key: cord-0867363-k0i0tee8
authors: Tsou, Hsiao-Hui; Cheng, Yu-Chieh; Yuan, Hsiang-Yu; Hsu, Ya-Ting; Wu, Hsiao-Yu; Lee, Fang-Jing; Hsiung, Chao A.; Chen, Wei J.; Sytwu, Huey-Kang; Wu, Shiow-Ing; Shih, Shu-Man; Wen, Tzai-Hung; Kuo, Shu-Chen
title: The effect of preventing subclinical transmission on the containment of COVID-19: Mathematical modeling and experience in Taiwan
date: 2020-08-06
journal: Contemp Clin Trials
DOI: 10.1016/j.cct.2020.106101
sha: f0d3cca322c1e8d9413b4b2e81ba2fa4bac09e05
doc_id: 867363
cord_uid: k0i0tee8

Abstract The control strategies preventing subclinical transmission differed among countries. A stochastic transmission model was used to assess the potential effectiveness of control strategies at controlling the COVID-19 outbreak. Three strategies included lack of prevention of subclinical transmission (Strategy A), partial prevention using testing with different accuracy (Strategy B) and complete prevention by isolating all at-risk people (Strategy C, Taiwan policy). The high probability of containing COVID-19 in Strategy C is observed in different scenario, had varied in the number of initial cases (5, 20, and 40), the reproduction number (1.5, 2, 2.5, and 3.5), the proportion of at-risk people being investigated (40%, 60%, 80%, to 90%), the delay from symptom onset to isolation (long and short), and the proportion of transmission that occurred before symptom onset (<1%, 15%, and 30%). Strategy C achieved probability of 80% under advantageous scenario, such as low number of initial cases and high coverage of epidemiological investigation but Strategy B and C rarely achieved that of 60%. Considering the unsatisfactory accuracy of current testing and insufficient resources, isolation of all at-risk people, as adopted in Taiwan, could be an effective alternative.

The high infectiousness of SARS-CoV-2 with its ability to transmit during incubation period or by subclinical cases results in global pandemic. The virus has caused 1,923,937 infections and 119,618 deaths worldwide (as of April 13) [1] . A previous modeling study [2] showed that a combination of contact tracing and cases isolation is beneficial to the containment of COVID-19. However, the presence of subclinical transmission hampers greatly the effect of such control measures because those unidentified cases might become the source of community outbreaks. A common approach of testing on at-risk people could only identify part of the subclinical cases.

It is therefore extremely difficult to contain the spread of SARS-CoV-2.

Around eighty miles from the coast of mainland China, Taiwan had been predicted to be the "second highest import risk" of COVID-19 in the world [3] . As the COVID-19 pandemic spreads around the world, Taiwan has only 393 confirmed cases with majority of them being imported cases, which ranks below 97 countries and regions (as of April 13) (Figure1) [4, 5] . The lack of large-scale outbreaks could be attributable to immediate quarantine upon identification of all at-risk people and follow-up, which mainly prevents the subclinical spread ( Figure 2 ) [6] . However, these measures may not be feasible in all countries. Due to a variety of control strategies worldwide, we used a stochastic transmission model, initially proposed by For each case of COVID-19, we assumed that the incubation period of each case was drawn from a Weibull distribution. That is, assumed that a random variable X represents the incubation period and follows a Weibull distribution with a shape parameter k and a scale parameter  , where the corresponding probability density function is

The mean and the variance are J o u r n a l P r e -p r o o f

respectively, where Γ is the gamma function. The parameters k and  were determined once mean and variance have been given (please see the incubation period in Table 1 ). Similarly, we assumed that the delay between symptom onset and isolation for each case was drawn from a Weibull distribution.

Let Y be the number of potential secondary cases produced by each primary case.

Assume that Y follows a negative binomial distribution with a mean equal to a reproduction number R. Each potential new infection was assigned a time of infection drawn from the serial interval distribution. The corresponding serial interval for each case was drawn from a skew normal distribution. More specifically, let S be a random variable to represent a time of infection for each new case and S follows a skew normal distribution [7] . Then the corresponding probability density function is

where  and  are the standard normal probability density function and the corresponding cumulative distribution function, respectively. The location parameter  of this skew normal distribution was set to drawn from the incubation period for the case and the scale parameter  is 2. The value of shape parameter  is used to control a set proportion of serials interval which were shorter than the incubation period (meaning that a set proportion of transmission happened before symptom Table 1 . Serial interval Incubation period (2) Assumed.

Initial cases 5, 20, 40 [10] J o u r n a l P r e -p r o o f We considered the effect of the three strategies in different scenarios that varied in the number of initial cases (5, 20, and 40), the reproduction number (R; 1.5, 2, 2.5, and 3.5), the proportion of at-risk people being investigated (40%, 60%, 80%, and 90%), the delay from symptom onset to isolation (long and short), and the proportion of transmission that occurred before symptom onset (<1%, 15%, and 30%). We assumed isolation prevented all further transmission in the model. Outbreak control was defined as no new infected cases between 12 and 16 weeks; outbreaks that 

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The authors thank Dr. Kung-Yee Liang, National Health Research Institutes, Taiwan