Keywords
COVID-19, prevalence, age, mixing, mitigation, lockdown, back-calculation, back-projection
This article is included in the Coronavirus (COVID-19) collection.
COVID-19, prevalence, age, mixing, mitigation, lockdown, back-calculation, back-projection
Coronavirus disease 2019 or COVID-19 is a novel human respiratory disease caused by the SARS-CoV-2 virus and was first identified in 20191. The surveillance of COVID-19 cases in Ireland was integrated into the existing national Computerised Infectious Disease Reporting (CIDR) system when the notification of the disease was made mandatory in February 20202. Since the first case of COVID-19 in Ireland was recorded policy makers have introduced mitigation measures to control the spread of infection3. These measures included public health advice to stay and work at home, restrictions on travel, the closure of educational settings, the cancellation of routine hospital procedures and the isolation and contract tracing of cases identified through testing centres3. It has been observed that during these periods of increased and subsequent decreased mitigation measures the reported number of positive cases has decreased and increased in line with the implementation and removal of the measures. These increases and decreases are referred to as epidemic waves4 and their relationship to the mitigation measures have been clearly established and modelled in Ireland5.
Infection we know is spread by both known cases and hidden, undetected asymptomatic cases. Asymptomatic individuals in the context of COVID-19 are people who are carriers of the virus but display no clinical symptoms. Current evidence reveals that this population is a major contributing factor to the spread of the disease, while escaping detection by public health surveillance systems5. As a result of this lack of detection public health systems can record only the daily incidence of new known cases and there is little or no knowledge of the actual scale of the hidden cumulative prevalence of all infections both asymptomatic and symptomatic. Furthermore, as governments plan for the roll out of imminent national immunisation programmes, the need to know the scale of the hidden prevalence and hence knowledge of the level of immunisation required is essential to produce the so called ‘herd immunity’ defined as ‘the protection of populations from infection which is brought about by the presence of immune individuals’5,6.
The aim of this research was to build on previous modelling work and provide an estimate of the hidden and asymptomatic prevalence of COVID-19 in Ireland during the second wave of infection from October to December 2020. Methods while developed nationally are applicable globally. The objectives were to provide a descriptive and comparative analysis of the first and second waves; to use the back-calculation method to provide an estimate of total prevalence of cases during the second wave and an estimate of the ratio of unknown asymptomatic cases to known symptomatic recorded cases and finally to provide recommendations for future research to enable effective immunisation modelling and planning.
A plot of the five-day moving average of the reported numbers of COVID-19 cases from the first recorded case on the 29th of February 2020 to the 8th of December 2020 was prepared. Descriptive statistics illustrating the numbers of known cases, hospitalised cases, intensive care cases and deaths during this period were computed and cumulate cases by age group were derived. The Chi-squared test of association was used to test the independence of the relationship between the number of cases during an epidemic wave and the numbers of cases reported by age group. This statistic was also used to test the relationship between the number of cases during an epidemic wave the number of hospitalised cases by age group.
Following the statistical analysis of the known cases from the Irish reporting system the back-calculation method was implemented to estimate the numbers of asymptomatic and unknown cases. The method of back-calculation also known as back-projection is well documented and implemented internationally for a wide variety of infectious and social epidemics, from HIV/AIDS to bio-terrorism to heroin use7–10. Previous use of the back-calculation model to predict the incidence and prevalence of disease, particularly AIDS, in the United States, the United Kingdom and Ireland is well documented11–14. The method is known as an indirect method and working with observed symptomatic cases and the known incubation period, the model predicts minimum estimates of the hidden numbers of infected cases. The model is given by,
Where CT(t) describes the change in the incidence of the treated and known cases over a defined time period, f(s) is the incubation period distribution of the disease and CU(t) is the unknown number of cases at time t we wish to solve for. The prevalence of the unknown cases over the defined time period is then given by,
Given varying forms in the growth of the known cases CT(t) and the incubation period f(s), the back-calculation model can be solved analytically as in Comiskey7,8, Comiskey and Hay15, Dempsey and Comiskey10,16 or numerically as in Comiskey and Ruskin13. The details of the incubation period distribution for COVID-19 f(t) are provided by Banka and Comiskey17 who in their international scoping review found a mean incubation period of 6.7 days with a standard deviation of 4.0 days. The mathematical solution of the back-calculation equation when f(t) is described by the Gamma distribution as identified by Banka and Comiskey (2020) and given by Γ(α, λ) when α = 6 and when α = 3 were originally provided by Dempsey and Comiskey10,16 and latterly for early COVID-19 modelling in Ireland by Comiskey, Snel and Banka18. These solutions were implemented here with data on daily COVID-19 cases reported to the national Computerised Infectious Disease Reporting (CIDR) system and available at website https://covid-19.geohive.ie/datasets/d8eb52d56273413b84b0187a4e9117be_0
This research received ethical approval from the Faculty of Health Sciences at Trinity College Dublin, The University of Dublin, Ireland.
A plot of the number of daily cases reported to the national system from the 29th of February to the 8th December 2020 are provided in Figure 1. From this we can clearly see that Ireland has recorded to date two epidemic waves each with an increasing and decreasing phase.
From the reported data we can see that during wave one and two a total of 74,439 cases were reported and perhaps more importantly we can also see that greater numbers of individuals were infected within wave two. A total of 25,189 cases were reported in wave one and this almost doubled and increased to 49,250 cases being reported in the second wave. A comparison of the reported cases by age distribution across the two waves is provided in Table 1.
A comparison of the distribution of known cases by age between wave one and wave two is provided in Table 2. We can see that there was a significant change in the age distribution of cases between the two time periods. Within wave one those aged over 65 years of age accounted for approximately between one fifth and one quarter of all reported cases while those under the age of 25 years approximately accounted for one tenth of all cases. Within wave two however this situation reversed with those over the age of 65 accounting for approximately one tenth of all cases and those under the age of 25 accounting for one third of all cases.
Clearly the dynamics of spread changed in wave two as societal mitigation measures were relaxed and prevention measures within older person settings were enhanced. Exploring wave two in more detail using the back-calculation method we initially fitted, using simple regression techniques, separate curves CT(t) to all of the known cases of COVID-19 during both the increasing and decreasing phase of wave two. This included cases where the age was unknown. These curves included exponential, logarithmic, quadratic and cubic models. Details of the best fitting curves amongst all curves fitted are provided in Table 3.
The solutions provided by Comiskey, Snel and Banka18 for the unknown number of cases CU(t) given the best fitting curve CT(t) were then applied and the results are provided in Table 4. From Table 4, we can see that regardless of the exact nature of the Gamma distribution chosen for the incubation period, the model predicts that for each known infectious case reported there exists approximately one unreported asymptomatic infectious case contributing to infection within the population.
The principal finding from this study illustrates that in Ireland the true prevalence of the scale of the COVID-19 epidemic may be twice that which has been recorded through testing. Results for the period from early June 2020 to early December 2020 suggest that the while the prevalence of known cases was approximately 48,000, the asymptomatic prevalence was estimated to be approximately a further 46,000 cases. Furthermore, a detailed analysis of the known number of cases illustrated that as of early December 2020 Ireland has experienced two COVID-19 epidemic waves. The second wave involved almost twice the numbers of cases as the first. Within the first wave most infections occurred among those aged 65 years and older. The age profile of the second wave was significantly different to the first and most cases were observed within those under the age of 25 years.
Results presented must be interpreted in light of their limitations. Reported numbers presented were not adjusted for potential reporting delays. In addition, results of the back-calculation method were computed solely for an incubation period described by a Gamma distribution and other distributions may be equally as applicable.
However, given these limitations the results presented do provide new and additional knowledge on the scale of asymptomatic prevalence within Ireland. Given the estimates of the asymptomatic prevalence during the second wave, and given that known cases are significantly younger than previously, and according to one study directly related to increases in the movement of people5 there is a clear need to focus on transmission between and more importantly from those in younger age groups. The impact of mixing patterns on the spread of disease from one age group to another is well established and it is known that mixing between age groups carries far greater risk to the spread of disease than mixing within age groups19. It is these mixing patterns which need to be addressed while Ireland awaits vaccine role out and avoids a potential third wave of a COVID-19 epidemic. Further research is needed on asymptomatic prevalence within age groups. Additional research illustrating the role of mixing patterns on spread needs to be disseminated to the wider public to adequately inform them how personal modifications in behaviour can contribute to the control of the epidemic. While universally imposed lockdowns and mitigation measures may be essential, personal behavioural mixing choices are powerful protectors.
Publicly available data was accessed from Our World in Data webpage: https://ourworldindata.org/coronavirus-data and the Health Protection and Surveillance Centre (HPSC) Computerised Infectious Disease Reporting (CIDR) system and available at website https://covid-19.geohive.ie/datasets/d8eb52d56273413b84b0187a4e9117be_0
Is the work clearly and accurately presented and does it cite the current literature?
Yes
Is the study design appropriate and is the work technically sound?
Partly
Are sufficient details of methods and analysis provided to allow replication by others?
Partly
If applicable, is the statistical analysis and its interpretation appropriate?
I cannot comment. A qualified statistician is required.
Are all the source data underlying the results available to ensure full reproducibility?
Yes
Are the conclusions drawn adequately supported by the results?
Yes
Competing Interests: No competing interests were disclosed.
Reviewer Expertise: Public Health and Virology
Is the work clearly and accurately presented and does it cite the current literature?
Yes
Is the study design appropriate and is the work technically sound?
Yes
Are sufficient details of methods and analysis provided to allow replication by others?
Yes
If applicable, is the statistical analysis and its interpretation appropriate?
Yes
Are all the source data underlying the results available to ensure full reproducibility?
Partly
Are the conclusions drawn adequately supported by the results?
Partly
Competing Interests: The first author, Professor Catherine Comiskey, was my PhD supervisor and we have published two papers together in the past. I have not worked with Professor Comiskey since 2003. I reviewed the manuscript impartially.
Reviewer Expertise: Mathematical modelling in infectious diseases, epidemiology.
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