# Containment, Contact Tracing and Asymptomatic Transmission of Novel Coronavirus Disease (COVID-19): A Modelling Study

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## Abstract

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## 1. Introduction

## 2. Methods

_{1}is the extinction probability given that a single symptomatic case is introduced, while π

_{2}is the extinction probability given that an asymptomatically infected individual invades the new location. Throughout the main text, we assumed the overdispersion parameter of the offspring distribution $k=1$ (geometric distribution) as a baseline for the comparison of the type-specific heterogeneity (e.g., [24]), and the possibility of superspreading (individual variation in the number of secondary cases produced) was also considered in the Supplementary Figure S4 [25,26,27].

## 3. Results

_{i}to take the value below 1, a greater proportion of contacts must be traced as R

_{0}increases. Assuming that the proportion of asymptomatic individuals was 40% as a baseline with 25% reduction in transmission among asymptomatic cases (q = 0.75), the probability of extinction given a symptomatic or asymptomatic individual with α = 0.25 (i.e., 75% of secondary transmissions were prevented by contact tracing and case isolation) and the reproduction number R among symptomatic cases at 2.5 was 32.0% and 38.8%, respectively (Equations (4) and (5)). Under these assumptions, even with 90% of symptomatic cases traced and isolated, the ${R}_{i}$ is not below the value of 1 (R

_{i}= 2.02), indicating the difficulty of containment when asymptomatic individuals persist in their capacity to transmit to susceptible individuals (Figure 1D).

## 4. Discussion

_{i}was above the value of one (Figure 1), the probability of a major outbreak will increase with the number of untraced symptomatic cases introduced to the population (Figure 2 and Figure 3). A broad range of asymptomatic ratios and relative infectiousness among asymptomatic cases was assumed, and they were shown to complicate the containment strategies of COVID-19. Moreover, since approximately 40% of secondary transmissions can occur prior to symptom onset, contact tracing and case isolating only after illness onset is difficult to prevent the epidemic to take off. Thus, our result emphasizes the value of active contact tracing among close contacts of an infected individual to identify and isolate asymptomatic and pre-symptomatic cases. Considering that the probability of successful containment by contact tracing and case isolation is determined by detailed ingredients of the next generation matrix, and thus basic reproduction number R, updating the estimated value of the R in real time is thus considered to be critical to judge the feasibility of containment in a timely manner.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The effective reproduction number, given different effectiveness of contact tracing among symptomatic cases $\left({R}_{i}\right)$ and the basic reproduction number (${R}_{0}$). The probability of a major epidemic was estimated with different effectiveness levels of contact tracing (25% ($\alpha =0.75$), 50% ($\alpha =0.5$), 75% ($\alpha =0.25$) and 90% ($\alpha =0.1$) for panels

**A**–

**D**) among symptomatic cases. Colored circles classify the relative infectiousness of asymptomatic individuals compared with symptomatic individuals, varied from 0.25−0.90. The asymptomatic ratio was assumed at 40% (i.e., p = 0.6). Equation (3) was used to compute the eigenvalue.

**Figure 2.**Probability of a major epidemic, given the number of untraced symptomatic cases and the reproduction number, R. Equation (6) in the main text was used. The probability of a major epidemic was estimated given different levels of success in contact tracing (25% ($\alpha =0.75$), 50% ($\alpha =0.5$), 75% ($\alpha =0.25$), and 90% ($\alpha =0.1$) for panels

**A**–

**D**) among symptomatic cases. Colored lines classify the reproduction number among symptomatic cases varied from 1.5–3.5. The relative infectiousness among asymptomatic individuals was assumed to be 75% (q = 0.75). The asymptomatic ratio was assumed as 40% (i.e., p = 0.6). The number of untraced symptomatic cases is below 1 in Figure 2D.

**Figure 3.**Probability of a major epidemic, given the number of untraced symptomatic cases and the relative infectiousness of an asymptomatic individual ($q$). Equation (6) in the main text was used. The probability of a major epidemic was estimated given different rates of success in contact tracing (25% ($\alpha =0.75$), 50% ($\alpha =0.5$), 75% ($\alpha =0.25$), and 90% ($\alpha =0.1$) for panels

**A**–

**D**) among symptomatic cases. Colored circles and lines classify the relative infectiousness of asymptomatic individuals compared to symptomatic individuals ($q$), which was assumed to vary from 0.25–0.90. The reproduction number among symptomatic cases was assumed as R = 2.5. The asymptomatic ratio was assumed as 40% (i.e., p = 0.6). The number of untraced symptomatic cases is below 1 in Figure 3D.

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**MDPI and ACS Style**

Kinoshita, R.; Anzai, A.; Jung, S.-m.; Linton, N.M.; Miyama, T.; Kobayashi, T.; Hayashi, K.; Suzuki, A.; Yang, Y.; Akhmetzhanov, A.R.; Nishiura, H. Containment, Contact Tracing and Asymptomatic Transmission of Novel Coronavirus Disease (COVID-19): A Modelling Study. *J. Clin. Med.* **2020**, *9*, 3125.
https://doi.org/10.3390/jcm9103125

**AMA Style**

Kinoshita R, Anzai A, Jung S-m, Linton NM, Miyama T, Kobayashi T, Hayashi K, Suzuki A, Yang Y, Akhmetzhanov AR, Nishiura H. Containment, Contact Tracing and Asymptomatic Transmission of Novel Coronavirus Disease (COVID-19): A Modelling Study. *Journal of Clinical Medicine*. 2020; 9(10):3125.
https://doi.org/10.3390/jcm9103125

**Chicago/Turabian Style**

Kinoshita, Ryo, Asami Anzai, Sung-mok Jung, Natalie M. Linton, Takeshi Miyama, Tetsuro Kobayashi, Katsuma Hayashi, Ayako Suzuki, Yichi Yang, Andrei R. Akhmetzhanov, and Hiroshi Nishiura. 2020. "Containment, Contact Tracing and Asymptomatic Transmission of Novel Coronavirus Disease (COVID-19): A Modelling Study" *Journal of Clinical Medicine* 9, no. 10: 3125.
https://doi.org/10.3390/jcm9103125