The coronavirus disease 2019 (COVID-19) pandemic has considerable impact on healthcare systems worldwide. It has caused considerable morbidity and mortality, with >500 million registered cases and 6 million deaths worldwide. ¹ Additionally, symptoms can persist or reemerge after the acute infection. ^{Reference Crook, Raza, Nowell, Young and Edison2} Although morbidity and mortality rates in children and adolescents are generally lower than in adults, potentially fatal hyperinflammatory disorders called pediatric inflammatory multisystem syndrome temporally associated with COVID-19 (PIMS-TS) and multisystem inflammatory syndrome associated with COVID-19 (MIS-C) have been described. ^{Reference Hoste, van Paemel and Haerynck3}

In the hospital setting, severe acute respiratory coronavirus virus 2 (SARS-CoV-2) poses a risk for healthcare workers and patients alike. Stringent infection control measures are necessary to prevent SARS-CoV-2 introduction and spread. Many hospitals have introduced surveillance testing for staff and patients, FFP2/N95 mask mandates for healthcare personnel and patients (whenever possible), organizational changes to reduce contacts between staff (limited unmasked contact during breaks), and between staff and patients. Positive patients are isolated and positive staff are banned from work. Furthermore, some countries (eg, France, Italy, Germany) implemented vaccine mandates for healthcare personnel.

In the setting of child and adolescent psychiatry, there are major challenges for infection control. A mask mandate for children aged <6 years is neither practical nor desirable since facial expressions play a much more important role in communication with children than with adults. ^{Reference Carpenter, Uebel and Tomasello4,Reference Freiberg, Horvath and Hahne5}

Limiting the contact between patients would prevent therapy in certain situations and seems infeasible given the therapeutic approaches used on an inpatient ward such as psychotherapy including parental guidance, play therapy, and particularly group therapy as well as multifamily therapy. ^{Reference Asen6} Reducing the number of patients in a ward would mean that fewer patients can be admitted, which counteracts the higher need for patient care during the pandemic. ^{Reference Racine, McArthur, Cooke, Eirich, Zhu and Madigan7}

Children have a higher rate of asymptomatic or oligosymptomatic infection, ^{Reference Cui, Zhao and Zhang8} which reduces the chance of detecting infection based on symptoms. Therefore, surveillance testing is highly relevant in child and adolescent psychiatry wards.

Little evidence indicates how often surveillance testing for staff and patients should be done and which type of test should be used. Generally, 2 types of tests with different test characteristics are available. Rapid antigen tests yield a result within 15–30 minutes, but they have lower test performance, especially regarding sensitivity. ^{Reference Truong, Dien Bard and Butler-Wu9} Polymerase chain reaction (PCR) tests are the gold standard for SARS-CoV-2 testing, and results can be obtained in <1 hour, but the usual time to reporting is ≥24 hours in many settings.

The individual contribution of time to reporting and test accuracy to successful mitigation of an outbreak is unclear. A simulation of a nursing home with 100 staff and residents suggested that daily antigen testing is superior to PCR testing with a time to reporting of 2 days. ^{Reference Holmdahl, Kahn, Hay, Buckee and Mina10} An epidemiological simulation of repeated population screening prioritized time to reporting over test sensitivity. ^{Reference Larremore, Wilder and Lester11} In a study of surveillance testing in 1,931 asymptomatic athletes, daily antigen testing was equivalent to PCR testing 2–3 times per week. ^{Reference Harmon12} However, in a modeling study, the benefits of surveillance testing were mostly negated if accompanied by decreased infection control practice. ¹³

Pandemics occur in waves with large regional differences. A particular challenge in the COVID-19 pandemic is the co-occurrence of SARS-CoV-2 variants with different epidemiological characteristics such as the speed of spread, incubation time, and viral load. For example, the SARS-CoV-2 omicron variant has drastically changed the dynamics of spread within the South African population compared to the previous delta variant. ^{Reference Grabowski, Kochańczyk and Lipniacki14} These factors complicate the prediction of future waves based on observational studies.

Modeling studies can help fill this gap because they can easily be adapted to the different characteristics of a virus variant. The 2 modeling frameworks employed in viral epidemics are compartmental models and agent-based models. Compartmental models are well suited for large populations, which are computationally expensive for agent-based models. ^{Reference Grabowski, Kochańczyk and Lipniacki14} However, agent-based models consider a described set of agents and their connections, which is useful if that knowledge is specifically available. In the spatially delineated setting of a hospital ward, agent-based models can capture relevant interactions for transmission. They allow researchers to vary the individual agent’s behavior in the model and to explore its effects on disease transmission in different scenarios. ^{Reference Patlolla, Gunupudi, Mikler and Jacob15}

We report a modeling study to assess the optimal frequency of SARS-CoV-2 surveillance testing in the setting of a child and adolescent psychiatry clinic. Using an agent-based model, we simulated the transmission of SARS-CoV-2 within the contact networks of healthcare personnel and patients. Different testing strategies were assessed through repeated simulations, and the likelihood and size of an outbreak were estimated. We further estimated the effect of weekly meetings on transmission dynamics.

Methods

Structure of the child and adolescent clinic

We created an agent-based model reproducing the structure and work processes of the child and adolescent psychiatric clinic in Magdeburg, Germany, under pandemic conditions. The clinic consisted of 4 separate wards, with a multidisciplinary team. Each team consisted of 14 nurses and 3 doctors who were responsible for 10 patients. Additional personnel included 4 therapists from various professions: psychologists, occupational therapists, music therapists, and play therapists. During the pandemic, we restructured the wards so that each ward constituted a separate “family unit.” Team conferences across wards were reduced to an absolute minimum or were conducted via videoconferencing. Therapists, who usually work on different wards, were allocated to just 1 ward, whenever possible.

Within a given ward, patients and staff were closely connected and transmission of SARS-CoV-2 could occur. The spread from one ward to another was less likely because spread could only occur through common staff, such as therapists, or through meetings of other staff members across wards.

Model and scenario setup

The model was programmed in MATLAB (MATLAB and Statistics Toolbox Release 2021a, The MathWorks, Natick, MA). Up to 112 agents were connected based on a graph version of the clinic structure (Fig. 1). Each node represented an agent (ie, a person). An edge connecting 2 nodes represented a face-to-face contact associated with a transmission probability. Different scenarios, regarding intervention strategies, meeting frequencies, and involvement of therapists on the wards, were set by varying the graph structure (cf, connection between nodes) and edge weights (cf, infection probabilities). Edges resulting from weekly meetings were only active on the day of the meeting.

Figure 1. Contact network of a child and adolescent psychiatry clinic with 4 wards. Each dot (node) represents a person. Patients (red), doctors (green), nurses (blue), and therapists (yellow) are connected by a “strong” edge (grey). Additionally, doctors and therapists are connected by a “weak” edge (red), which denotes the connection through weekly meetings.

We assessed 3 network setups with varying degree of interconnectivity, reflecting possible interventions to reduce mixing of hospital staff. In the “separated” setup (I), there were no interconnections between the 4 different wards. In the “restricted” setup (II), we added weekly staff meetings between all doctors from the 4 wards but sessions by therapists were suspended. In the “regular” setup (III), therapists were connected with different individual children across all 4 wards and weekly staff meetings were held.

Within the different setups, we tested how variations in surveillance testing and SARS-CoV-2 variants affected transmission dynamics. To this end, we simulated scenarios with parameters reflecting a PCR test and a rapid antigen test. Rapid antigen testing was modeled with test sensitivities of 50%, 60%, 70%, and 80% for the delta variant and the omicron variant, as well as different frequencies of surveillance testing and different times to result (Table 1).

Table 1. Overview of the Scenarios Simulated. The Network Setup was Either “Separated” (I), “Restricted” (II), or “Regular” (III)

Note. PCR, polymerase chain reaction.

Outbreak simulation

We simulated different scenarios over 60 days with 1,000 simulations each. A simulation of 60 days was typically sufficient for transmission to stop, either by infecting every person or by having eliminated all infections.

At each run, we first initialized the model by setting the transmission probability (time dependent probability of infecting another person) of each agent to a random value from the probability distribution table. The distribution of probabilities for transmission and detection by either PCR- or antigen-test are shown in Figure 2 for the omicron variant (for the delta variant, see Supplementary Fig. 1 online). We chose parameters based on published data on symptom onset, ^{Reference Jang, Rhee, Wi and Jung16–Reference Chen, Bobrovitz, Premji, Koopmans, Fisman and Gu20} kinetics of viral load, ^{Reference Jang, Rhee, Wi and Jung16,Reference Huber, Schreiber and Scheier21,Reference Fox-Lewis, Fox-Lewis and Beaumont22} the rate of oligosymptomatic or asymptomatic persons, ^{Reference Johansson, Quandelacy and Kada19,Reference Huber, Schreiber and Scheier21,Reference Al-Rawahi, Prakash and Al-Wahaibi23–Reference Kotsiou, Papagiannis and Fradelos25} the course of infectiousness, ^{Reference Jang, Rhee, Wi and Jung16,Reference Meyerowitz, Richterman, Gandhi and Sax18,Reference Chen, Bobrovitz, Premji, Koopmans, Fisman and Gu20,Reference Jones, Biele and Mühlemann26} and household transmission rate (Supplementary Table 1 online). ^{Reference Viner, Waddington and Mytton27–29} Then, we randomly selected an agent as the index case and a weekday as the day when the infection was first introduced into the model. Depending on the scenario, network edges were added for therapists and staff meetings.

Figure 2. Parameters of transmission kinetics for the SARS-CoV-2 omicron variant. (a) Distribution of time to first symptom after exposure; 20% of cases were assumed to be asymptomatic. (b) Distribution of the probability for transmission and for a positive test result from start of symptoms. (c) Distribution of transmission and distribution of a positive test result for asymptomatic cases from day after exposure. Note. Polymerase chain reaction test (o), antigen test (x), and transmission (*).

A time-stepping algorithm moved through each day and performed the following routine: (1) calculation of test results according to the test strategy; (2) removal of agents that tested positive (immediately for antigen tests, the day after for PCR, and 2 days after for the scenario with a delayed PCR reporting), leading to fewer agents in the system; and (3) computation of newly exposed neighbors according to transmission probability of the individual multiplied by the edge transmission (0.21 for the delta variant and 0.31 for the omicron variant).

Model calibration and validation

To calibrate the model, we plotted transmission rate, connectivity, number of runs against outbreak size and visually confirmed continuity of outcome variables (Supplementary Fig. 4 online). Furthermore, we checked whether outcome parameters were within the possible range. To validate the model, we checked model output for plausibility; however, no real-world data were available for a full model validation.

Analyses

For each testing scenario, we assessed the total number of infected persons (outbreak size), the maximum number of persons infected on one day (outbreak peak), and the number of days until the last person was infected (outbreak duration) as outcome measures. The Kruskal-Wallis test was used to test for statistical significance for continuous variables.

Results

As a baseline, we first simulated transmission dynamics for the SARS-CoV-2 delta and omicron variants without any surveillance testing for the 3 network setups: separated, restricted, and regular (Fig. 3). In the separated setting, wards were not connected, and the maximum outbreak size was 27, which means that all staff and patients of the ward were infected. Outbreaks with the omicron variant were faster and more intense than with the delta variant. The maximum outbreak size was reached in 88% for the omicron variant and in 57% for the delta variant. The average outbreak size was 26 versus 24 (P = e-50), and the average outbreak duration was 30 days versus 38 days (P < .001), respectively.

Figure 3. Outbreak size without containment through surveillance. Violin plots of 1,000 simulations of outbreak size for the 3 network setups, separated (I), restricted (II), and regular (III) for the SARS-CoV-2 delta variant (a) and the omicron variant (b) when no test strategy was implemented.

Similar dynamics were identified for other network settings. In the restricted setting, wards were connected by regular staff meetings. Outbreak size was significantly higher with the SARS-CoV-2 omicron variant versus the delta variant (median, 55 vs 28; P < .001). For the omicron variant, 72% of outbreaks extended to 1 or more other wards, 55% of outbreaks extended to >2 wards, and 36% of outbreaks extended to all 4 wards.

In the regular setting, wards were additionally connected by shared therapists. In this scenario, with the SARS-CoV-2 omicron variant, 87% of outbreaks extended to 1 or more other wards, 84% of outbreaks extended to >2 wards, and 80% of outbreaks extended to all 4 wards were affected for the omicron variant. The median outbreak size was 111 in the regular setting versus 55 (P < .001) in the restricted setting.

Surveillance PCR testing in a frequency of up to 1 test every 9 days showed a smaller size, shorter duration, and lower outbreak peak compared to the setting without surveillance tests (Fig. 4).

Figure 4. Influence of test frequency on outbreak duration (left panels), peak (middle panels), and size of the outbreak (right panels) in the separated (I), restricted (II), and regular (III) setup. The colored lines denote polymerase chain reaction (PCR) test and rapid antigen tests with different sensitivities (50%, 60%, 70%, and 80%). All data are for the SARS-CoV-2 omicron variant.

Interestingly, we observed a higher median outbreak size in the restricted and regular settings at a test frequency of every 7 days compared to every 6 or 8 days for PCR testing (Fig. 4). This finding is related to the fact that regular meetings of staff between wards were scheduled every 7 days on Mondays, whereas the weekday of PCR testing varied between simulations.

Antigen tests showed a lower effect than PCR testing in all 3 performance measures. Increased testing frequency as well as increased test sensitivity led to a decreased outbreak duration, outbreak peak, and outbreak size (Fig. 4, Supplementary Fig. 2 online for the delta variant).

For both SARS-CoV-2 variants, rapid antigen testing with at least 80% sensitivity could prevent extension of the outbreak to other wards in 99% of cases with a test frequency of every day or every other day. Outbreaks were small with a median outbreak size of <5 (Figs. 5 and 3 and Supplementary Table 2 online).

Figure 5. Outbreak size for 2 testing frequencies (every day to every 4 days). Simulations were performed for the SARS-CoV-2 omicron variant with 3 network setups, that is, separated (I), restricted (II), and regular (III), polymerase chain reaction test (1), and rapid antigen tests with 80% sensitivity (2).

Under surveillance conditions, increased connectivity between wards by adding weekly meetings and cross-ward therapists did not significantly change transmission dynamics. The median outbreak size was 1 in both cases (P = .214), when comparing the restricted versus the regular setting with daily antigen testing and median outbreak in the separated setting was also 1 with P = .277 and P = .865 compared with the regular and restricted setting.

Comparing typical test frequencies for antigen tests and PCR tests, the median outbreak size was 1 for daily rapid antigen testing and 3 for every-other-day testing in the regular setting for the SARS-CoV-2 omicron variant. For PCR testing every other day, the median outbreak size was 3 and for twice-weekly PCR testing, the median outbreak size was 22 (P < .001 for daily antigen testing versus twice weekly PCR testing) (Fig. 6). Therefore, twice-weekly PCR testing was inferior to daily antigen testing and was not sufficient to confine an outbreak to a single ward in 30% of cases.

Figure 6. Outbreak size (a) and peak size (b) for no surveillance testing, daily antigen testing, every-second-day antigen testing, every-second-day polymerase chain reaction (PCR) testing, twice-per-week (biweekly) PCR testing with time to report of 1 day, and PCR testing with delayed time-to-report of 2 days. Data shown are for the SARS-CoV-2 omicron variant in the regular setting.

A shorter time to reporting the test result reduced outbreak size. Twice-weekly PCR testing with a time to reporting of 2 days showed a median outbreak size of 46, whereas a time to reporting of 1 day showed a median outbreak size of 22 (P < .001) (Fig. 6).