key: cord-0830046-qqk3gq1k
authors: Yu, Zhuoting; Keskinocak, Pinar; Steimle, Lauren N.; Yildirim, Inci
title: The Impact of Testing Capacity and Compliance with Isolation on Covid-19: A Mathematical Modeling Study
date: 2022-05-20
journal: nan
DOI: 10.1016/j.focus.2022.100006
sha: 3284293ecd1773769aaf35a079b95cad0b17d16c
doc_id: 830046
cord_uid: qqk3gq1k

Diagnostic tests can play an important role in reducing the transmission of infectious respiratory diseases, particularly during a pandemic. The potential benefit of diagnostic testing depends on at least four factors: 1) how soon testing becomes available after the beginning of the pandemic, and 2) at what capacity; 3) compliance with isolation after testing positive; 4) compliance with isolation when experiencing symptoms, even in the absence of testing. To understand the interplay between these factors and provide further insight into policy decisions for future pandemics, we developed a compartmental model and simulated numerous scenarios using the dynamics of COVID-19 as a case study. Our results quantified the significant benefits of early start of testing and high compliance with isolation. Early start of testing, even with low testing capacity over time, could significantly slow down the disease spread if the compliance with isolation is high. By contrast, when the start of testing was delayed, the benefit of testing on reducing infection spread was limited, even when testing capacity was high; the additional testing capacity required increased superlinearly for each day of delay, to achieve a similar infection attack rate as in starting testing earlier. Our study highlighted the importance of the early start of testing and public health messaging to promote isolation compliance when needed, for an ongoing effective response to COVID-19 and future pandemics.

The impact of pandemics on health and society has been significant throughout history and continues to grow [1] . For example, Coronavirus disease 2019 (COVID-19) has caused more than 5.57 million deaths worldwide (as of January 20, 2022) [2] . To control the spread of infectious diseases, governments and public health agencies rely on non-pharmaceutical interventions, such as physical distancing, and pharmaceutical interventions, such as vaccines or therapeutics. Widespread and frequent diagnostic testing can help contain infection spread when the individuals who test positive comply with isolation [3] [4] [5] , which significantly reduces disease transmission [6, 7] . However, it takes time to start implementing testing programs due to the challenges associated with the development and distribution of testing kits, the collection of patient samples, and the limited laboratory capacity available for testing [8] . For example, although the Centers for Disease Control and Prevention (CDC) confirmed the first COVID-19 case in the United States on January 20, 2020 [9] , the total number of specimens tested daily for COVID-19 in the U.S. remained below one thousand until March 4, 2020 [10] , while the number of confirmed cases reached 1,234 on March 15, 2020 [11] . Moreover, it is estimated that only one in four COVID-19 infections were reported [12] . The impact of testing also depends on the individuals" compliance with isolation protocols after receiving a positive test result or when experiencing symptoms (even in the absence of testing). In practice, there is high variability in self-isolation compliance across different settings. According to surveys, estimates of compliance with isolation across different communities worldwide ranged from 18% to 95% [13] [14] [15] [16] and from 40% to 95% in the United States [17, 18] . An individual"s compliance with isolation depends on many factors, e.g., the availability of financial support during isolation and/or the presence of symptoms [19, 20] .

The effectiveness of diagnostic testing during an infectious disease outbreak depends on at least the following four factors: 1) how soon testing becomes available since the beginning of the pandemic, and 2) at what capacity; 3) compliance with isolation after testing positive; 4) compliance with isolation when experiencing symptoms. To understand the impact of these factors and their interactions on health outcomes, we developed a compartmental model [21] to simulate the transmission dynamics under various levels of diagnostic testing capacity and compliance with two types of isolation: (i) post-testing isolation, where an individual selfisolates after receiving a positive test result, and (ii) symptomatic isolation, where an individual self-isolates when experiencing symptoms, in the absence of a diagnostic test. The compliance rate refers to the fraction of individuals who comply with post-testing or symptomatic isolation, respectively. Across different scenarios, we estimated and compared the infection attack rate (IAR) and isolation percentage (IP), i.e., the percentage of the population who self-isolated at some point during the pandemic. Furthermore, we quantified the impact of the start day of testing (relative to Day 1, when the first case occurred) on the spread of the disease and identified the amount of additional testing capacity required to maintain an IAR similar to that of an equivalent scenario with an earlier start day of testing.

Compartmental models [21] , including basic and extended "Susceptible-Infected-Recovered" (SIR) models, have been widely used in modeling the progression and spread of infectious diseases [22, 23] , the impact of behaviors [24] , and interventions such as lockdowns or vaccines [25] [26] [27] [28] . Complementing and extending prior work (e.g., [29, 30] ), the compartmental model proposed in this work explores the impact of the complex interactions between the testing start day, the dynamically changing daily diagnostic testing capacity, and the population behaviors (i.e., compliance with self-isolation) on health outcomes, to help inform decisions regarding effective deployment of interventions.

The compartmental model [21] (an extended SIR model) developed in this study consists of twelve states, which fall under four main groups: (i) : Susceptible; (ii) : Infected (including :

pre-symptomatic, : symptomatic, : asymptomatic); (iii) : Recovered ( : recovered and diagnosed with a test, : recovered but have not been diagnosed due to absence of testing); (iv)

: Dead. Figure 1 shows the definitions of the states and transitions between the states. In Let and denote the compliance rates of post-testing (with or without symptoms) and symptomatic isolation (without testing), respectively, i.e., the proportion of diagnosed (with a positive test) or symptomatic (but not tested/diagnosed) patients who selfisolate. We assumed that the compliance rate of post-testing isolation for symptomatic ( patients is greater compared to that for asymptomatic patients ( , i.e., , and the compliance rate of post-testing isolation for symptomatic patients ( is greater than the compliance rate of symptomatic isolation, i.e., . The parameter represents the proportion of infections that were symptomatic, with an estimate of [31] . Appendix Table 1 presents the parameters and their values/ranges [32] [33] [34] [35] . Note that due to non-pharmaceutical interventions which contribute to the reductions in the basic reproduction number [36] , we assumed that the transmission rates, and , linearly decrease during the first four months after the identification of the first case and then stabilize.

When there was limited testing capacity, we assumed that symptomatic individuals were prioritized for diagnostic testing; if the capacity was sufficient to test all symptomatic individuals, the remaining capacity would be uniformly distributed among all other individuals who have not been diagnosed before. We assumed that the available testing capacity increased linearly daily.

Using the model described above, we simulated a cohort of 500,000 individuals for a one-year time horizon and estimated the number of infections and isolations. The cohort size was selected based on the rough median population of the largest 100 cities in the US. For example, the population in Atlanta was estimated to be 498,715 in 2020 [37] . The simulations were initialized with one infected and symptomatic individual on Day 1. The simulation was coded using the statistical software R [38] , and the package "deSolve" was used to solve the differential equations [39] .

We simulated various scenarios to investigate the impact of testing start day and testing capacity, as well as compliance with isolation, on IAR and other metrics. The simulated scenarios are shown in Table 1 , where each scenario is defined by: the start day of testing, capacity (daily testing capacity increments), post-testing isolation compliance rates (symptomatic and asymptomatic), and symptomatic isolation (without testing) compliance rate. We referred to testing start days of 30, 45, and 60 as Early, Moderate, and Late, respectively. We referred to daily testing capacity increments of 100, 500 and 1000 as Low, Medium, and High capacity, respectively. In each scenario, the post-testing isolation compliance rate for (i) symptomatic patients was 0.95 or 0.80, labeled as High and Low, respectively; (ii) asymptomatic patients was 0.90, 0.50, or 0.10, labeled as High, Medium, and Low, respectively. Therefore, we used a pair of labels to denote the post-testing isolation compliance rate combinations for symptomatic and asymptomatic patients, as shown in Table 1 . For example, (High, High) represents that the posttesting isolation compliance rates for both symptomatic and asymptomatic patients are High, i.e.,

. Moreover, we considered two levels of compliance with symptomatic isolation, i.e., and , which were labeled as High and Low, respectively. To emphasize the impact of testing and the corresponding post-testing isolation compliance, we fixed the symptomatic isolation compliance rate in the main body to be High ( .

In the baseline scenario, there was no testing or self-isolation. The intervention scenarios included testing, post-testing isolation, and symptomatic isolation, assuming that symptomatic isolation started on Day 45, and post-testing isolation started when testing capacity became available.

As summarized in Table 1 

To assess the impact of testing capacity and isolation compliance in different scenarios, we evaluated: IAR assesses the public health impact; IP serves as a proxy for assessing the potential social and economic impact [40] of the disease, and reveals the trade-off between testing start date/posttesting isolation compliance and testing capacity.

In the baseline scenario, IAR is 69.43% and IP is 0.00%, since there are no interventions. 

Diagnostic testing plays a significant role in controlling the spread of infectious diseases by enabling the early detection of infected individuals, encouraging self-isolation, and reducing transmission [6, [41] [42] [43] . The effectiveness of testing in preventing or controlling an outbreak depends on when (how early) testing becomes available, how quickly the testing capacity ramps up, and the willingness of individuals to self-isolate (i.e., compliance) when they test positive or have symptoms. The infection attack rate (IAR) and the isolation percentage (IP), i.e., the proportion of the population who self-isolate either due to symptoms or a positive test result, are two metrics used in this study to assess public health and social impact of testing programs.

Moreover, we introduced the capacity counterbalance factor metric to assess the trade-off between testing start date/post-testing isolation compliance and testing capacity.

The results of this study suggest that starting testing early with a lower capacity is more effective in reducing the infection spread compared to starting late with a higher capacity, especially when the individuals who tested positive have high compliance with self-isolation (each column in Table 2 presents results for a particular compliance rate). Moreover, early start of testing with higher testing capacity leads to lower IP in general, even when the compliance is high. When an early start of testing is not possible, improving compliance with symptomatic isolation is important in reducing the spread of the disease.

When the start of testing is delayed, the additional capacity required (capacity counterbalance factor) grows superlinearly to achieve an IAR similar to that in Scenario SI. The results highlight the importance of complying with post-testing isolation, especially for symptomatic patients. Let us consider "small delay scenarios" (the start of testing is delayed by less than 4 days, compared

to Scenario SI, where the testing start day is 45). Comparing these small delay scenarios: when fixing the testing start day, a decrease in post-testing isolation compliance of asymptomatic patients ( ) does not significantly increase the capacity counterbalance factor, because the testing capacity is low and thus, during the first 4 days after testing starts, symptomatic patients would be prioritized for testing. However, a decrease in post-testing isolation compliance of the symptomatic patients ( ) significantly increases the capacity counterbalance factor; for example, when the start of testing is delayed to day 49, under (High, Medium) post-testing compliance, compared to under (Low, Medium) post-testing compliance.

While the importance of early testing has been acknowledged [44] , to the best of our knowledge, this study is the first one that considers the complex interplay between multiple factors to evaluate the impact of testing and self-isolation on public health outcomes. The results of this study highlighted the benefits of the early start of testing and high compliance with isolation. In practice, the testing capacity may not be sufficient to meet the demand [45] , especially during the initial stages of the infection spread, and compliance with self-isolation may be low, even in the presence of symptoms. For example, 65% to 90% of working adults reported going to work when they had cold/flu symptoms [6, 42, 46] due to a variety of reasons such as high workload, not wanting to use or limited sick time, perceived pressure or fear of judgment [46, 47] . The results of this study show that low compliance with self-isolation can significantly increase the IAR, underscoring the importance of reducing barriers to self-isolation, which, in turn, could increase self-isolation compliance and reduce infectious disease spread. To improve public health outcomes and reduce social and economic impact of the diseases spread, it is important to communicate the importance of self-isolation via public health campaigns, community-based organizations, etc., as well as to encourage or require businesses; at a systems level, legal requirements for to remove (perceived) penalties or increase incentives for their employees to self-isolate when needed.

The extended SIR model assumes homogenous mixing of the population and is not able to account for demographic- [23] or geographic-dependent information, e.g., as in agent-based models [33, 48] . In the computational study, the testing capacity linearly increased over time, while in practice, the capacity increase might follow different patterns. Other factors, such as the willingness to test or compliance with other interventions, would also impact health outcomes. In willing to self-isolate might also be more likely to get tested or follow other interventions and recommendations. Exploring these additional complex interactions is an important direction for future research. Despite these limitations due to modeling assumptions and parameter values, the model proposed in this study can capture the salient characteristics of disease spread dynamics considering the complex interplay between multiple factors related to diagnostic testing and selfisolation.

In this work, we developed and used an extended SIR model to analyze the impact of diagnostic testing availability (including the start day and capacity of testing programs), compliance with post-testing isolation and compliance with symptomatic isolation on the disease spread. We quantified the significant advantages and effectiveness of early start of testing and high compliance with self-isolation. Investments in the early start of testing programs and public health education of self-isolation can lower the infection attack rate significantly. 

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The authors thank the anonymous referees for their valuable suggestions for improving this paper.

This research has been supported in part by Cooperative Agreement number NU38OT000297 from The Centers for Disease Control and Prevention (CDC) and CSTE and does not necessarily represent the views of CDC and CSTE. This research was also supported in part by the William