COVID-19 inequalities in England: a mathematical modelling study of transmission risk and clinical vulnerability by … – BMC Medicine
April 16, 2024
We developed an age-stratified dynamic transmission model for SARS-CoV-2, which was further stratified by IMD decile, and by urban or rural classification in England. Here, we detail how the model was modified to incorporate the characteristics of each decile and geography.
Each epidemic was simulated on the population of a given IMD decile in either an urban or rural area, to account for the distinct underlying age structures in these areas. We used 17 age groups (01, 15, every 5 years to 75, and over 75). The mid-2020 (30 June) age-specific population of each lower layer super output area (LSOA), which is on average 1500 people, was linked via LSOA codes to their IMD decile and urban/rural classification (where urban is defined as a settlement with over 10,000 residents) [16,17,18,19]. We calculated the size of each age group, specific to each IMD decile and geography, and used this to determine the average age structure of each IMD- and geography-specific population, (n=({n}_{1},dots ,{n}_{17})), where (sumlimits_{a=1}^{17}{n}_{a}=1) in each population. We also calculated the median age for each urban and rural IMD decile and the proportion of each IMD decile residing in urban or rural LSOAs (Additional file 1: Section 1).
To define contact between the age groups, we used age-specific social contact data for the United Kingdom (UK) for physical and conversational contacts, accessed via the socialmixr R package [20, 21]. The contact matrices are highly age-assortative, with the highest daily contact patterns occurring between individuals in the same age group for those aged 519. We projected the contact patterns onto the age structure of each IMD- and geography-specific population in 2020, using the density correction method, by constructing an intrinsic connectivity matrix and scaling this matrix to match the populations age structure [22].
The intrinsic connectivity matrix was calculated from the 2006 UK contact matrix ({M}^{2006}={left({M}_{ij}^{2006}right)}_{i,j=1,dots ,17}) and age structure ({N}^{2006}=left({N}_{1}^{2006}, dots ,{N}_{17}^{2006}right)) as follows:
$$Gamma ={left({Gamma }_{i,j}right)}_{i,j=1,dots ,17}$$
$${Gamma }_{i,j}={M}_{ij}^{2006}frac{sum_{a=1}^{17}{N}_{a}^{2006}}{{N}_{j}^{2006}}$$
The new contact matrix for a population with age group sizes (N=left({N}_{1},dots ,{N}_{17}right)) and proportions (n=left({n}_{1},dots ,{n}_{17}right)) had entries:
$${M}_{ij}=frac{{Gamma }_{ij}{N}_{j}}{sum_{a=1}^{17}{N}_{a}}={Gamma }_{ij}{n}_{j}$$
We separated infections of SARS-CoV-2 as in [23], into clinical or subclinical cases. Clinical cases of COVID-19 are infections that lead to noticeable symptoms such that an individual may seek clinical care. Subclinical infections do not seek care and are assumed to be less infectious than clinical cases. We defined a populations clinical fraction as the probability of an individual in the population developing a clinical case of COVID-19 upon infection. Here, we related an individuals probability of being a clinical case of COVID-19 to the self-reported health status of their IMD- and age-specific population in England, as a proxy for the relative presence of comorbidities in each population, and then examined how differences in self-reported health status by IMD decile, coupled with differences in age distribution, affect the burden in each IMD decile.
To define health status, we used data from the 2021 Census, specifically the question How is your health in general?, with response options of very good, good, fair, bad, and very bad [24]. This is provided by the Census stratified by IMD and by age. We then defined health prevalence as the proportion of individuals reporting very good or good general health, stratified by the same age groups and the deciles of IMD:
$$Health;prevalence;=;frac{Number;in;'Very;good';health;+;Number;in;'Good';health}{Number;in;all;health;statuses}$$
(1)
To map a populations health prevalence to clinical fraction, we used locally weighted regression (LOESS), which fits a smooth curve without any assumptions about the underlying distribution of the data, trained on age-specific health prevalence data from Census 2021 and age-specific clinical fraction values from Davies et al. [23, 24]. Any populations with health prevalences outside of the training datasets range were assigned the most extreme clinical fractions found by Davies et al. [23], to avoid extrapolation outside of observed values. Health prevalence was highest in children, but children have separate risk factors for severe disease (such as smaller airways), and children under 10 have been found to be subject to a higher risk of clinical COVID-19 cases and a greater infection fatality ratio (IFR) [23, 25] (as observed for other infections such as influenza [26]). Therefore, we fixed the clinical fraction of the 09 age group at 0.29, matching that found by [23].
The transmission model includes a single SARS-CoV-2 variant, no existing immunity in the population, and natural history parameters drawn from the first wave of the pandemic. We considered the non-pharmaceutical intervention (NPI) of school closures and also explored the effect of vaccinating adults over the age of 65. We developed an age- and IMD-stratified deterministic compartmental model in R (version 4.3.1) (Fig. 1c). There is no mixing between IMD deciles in the model. The aim is to demonstrate the importance of health prevalence and differences in age and social mixing in epidemic impact, rather than to reproduce the COVID-19 epidemic in England.
a Proportion of each geography-specific IMD decile in each age group. b Age- and IMD-specific health prevalence (1, most deprived decile; 10, least deprived). c Age-stratified SEIRD model, specific to IMD decile and geography. Subscript a denotes age-specificity, c clinical parameters, and s subclinical parameters
Individuals are first assumed to be susceptible (S) and become exposed (E) but not yet infectious after effective contact with an infected individual (Fig. 1c). Each exposed individual then progresses to one of two infected states: subclinical infection (Is) and clinical infection, which is represented by a pre-symptomatic (but infectious) compartment (Ip) followed by a symptomatic compartment (Ic). Each individual then moves into the recovered (R) or dead (D) compartment, at which point they are assumed to no longer be infectious and to be immune to infection. This susceptible-exposed-infectious-recovered-dead (SEIRD) is an extension of [23], with the addition of a D compartment. We ran the epidemic for 365 days, which allowed the completion of each epidemic in each decile and geography. Each epidemic was run on a synthetic population of a fixed IMD decile and urban/rural geography, with no births, non-infection-related deaths, or ageing between the age groups, as the time frame of each epidemic was less than a year. The model also assumed that contact patterns remain constant throughout the epidemic.
The force of infection in age group k is given by:
$${lambda }_{k}=psum_{a=1}^{17}{M}_{ak}frac{{Ip}_{k}+{Ic}_{k}+{xi Is}_{k}}{{n}_{k}}$$
where (p) is the probability of a contact between an infected and susceptible individual resulting in transmission of infection, ({M}_{ak}) is the mean daily number of contacts that an individual in age group a has with individuals in age group k, and (xi) is the relative infectiousness of subclinical cases. The age-specific clinical fraction is denoted by ({pi }_{a}) and depends on the IMD decile. Rates of transition from each disease state are given in Table 1.
We assumed the relative subclinical infectiousness ((xi)), to be equal to 0.5, and tested this assumption in a sensitivity analysis (see Additional file 1: Section 12). The transmission probability during a contact was assumed to be (p=0.06) as in [23]. The remaining parameter estimates were taken from [23] where possible, to replicate the conditions used to derive the clinical fraction estimates. The mortality probability of subclinical infections was assumed to be 0 for all age groups ((a)). The age-specific probability of mortality of clinical cases was estimated using age-specific IFRs (left({phi }_{a}right)) found by Verity et al. in 2020 [27] (Additional file 1: Table S4). As the IFR is ({phi }_{a}={pi }_{a}{mu }_{ca}+left(1-{pi }_{a}right){mu }_{sa}={pi }_{a}{mu }_{ca}), since ({mu }_{sa}=0), the age-specific clinical mortality probabilities were estimated by:
$${mu }_{ca}=frac{{phi }_{a}}{{pi }_{a}}$$
where ({pi }_{a}) is the age-specific clinical fractions for the general population in [23] (Additional file 1: Table S4).
We calculated the total infections, clinical cases, and fatalities per 1000 people, the peak number of clinical cases per 1000 people, the IFR, and the basic reproduction number (R0) for each IMD decile in urban and rural areas. We also calculated age-standardised measures of total infections, clinical cases, and fatalities within a specific geography for increased comparability. The age-standardised results were of the form:
$${D}^{{text{standard}}}left(365right)=sum_{a=1}^{17}frac{{D}_{a}left(365right){n}_{a}^{u}}{{n}_{a}}$$
where ({n}^{u}=left({n}_{1}^{u},dots ,{n}_{17}^{u}right)) is the standard urban population, defined as the proportion of people living in urban LSOAs who are in each age group, similarly ({n}^{r}=left({n}_{1}^{r},dots ,{n}_{17}^{r}right)) for rural areas.
R0 in each IMD decile in urban and rural areas was calculated as the absolute value of the largest eigenvalue of the next-generation matrix N:
$$N={left({N}_{ij}right)}_{i,j=1,dots ,17}$$
$${N}_{ij}={pM}_{ij}left({pi }_{j}left(gamma +{r}_{c}right)+xi left(1-{pi }_{j}right){r}_{s}right)$$
To determine the epidemic burden attributable to the difference in underlying health status between IMD deciles, we created the counterfactual health prevalence scenario, where all deciles were assigned the age-specific health prevalence of decile 10 (the least deprived). We calculated the total clinical cases and fatalities in each IMD decile under this assumption. In order to reflect the size of each population (while each IMD decile comprises 10% of the population of England, geography-specific IMD deciles vary widely in size, see Additional file 1: Table S1), we scaled mortality to mid-year 2020 population sizes and totalled over the 20 populations.
We also created the counterfactual scenario of constant age structure, where we held the age structure constant at the average of each geography-specific England population, independent of the IMD decile. This allowed us to determine the impact of clinical vulnerability separately from the differences in age distribution in each IMD decile. The health prevalence by age remained at the IMD-specific value.
School closures were a major NPI implemented in the UK during the pandemic, and were implemented evenly across all IMD deciles, unlike some other contact-reducing interventions. We therefore modelled school closures to determine the impact of this intervention across IMD deciles. To quantify the potential differences in the impact of school closures in different IMD deciles, we calculated the effect of school closures on R0 and total fatalities. The social contact data used is a combination of location-specific contact matrices, defined by home, work, school, and other locations. We removed the school-specific contacts from the contact matrix (retaining contacts in home, work, and other locations), re-projected onto the 2020 age structure, and recalculated the next-generation matrix, N, and its largest eigenvalue, R0. While assuming that the closure of schools results in a complete subtraction of school-specific contacts may not be realistic (as some contacts would likely be replaced by social interactions in other locations [28]), the results demonstrate the maximum potential impact of school closures.
We simulated the closure of schools after a certain cumulative proportion, P, of the population developed clinical COVID-19 cases. The use of cumulative clinical cases as a threshold for implementation is reflective of using total confirmed cases as a measure of the size of an early epidemic. We assumed a value of P = 0.05 but tested different values in sensitivity analyses (Additional file 1: Section 11).
To quantify the relative impact of vaccination rollouts on populations of different levels of deprivation, we calculated the change in mortality rates in each population after vaccinating all adults over the age of 65. This correlates with the earliest vaccination programmes in England, where the first target populations were individuals of older ages. We assumed that vaccination reduced the likelihood of an individual developing a clinical case of COVID-19 upon infection but did not prevent infection. We assumed 76.5% vaccine efficacy against symptomatic infection [29] and reduced the clinical fraction of vaccinated individuals in line with this estimate. To estimate the maximum impact of vaccination, we assumed coverage in over 65s of 100%. We then calculated the change in mortality rates and the number of deaths prevented in each population. We also calculated how many vaccine doses would be given to each population.
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COVID-19 inequalities in England: a mathematical modelling study of transmission risk and clinical vulnerability by ... - BMC Medicine
