# Time from Symptom Onset to Hospitalisation of Coronavirus Disease 2019 (COVID-19) Cases: Implications for the Proportion of Transmissions from Infectors with Few Symptoms

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Time from Symptom Onset to Hospitalisation

#### 2.2. Time-Varying Reproduction Number

#### 2.3. Proportion of Transmissions from Individuals with Few Symptoms

## 3. Results

#### 3.1. Time from Symptom Onset to Hospitalisation

#### 3.2. Reproduction Number and Proportion of Transmissions from Individuals with Few Symptoms

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Changes in the period between symptom onset and hospitalisation (the assumed symptomatic infectious period) from 2 January 2020 to 22 January 2020. (

**A**) Schematic showing the assumed epidemiology of infected hosts. Infected individuals initially have no or few symptoms. Later in infection, infected individuals develop clear symptoms. (

**B**) Estimated mean period between symptom onset and hospitalisation (blue), along with the corresponding 95% confidence interval for the mean value (grey shaded region). Circle areas are proportional to the numbers of individuals with symptom onset date t who were hospitalised $1/{\gamma}_{t}$ days later.

**Figure 2.**The reproduction number (${R}_{t}$ ) and the proportion of transmissions from hosts with few symptoms (${\alpha}_{t}$) vary in response to changes in the period between symptom onset and hospitalisation. (

**A**) Variation in ${R}_{t}$ and ${\alpha}_{t}$ between 2 January and 22 January 2020 due to changes in the mean time from symptom onset to hospitalisation ($1/{\gamma}_{t}$ days; see Figure 1B), under the assumption that ${R}_{0}=2$. Values of ${R}_{t}$ and ${\alpha}_{t}$ were calculated using Equations (1) and (2), respectively. Lines represent different values of the initial proportion of transmissions from hosts with few symptoms (${\alpha}_{0}$). Values of ${\alpha}_{0}$ between 0 and 0.4 were considered in steps of 0.05 (i.e., nine values in total). In the period from 2 January to 22 January 2020, transmissions from hosts with clear symptoms were typically prevented increasingly effectively, leading to a temporal trend from the tops to the bottoms of the lines shown. (

**B**) Equivalent figure to panel A, but with ${R}_{0}=3$. (

**C**) Equivalent figure to panel A, but with ${R}_{0}=4$. (

**D**) Required time within which symptomatic infectious hosts must be isolated on average ($1/{\gamma}_{t}$ days) so that ${R}_{t}$ is less than one (i.e., the outbreak is controlled), calculated using Equation (1) for different pairs of values of ${\alpha}_{0}$ and ${R}_{0}$. In panels A-C, the horizontal black line shows the threshold value of ${R}_{t}$ for outbreak control (${R}_{t}=1$). The value of $1/{\gamma}_{0}$ used in all panels is 6.7 days (as estimated in Figure 1B).

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**MDPI and ACS Style**

Thompson, R.N.; Lovell-Read, F.A.; Obolski, U.
Time from Symptom Onset to Hospitalisation of Coronavirus Disease 2019 (COVID-19) Cases: Implications for the Proportion of Transmissions from Infectors with Few Symptoms. *J. Clin. Med.* **2020**, *9*, 1297.
https://doi.org/10.3390/jcm9051297

**AMA Style**

Thompson RN, Lovell-Read FA, Obolski U.
Time from Symptom Onset to Hospitalisation of Coronavirus Disease 2019 (COVID-19) Cases: Implications for the Proportion of Transmissions from Infectors with Few Symptoms. *Journal of Clinical Medicine*. 2020; 9(5):1297.
https://doi.org/10.3390/jcm9051297

**Chicago/Turabian Style**

Thompson, Robin N., Francesca A. Lovell-Read, and Uri Obolski.
2020. "Time from Symptom Onset to Hospitalisation of Coronavirus Disease 2019 (COVID-19) Cases: Implications for the Proportion of Transmissions from Infectors with Few Symptoms" *Journal of Clinical Medicine* 9, no. 5: 1297.
https://doi.org/10.3390/jcm9051297