The need globally to accurately model COVID-19 mitigation strategies and asymptomatic transmission in order to plan for the burden on hospital admissions was identified early in the pandemic . The impact of mitigation scenarios on asymptomatic cases is also clearly articulated in the modeling work of Davies et al . Within their models in the United Kingdom they have predicted that extreme measures are probably required to prevent an excess of demand on hospital beds, especially those in ICUs during 2021. Similarly in France, Di Domenico et al  have used modeling techniques calibrated with hospital admission data to model the impact of mitigation strategies to predict the scale of the epidemic within the Ile-de-France region. In the same way, we provide estimations of the dynamics of the COVID-19 epidemic in Ireland and its key parameters. We also quantify the effects of mitigation measures on the virus transmission before, during and after the lockdown. The main characteristics of our approach is accounting for non-stationarity by embedding time-varying parameters in a stochastic model coupled with Bayesian inference. This allows us to describe the time evolving COVID-19 epidemic based purely on the available data without specific hypothesis on this time evolution.
Using known reported hospitalized cases, we present the first Irish modeling estimates of hidden asymptomatic cases and resulting short term predictions of numbers hospitalized and number recovering. The model presented predicted that in Ireland as of the 31st July between 0.44% and 2.14% of the population had been infected either as a symptomatic or asymptomatic case. Within the population of 5.1 million this equates to over 55,000 individuals. The number known through testing at the same time was 26,027 individuals [3, 5] and we can see from these figures that the number of predicted cases from the model in Ireland at the end of July may have been almost 2 times the number identified through testing centers.
This disparity between estimated number infected and known is not to be unexpected and similar percentages of infections have been observed in other countries in these early stages of the epidemic. Li et al  estimate that in the early stages of the epidemic in China before the 23 January 2020 travel restrictions 86% of all infections were undocumented (95% CI: 82–90%). Similar proportions are evident when we compare the known and estimated cases in Ireland. However perhaps what is more important according to Li et al  was that the transmission rate of undocumented infections per person was 55% the transmission rate of documented infections (95% CI: 46–62%), yet, because of their greater numbers, undocumented infections were the source of 79% of the documented cases.
Undocumented infections particularly asymptomatic infections are known to be the silent drivers of infection. The European Centre for Disease Prevention and Control  in their update on the role of asymptomatic and pre-symptomatic individuals on August 10th 2020 report that similar viral loads in asymptomatic versus symptomatic cases have been reported, indicating the potential of virus transmission from asymptomatic patients. Furthermore viral loads in asymptomatic patients from diagnosis to discharge tended to decrease more slowly than those in symptomatic (including pre-symptomatic) patients.
Aguilar et al  in their study investigating the impact of asymptomatic carriers on COVID-19 transmission state that, in a public health context, the silent threat posed by the presence of asymptomatic carriers in the population results in the COVID-19 pandemic being much more difficult to control. Their study shows that the population of individuals with asymptomatic COVID-19 infections is driving the growth of the pandemic.
Given the increases in cases in Ireland in September 2020 (see Fig. 2B) where a second wave is emerging from the capital city and in some rural regions in spite of a period of increased testing and sustained mitigation strategies the role of the silent asymptomatic cases is now more important than ever. One rural region in the Republic of Ireland currently experiencing a second wave is in close proximity to a border city in Northern Ireland where different mitigation strategies, different testing protocols and different definitions are in operation, These emerging second waves highlight the unique challenges facing policy makers within and across borders.
It is interesting to compare this model prediction with recent preliminary national serological results, which found that among 12 to 69 year olds living in Ireland the sero-prevalence rate was estimated in July 2020 at 1.7% (95% CI: 1.1–2.4%) but at 0.6% (95% CI: 0.2–1.4%) in the Sligo province (a lower incidence of COVID-19 cases area) . Despite the fact that the HSE model is age and region limited and given that the majority of cases in Ireland in the early stage of the epidemic were in those over the age of 65 years, the observed range is in the same order of magnitude as our predictions.
Our seroprevalence predictions contrast with those of more densely populated areas. Comparing the Davies et al  model predictions on serological prevalence with recent serological study results in the UK we see that Davies et al  assumes that subclinical or asymptomatic rates are 50% of all infections and under this and other model assumptions authors find in their scenario analyses that extreme measures are probably required to bring the epidemic under control and to prevent very large numbers of deaths and an excess of demand on hospital beds, especially those in ICUs. To date estimated serological prevalence in the United Kingdom based on a random sample of home based testing has found that 6.0% (95% CI: 5.8–6.1%) of individuals tested positive, of these one third (32.2%, (95% CI, 31.0–33.4%)) reported no symptoms and were asymptomatic . Overall the authors estimated that 3.36 million (3.21 million to 3.51 million) people had been infected with SARS-CoV-2 in England by the end of June 2020. This estimate was substantially higher than the recorded numbers in the UK of 315 000 cases. This is in accordance with observations from Spain where between April and May 2020, seroprevalence was 5,0% and only few cases of these people had a PCR test . Within the Di Domenico et al  study on the Ile-de-France authors estimate that the population infected by COVID-19 as of April 5 and prior to lockdown to be in the range 1–6%. This was predicted using two values of the probability of being asymptomatic, namely 20% and 50%.
Our study is not without limitations. Our model like all complex SEIR models developed for COVID-19 is non-identifiable which means that it is likely that several solutions exist and we only present one of the most likely. This point is always overlooked but see Li et al . The major limitation is the use of the classical homogeneous mixing assumption in which all individuals are assumed to interact uniformly and ignores heterogeneity between groups by sex, age, geographical region. In all cases taking an age structure and mixing matrix appears insufficient and heterogeneity of contact is important (see ). However this kind of data is not easily available. Another weakness is perhaps the neglect of age-structure in the model to simulate age-based predictions as we enter the time of children returning to school. These weaknesses are however a future research development given the performance of the current model. Nevertheless in our opinion, these limitations are compensated for taking non-stationarity of this epidemic into account and by the fact that our results are mainly driven by hospital data, which is more accurate than the number of infected cases. Precise data from serological studies would significantly reduce the uncertainties of the model predictions [23–24].
The key strength of the current Irish study is the fit of the model to the current observed data on hospitalizations, deaths and ICU cases. The first estimate of the asymptomatic cases predicted by this model is also reflecting the emerging data from the Irish serological prevalence study. We also found a reduction of transmissibility of the SARS-CoV-2 of 78%-82% that is in accordance with the results published on the effects of mitigation measures in Europe [25–26]. For example, Garchitorena et al  by comparing 24 non-pharmaceutical interventions found that the median decrease in viral transmission was 74%, which is enough to suppress the epidemic and that a partial implementation of different measures resulted in lower than average response efficiency. Our results also highlighted that the observed confirmed cases are only a small fraction of the total number of cases, only the tip of the iceberg (see . Then data from hospital system published by health authorities are crucial for understanding the course of this epidemic. These data are well measured, but are observed with a delay in relation to contamination. Nevertheless, these delays can be easily account for by mathematical models.