Simulated Identification of Silent COVID-19 Infections Among Children and Estimated Future Infection Rates With Vaccination

Key Points Question Is a targeted strategy for identification of silent COVID-19 infections among children in the absence of their vaccination associated with reduced infection rates in the general population? Findings In this simulation modeling study, identifying 10% to 20% of silent infections among children within 3 days after infection would bring attack rates below 5% if only adults were vaccinated. If silent infections among children remained undetected, achieving the same attack rate would require an unrealistically high vaccination coverage (≥81%) of this age group, in addition to vaccination of adults. Meaning These findings suggest that rapid identification of silent infections among children may achieve comparable effects as would their vaccination.


eMethods. The Model
We modelled the transmission of SARS-CoV-2 by extending an age-structured SEIR (Susceptible, Exposed, Infectious, Recovered) to include additional compartments of asymptomatic, pre-symptomatic, symptomatic, and isolation of infected individuals (eFigure 1). We further included compartments to describe vaccination dynamics. The total population was divided into five age groups as specified in the main text. We omitted the demographic variables of births and deaths. With the variables described in eTable 1, the model is expressed by the following system of equations:  In this model, is the transmission parameter (calibrated to an effective reproduction number . The reproduction number denotes the average number of secondary infections caused by an infected individual before recovering and becoming immune (or dying) in the presence of measures that aim to control disease spread. We calibrated the transmission parameter by calculating the spectral radius of the next-generation matrix [1]. A full description of all model parameters is given in eTable 2. The population was stratified into six age groups: 0-4, 5-10, 11-18, 19-49, 50-64, 65+. Transmission between and within age groups was based on heterogeneous mixing with rates determined by age-specific contact matrices [2,3]  where in each matrix, the elements { ij | , ∈ (1, ⋯ ,6)} denote the average contact rates between age groups and .
In our model, all newly infected individuals start in the latent stage for an average period of 1/σ days. After this period has elapsed, infected individuals move to a communicable silent infection stage (i.e., asymptomatic or pre-symptomatic). Unlike asymptomatic cases, those who enter pre-symptomatic stage will develop symptoms. We assumed that all symptomatic cases initiate self-isolation within 24 hours of their symptom onset. The average infectious periods in different stages of the disease and their associated distributions are summarized in eTable 2. Recovery from infection was assumed to provide immunity against re-infection during the simulations.
To include vaccination dynamics, we considered age-dependent vaccination rates to achieve a 40% vaccine coverage in adults within 1 year, with a distribution of 80% for age groups 50+ and 22% for individuals aged 19-49. Vaccination was assumed to prevent infection with an efficacy that is 50% lower than its efficacy against symptomatic disease (and 95% in additional scenarios presented in as sensitivity analysis in this appendix). If infection occurred postvaccination, we assumed the probability of developing symptomatic disease is reduced by a factor a corresponding to the vaccine efficacy of 95% [13].
For simulating the model, we used a non-standard numerical method to discretize the system and ran the simulations (in MATLAB©) with introducing one latent individual into each age group in the model.

= . and Reduced Susceptibility of Children
Evidence is accumulating that young children may have a reduced susceptibility to SARS-CoV-2, with stronger immune responses that may prevent the development of symptomatic or severe disease [14,15]. We therefore simulated the model by considering a 50% reduction of susceptibility for children under 10 years of age. Qualitatively, the effect of identifying silent infections on the reduction of attack rates remains intact and the speed of identification is critical for outbreak control. Projected attack rates for the range of 2-5 days delay in identification of silent infections among children, when only adults are vaccinated, are presented in eFigure 2.
We also simulated the model to determine the effect of vaccine coverage on the minimum level of silent infections required to be identified among children in order to bring the overall attack rate in the population below 5% (eFigure 3).

= . and 95% Vaccine Efficacy Against Infection
In the absence of data on vaccine efficacy against infection, we further simulated the model with the same efficacy of 95% against symptomatic disease, while also considering 50% reduced susceptibility for children under 10 years old. The results presented in eFigure 4 below illustrate a qualitative similar pattern to those presented in Figure 2 of the main text, indicating that the sharpest decline of attack rates occur with rapid identification of 0% -15% silent infections among children within 2-3 days post-infection. = .
Depending on various factors (e.g., the characteristics of the disease, interventions, and other heterogeneities in the population), the reproduction number of diseases may change. As sensitivity analysis, we simulated the model when the reproduction number was increased to = 1.5. Not surprisingly, attack rates were estimated to be higher and a greater proportion of silent infections in the population (without vaccination) and among children (with vaccination of adults) would need to be identified in order to suppress the overall attack rate below 5%. eFigures 5-7 show the results without vaccination, and when the vaccination coverage of adults is reached 40% over the course of 1-year. These simulations also consider reduced susceptibility of children under 10 years of age in scenarios with varying vaccine efficacy against infection (i.e., the same or 50% lower than the efficacy against symptomatic disease).  When the reproduction was below one (simulated with = 0.9), we found that with a 40% vaccine coverage, attack rates remained below 5% irrespective of the proportion of silent infection identified in the population or among children. However, as identification of silent infections increases with shorter delay post-infection, an earlier control of outbreak can be achieved.