COVID-19 in Northamptonshire: a summary based on mortality data from March to July 2020

By Nick Petford and Jackie Campbell, University of Northampton

Since the global outbreak of SARS-CoV-2 in December 2019, the UK has been one of the hardest hit nations in reported mortality rates, with deaths per 1 million of the population currently third behind Belgium and Peru. Lockdown in the UK started on March 24, 2020, several weeks later than elsewhere in mainland Europe.

So how has Northamptonshire, and its subdistricts, faired in the five months since lockdown, compared to the East Midlands and the UK more generally? And what can we learn about its impact on the community using publicly available statistics and mathematical modelling that might help manage the situation, now and in the future?

These are the questions that Professor Jackie Campbell, a statistician in the Faculty of Health Education and Society, and I have been asking. Our provisional results, looking in detail at mortality rates due to Covid-19 in Northamptonshire, can be found in a paper submitted here to medRxiv (pronounced “med-archive”) a specialist archive for preliminary medical-related papers that are undergoing peer review but have not yet been published in a research journal.

Our goal is to combine openly available public health data with mathematical models for disease spread, to help prepare for better long-term regional planning in event of a second (or more) waves of Covid-19, should they occur. Given the increase in Covid-19 cases in Northampton, and the possible threat of local lockdown, it is more important than ever that available data are used to seek to understand how the virus is spread in our local area.

Fig. 1. Northamptonshire showing subdistricts and new unitary structure from 2021.

What data are available?

The UK Office for National Statistics (ONS) is responsible for collating and distributing statistical data for the UK. Although the available Covid-19 mortality data are aggregated together, it is possible to get breakdowns by age and sex (male/female) at a coarse (e.g. county and district) level, but more detailed information on, for example, ethnicity, date of death and postcode, require special clearance from the ONS, assuming the data have been collected at local level by hospitals or other public health outlets. Thus, while right now our analysis is limited, publicly available mortality data in Northamptonshire can be benchmarked nationally and regionally to help set the context for more detailed analysis to follow, once approvals have been granted.

Fig. 2. Mortality rates in Northamptonshire by district, week 12 (March 16) to week 28 (July 12).

Some may be wondering why are we concerned mostly with death (mortality) rates? Isn’t this a bit insensitive? After all, each data point on the charts represents a life lived and now taken, perhaps prematurely, by a deadly virus. While true, there are two responses to this. Firstly, deaths are by far the most reliable data we have. And that is with caveats including uncertainties about ‘dying with’ versus ‘dying because’ of Covid-19, and the source and timing of the data themselves. As we shall see, our model suggests that the number of recovered cases could be much higher than expected. Also, mortality is not indiscriminate. Covid-19 deaths are confined largely to the elderly (65 years+) with pre-existing conditions. Understanding the baseline is thus vital, as this tells us what is happening on average. Knowing what happens on average, rather than the anomalies and outliers picked up by the media, allows us to make rational interventions.

We started our analysis using data on age standardised mortality rates involving Covid-19 over the period March to June 2020, published on July 24 by the ONS for each of the seven districts and local authorities in Northamptonshire. However, as the existing boroughs and district councils are to be replaced by two unitary authorities of West and South Northamptonshire in 2021, we also wanted to look also for any differences between these.

Northamptonshire has a population of 753,278 (Mid-2019, ONS), with Northampton, the major urban centre, comprising approximately one third of the total. The 2011 census showed the county split evenly between males (49.5%) and females (50.5%), with 18.1% of the population aged 65 years and older. Nearly 90% of the population are white (British or other).

Analysis

When disaggregated into the seven comprising districts it becomes clear that Northampton has the highest Covid-19 mortality rate. This is statistically different, at the 5% level, from all other local authority areas except for Corby. South Northamptonshire has the lowest Covid-19 mortality rate, although only the differences with that of Northampton and Kettering are statistically significant. Compared regionally, Northamptonshire has a statistically higher Covid-19 mortality rate than for the East Midlands as a whole. Both the East Midlands region and Northamptonshire have statistically significantly higher rates than for England as a whole.

Fig. 3. Age-standardised death rates (per 100,000) from Covid-19 for all sexes between March-June 2020. Blue circles indicate the rates for the current Northamptonshire local authorities, red circles denote regional comparators and green circles are the rates for the new Unitary Authority areas.

However, if the new Unitary Authorities were in place, then there would be no statistically significant difference in the Covid-19 mortality rates between them. This is because Northampton, with the highest rate in the county, and South Northamptonshire, with the lowest, are both in the West Northamptonshire Unitary Authority. Regarding place of death, the majority (c. 65%) have occurred in hospital.

There is also a relationship between the population density in each district and the standardised number of fatalities. This is perhaps not surprising, as people who live closer together stand more chance of transmitting the virus. Northampton has the highest population density per square kilometre in the county and highest death rate, South Northants has the lowest death rate and second lowest population density.

Fig. 4. Northamptonshire districts by population density and mortality rates. The R² of 0.785 means 78.5% of the variation in mortality rate is explained by population density.

How deadly has Covid-19 been so far?

From watching the news, you would be forgiven for thinking that leaving your house is a life-threatening event. Unless of course you end up one of the 6,000 people who die in the UK every year from accidents in the home. The daily reported death tally due to Covid-19 needs to be put into context, alongside other activities which result in fatalities. Registered deaths due to Covid-19 in Northamptonshire over the period of study are 715 out of a total of 2902. Thus, about one quarter of all registered deaths between March and July were Covid-19 related, giving an annualised rate of about 12 per month, four times lower than non-Covid deaths of 48 per month. However, the Covid-19 rate is not randomly distributed in the population. Instead it is confined mostly to c. 18% of the population who are aged 65 and over, a pool of about 130,000 people. Put another way, 4 out of 5 people have a vanishingly small chance of dying from Covid-19, and within the under 20 age group (16 deaths so far in England and Wales), those aged between 1 and 14 are only marginally less likely of being killed by lightning. Compare that to the 1916 polio outbreak in New York where 90% of fatalities were in children under 5. It was only in 1955 that a vaccine was found.

In order to communicate Covid-19 mortality risk in context, we have taken up the idea, proposed by the mathematician John Allen Paulos, who suggested using a logarithmic scale (sorry more maths!), like the Richter scale used by geologists to measure the power of earthquakes, to compare different outcomes more easily. The smaller the number, the bigger the risk, or likelihood, of the event occurring. Our ‘Safety Scale’ is shown in the table below. But because it is in log10, going from 1 to 2 (or going up by 1 anywhere on the scale), is a ten-fold increase.

Paulos also makes the point — perhaps rather unkindly — that a common trait in those who struggle to think quantitatively is a tendency to place undue significance on exceptions to the rule. This personalisation bias may explain why people respond differently to the same (average) risk. That said, because they already exist in the world independent of Covid-19, your gross risk exposure is the sum of everything listed plus all other life-threatening ailments in circulation. Yet despite these odds, average life expectancy in the UK has increased by 10 years since 1960, from 71 to 81 years.

There is however a clear warning in the data. The most vulnerable 65+ group is set to increase to 26% of the Northamptonshire population by 2026. Combined with high obesity rates, this means the population overall may become increasingly more susceptible to future Coronavirus outbreaks.

How can mathematical modelling help?

It might not be immediately obvious what the link between maths and a lethal virus is. After all, calculus can’t look after or cure sick people. However, it has played a fundamental role in helping public health officials understand the spread of disease, in both human and animal populations. The original formulations were derived in the early 20th century by Kermack and McKendrick among others, and have been used and improved upon since then, for example in modelling the 2001 UK Foot and Mouth outbreak and the 2009 H1N1 influenza pandemic.

Let’s take a brief look at how it works.

Imagine a population — say a country or a city — and divide it into four ‘compartments’ made up from susceptible S, exposed (meaning infected but not yet infectious) E, Infectious, I and recovered R inhabitants. This is the basis of the SEIR model. Individuals move (flow) between each compartment, passing on the disease, and recovering, at a rate determined by four interlinked ordinary differential equations. This is where the mathematical bit comes in.

By solving the differential equations that link each box above, the model allows us to predict how fast the disease will spread if left to its own devices, or ‘explore’ the effect of changing key variables that govern the spread of the virus as a computer experiment. Nobody gets hurt, and we can look at how the population responds to changes in for example, the transmission rate between infectious individuals (β), the average number of days a person is infectious (n), and the recovery rate γ (1/n). These variables are related via:

where R₀ is the basic reproduction number we have all heard so much about over the last few months.

Using the SEIR model we have looked at two scenarios. One is where the virus is left to run its course after the first registered deaths in March, for a period of 120 days, that is, up until late July 2020.

The second model follows the UK Government response with lock down mitigations imposed on March 24. It mimics the effects of social distancing by reducing the transmission rate by 40% from its pre-lockdown value. Why 40%? Remember, the SEIR model is calibrated against the most reliable data we have — the actual number of deaths. In simple terms, 40% gives the best fit in the model to the actual number of registered ONS fatalities in Northamptonshire over the same period.

Fig. 5. SEIR model for Northamptonshire calibrated against mortality rate showing numbers of cases and deaths, along with exposed, infectious and recovered, for a simulation time 120 days. (a). Do nothing case. (b). With reductions, starting March 24, 2020.

So, what does the model tell us? Allowed to spread uninhibited, total estimated deaths in Northamptonshire exceed 4500 against an actual (ONS registered) of 715 to the end of July, over six times higher than reported. The potential number of infected individuals is reflected in the number of recovered (R) cases. The model also predicts up to136,000 discrete exposures to the virus over the simulation period, equating to approximately 18% of the total population. This value is far in excess of cases reported for Northamptonshire and as such must be treated with caution. It is however consistent with evidence for significant underreporting of infections during the initial phase of the pandemic. For example, only around 15% of active cases were registered during the initial outbreak in Wuhan. And new research by Imperial College suggests that 13% of the population of London has already contracted and recovered from the virus.

Implications for vaccination and herd immunity

Mathematical analysis also provides unexpected insights not picked up from studying only raw data, including the fact that vaccination against a disease can work without making everyone immune.

It works like this. The critical fraction (C’) of the total susceptible population (S) needed to be vaccinated to ensure herd immunity is a threshold value equal to 1–1/R₀.

At the onset of a new infection where there are no prior cases, it is reasonable to assume S = C’, the proportion that require vaccination. In this case, the number of people needing vaccination is controlled by the basic reproduction number.

For example, if R₀ = 3.0, like the initial value in our SEIR model, then for Northamptonshire, C’ = 0.66, meaning 66% of the population require vaccination to achieve herd immunity, assuming it is 100% effective.

However, the SEIR model reveals a sizeable (hidden) fraction of recovered cases (R). Should these individuals still be counted as requiring a vaccination, or should they be removed from the pool? Put another way, does infection and successful recovery impart a level of immunity? This is a critical (and yet unanswered) question.

If yes, and these individuals can be excluded, it reduces the overall size of the susceptible population by some fraction up to a maximum defined by total number of recoveries. The problem is, we don’t know what the size of this immune fraction is. Again, maths can help. Instead of looking for a single, unique value, we can use the model to predict a range of likely critical thresholds based on what we know about the basic reproduction number and estimated recovery rates, plus the assumed effectiveness of any future vaccine, set arbitrarily here at 80%.

In the SEIR model, the differential equation for the recovery R is:

where (after integrating both sides by t),

allowing the number of recovered individuals to be simulated over time. The graph in Fig. 6 shows the output. Depending upon the mix of variables, the number of individuals requiring vaccination to prevent a further outbreak (blue shaded) ranges from about 14% to 84% with a model average of 43%.

Fig. 6. Plot showing estimated range (blue) in Covid-19 vaccination thresholds for Northamptonshire.

Interestingly, new research suggests that a significant fraction of people worldwide may have some level of pre-existing immunity (so-called ‘memory cells’ formed after previous flu and coronavirus infections) against SARS-CoV-2. Similar immunity was found in the population at large against H1N1 in 2009.

Finally, caution is required when using data early in the pandemic, as results may need to be revised as further information comes to light. Future research work by the University will seek to look more closely at the geographical and demographic variations across the county to help refine SEIR models and provide a deeper understanding of the dynamics of Covid-19 in Northamptonshire.

References

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Note: MedRxiv publishes preliminary scientific reports that are not peer-reviewed and should not be used as a conclusive guide to medical or public health practice.

Biographies

Nick Petford is Vice Chancellor of the University of Northampton. Although a geologist by training he has published several medical-related research articles on topics malaria prevention, mathematical modelling of blood flow in stroke victims and the three-dimensional structure of animal skin. He is also Chair of Northamptonshire Health and Wellbeing Board, one of over 100 statutory bodies responsible for developing integrated health and social care strategies and reducing health inequalities. View ORCID Profile

Jackie Campbell initially qualified as a physicist before working as a researcher into the processes of pain and pain relief at the Pain Relief Institute in Liverpool. She has worked in the healthcare sector of higher education since 1987 and is the part-time Professor of Neurophysiology at the University of Northampton and is Chair of the NIHR East Midlands Research Design Service Regional Advisory Board. She is a chartered statistician, has served as the statistician member of an NHS Research Ethics Committee and teaches statistics and research methods to doctoral level. She is a reviewer for many major funding bodies and academic journals, including membership of the statistical review panel for The Lancet group. View ORCID Profile