.

By exploring a range of scenarios and their impact on the populace in advance, mathematical epidemiologists can determine the best response to such events and appropriately prepare. They can also use the models to track ongoing incidents, helping authorities to target their response, such as where and when to impose quarantine and provide extra healthcare resources.

How has epidemiology been used during the Coronavirus pandemic?

Government officials have been working with scientists at public health agencies and universities around the UK, to monitor the spread of the virus and plan how to combat the pandemic.

By analysing data, they determined the stages of infection, estimated parameter values, and the proportion of people requiring treatment. Disease models could then be created to forecast the future spread of the virus, the number affected and the resulting impact on healthcare provision.

Based on these results, combined quarantine and lockdown measures were implemented by the UK government. This represented a multi-pronged approach aimed at slowing the spread of the virus. Here the goal was to protect those most at risk from serious complications if they caught the virus and protect healthcare services from being overwhelmed by seriously ill patients. Hand-washing was also recommended to the public in order to minimise the chance of infection after contact with the virus.

Epidemiological models have been integral to the UK’s response to the Coronavirus pandemic. They have been used to track the progress of the virus throughout the pandemic and predict its future progress with and without intervention.

CrystalCast, a capability developed by a Dstl-led effort and supported by Riskaware, is a disease forecasting tool that has played an important role in informing the UK government on COVID-19 predictions to support response strategies. It delivers consolidated forecasting from a broad spectrum of model prediction data to feed into the weekly SAGE and devolved nation government meetings, informing on trends as well as predicted behaviour of the virus.

Based on information such as this, the level of intervention required, the most effective mitigation strategies were identified. Models continue to be used to track and predict the spread of the virus, guiding the government with their timeline for slowly re-opening the country.