# De-Escalation by Reversing the Escalation with a Stronger Synergistic Package of Contact Tracing, Quarantine, Isolation and Personal Protection: Feasibility of Preventing a COVID-19 Rebound in Ontario, Canada, as a Case Study

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## Abstract

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## 1. Introduction

**Escalation-Phase****0**:- Monitoring and international travel advisories;
**Escalation-Phase****1**:- School closure;
**Escalation-Phase****2**:- Emergency declaration, with closure of public events and recreational venues;
**Escalation-Phase****3**:- Closure of all non-essential workplaces.

## 2. Materials and Methods

#### 2.1. The Transmission Dynamics Model

#### 2.2. Data

#### 2.3. The Parameter Identification and Estimation of Intervention Effectiveness in Different Escalation Phases

## 3. De-Escalation Considerations

**De-escalation-Phase****1:**- Opening of workplaces;
**De-escalation-Phase****2:**- Resumption of public events and activities;
**De-escalation-Phase****3:**- School opening.

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The flowchart of the transmission dynamics model, where the population is stratified by susceptible, exposed, asymptomatic infectious, symptomatic infectious, and recovered status, and by quarantine and isolation status.

**Figure 2.**Data fitting and projection. (

**A**) The red circles represent the cumulative confirmed cases in Ontario, Canada. (

**B**–

**D**) Based on the mean curve of the 500 times estimation, the population of $I\left(t\right)$, $A\left(t\right)$ and $D\left(t\right)$ reach their peak times around April 12, April 16 and April 21 while the peak values are around 1538, 1469 and 2444, respectively. The final cumulative confirmed cases projected by the model is about 23,940.

**Figure 3.**Estimated effective reproduction number ${R}_{t}$ in Ontario, Canada as a function of time (mean value and 95% confidence interval).

**Figure 4.**Values of ${R}_{c}$ in the plane $(q,1/{\delta}_{I})$, with baseline parameters estimated on March 24 (top-left panel), and under different scenarios of contact rate reduction (other panels). The red line corresponds to ${R}_{c}=1$ (with dashed lines showing confidence intervals in the baseline scenario). The black crosses correspond to the parameters (max/min) estimated after March 24 (last day of the estimation period is April 21).

**Figure 5.**Same as Figure 4, with baseline parameters estimated in the period March 14–18.

**Figure 6.**Same as Figure 4, with baseline parameters estimated in the period before March 14.

**Figure 7.**Values of ${R}_{c}$ in the plane $\left(q,\beta \right)$, with baseline parameters estimated on March 24 (top-left panel), and under different scenarios of contact rate reduction (other panels). The red line corresponds to ${R}_{c}=1$ (with dashed lines showing confidence intervals in the baseline scenario). The black crosses correspond to the parameters (max/min) estimated after March 24 (last day of the estimation period is April 21).

**Figure 8.**Same as Figure 7, with baseline parameters estimated in the period March 14–18.

**Figure 9.**Same as Figure 7, with baseline parameters estimated in the period before March 14.

**Figure 10.**Values of ${R}_{c}$ in the plane $\left(q,c\right)$ for different values of the time for diagnosis ($1/{\delta}_{I}$). The red line corresponds to ${R}_{c}=1$ (with dashed lines showing confidence intervals).

**Figure 11.**Values of ${R}_{c}$ in the plane $\left(q,{\delta}_{I}/({\delta}_{I}+\alpha +{\gamma}_{I}\right))$, for different values of the contact rate. The red line corresponds to ${R}_{c}=1$ (dashed lines showing confidence intervals).

**Figure 12.**Left panel: values of ${R}_{c}$ in the plane $\left(\alpha ,\beta \right)$. Right panel: values of ${R}_{c}$ in the plane $\left({\gamma}_{I},\beta \right)$. The other parameters are those estimated on March 24. The red line corresponds to ${R}_{c}=1$ (dashed lines showing confidence intervals).

**Table 1.**School closure, emergency and public health emergency declarations in Canada by province and territories.

Province | School Closure | Date of Emergency Declaration and Type | Date of Closure of Non-Essential Establishments |
---|---|---|---|

British Columbia | 14-March-2020 | 18-March-2020 (public health emergency) | 21-March-2020 |

Alberta | 14-March-2020 | 17-March-2020 (provincial public health emergency) | 27-March-2020 |

Saskatchewan | 21-March-2020 | 18-March-2020 (provincial state of emergency) | 20-March-2020; Expanded 23-March-2020 |

Manitoba | 14-March-2020 | 20-March-2020 (provincial state of emergency) | 20-March-2020 |

Ontario | 14-March-2020 | 17-March-2020 (provincial state of emergency) | 23-March-2020; Expanded 25-Mar-2020 |

Quebec | 14-March-2020 | 13-March-2020 (provincial public health emergency) | 15-March-2020; Expanded 23-March-2020; Expanded further 28-March-2020 |

Newfoundland & Labrador | 14-March-2020 | 18-March-2020 (public health emergency) | 18-March-2020; Expanded 23-March-2020: |

New Brunswick | 14-March-2020 | 19-March-2020 (provincial state of emergency) | 19-March-2020 |

Nova Scotia | 14-March-2020 | 22-March-2020 (provincial state of emergency) | 24-March-2020 |

Prince Edward Island | 14-March-2020 | 16-March-2020 (public health emergency) | 18-March-2020 |

Yukon | 14-March-2020 | 18-March-2020 (public health emergency) | |

Northwest Territories | 14-March-2020 | 19-March-2020 (public health emergency) | |

Nunavut | 14-March-2020 | 19-March-2020 (public health emergency) |

Parameter | Definitions | Mean (Std) | Source | |

${c}_{0}$ | Contact rate before March 14 | 11.5801 (0.3456) | Estimated | |

${c}_{1}$ | Contact rate between March 14 to March 18 | 10.1202 (0.9185) | Estimated | |

${c}_{2}$ | Contact rate between March 18 to March 24 | 8.0495 (0.2787) | Estimated | |

$c\left(t\right)$ | ${c}_{2}$ | Constant contact rate at March 24 | 8.0495 (0.2787) | Estimated |

${r}_{1}$ | Exponential decrease in contact rate | 0.0466 (0.0152) | Estimated | |

${c}_{b}$ | Minimum contact rate after March 24 | 2.1987 (0.2400) | Estimated | |

$\beta $ | Probability of transmission per contact | 0.1469 (0.0023) | Estimated | |

${q}_{0}$ | Fraction of quarantined exposed individuals before March 24 | 0.1145 (0.0114) | Estimated | |

$q\left(t\right)$ | ${q}_{0}$ | Quarantine fraction at March 24 | 0.1145 (0.0114) | Estimated |

${r}_{2}$ | Exponential increase in quarantine fraction | 0.1230 (0.0123) | Estimated | |

${q}_{b}$ | The maximum quarantine fraction | 0.3721 (0.0371) | Estimated | |

$\sigma $ | Transition rate of exposed individuals to the infected class | 1/5 | [9] | |

$\lambda $ | Rate at which the quarantined uninfected contacts were released into the wider community | 1/14 | [7] | |

$\varrho $ | Probability of having symptoms among infected individuals | 0.7036 (0.0261) | Estimated | |

${\delta}_{I}$ | Transition rate of symptomatic infected individuals to the quarantined infected class | 0.1344 (0.0134) | Estimated | |

${\delta}_{q}$ | Transition rate of quarantined exposed individuals to the quarantined infected class | 0.1237 (0.0086) | Estimated | |

${\gamma}_{I}$ | Recovery rate of symptomatic infected individuals | 0.1957 (0.0111) | Estimated | |

${\gamma}_{A}$ | Recovery rate of asymptomatic infected individuals | 0.139 | [7] | |

${\gamma}_{D}$ | Recovery rate of quarantined diagnosed individuals | 0.2 | [8] | |

$\alpha $ | Disease-induced death rate | 0.008 | [8] | |

$\theta $ | Modification factor of asymptomatic infectiousness | 0.0275 (0.0128) | Estimated | |

Initial values | Definitions | Mean (Std) | Source | |

$S\left(0\right)$ | Initial susceptible population | $1.471\times {10}^{7}$ | Data | |

$E\left(0\right)$ | Initial exposed population | 8.9743 (0.6558) | Estimated | |

$I\left(0\right)$ | Initial symptomatic infected population | 5.3887 (0.9442) | Estimated | |

$A\left(0\right)$ | Initial asymptomatic infected population | 19.4186 (3.9406) | Estimated | |

${S}_{q}\left(0\right)$ | Initial quarantined susceptible population | 0 | Data | |

${E}_{q}\left(0\right)$ | Initial quarantined exposed population | 0 | Data | |

$D\left(0\right)$ | Initial quarantined diagnosed population | 5 | Data | |

$R\left(0\right)$ | Initial recovered population | 0 | Data |

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## Share and Cite

**MDPI and ACS Style**

Tang, B.; Scarabel, F.; Bragazzi, N.L.; McCarthy, Z.; Glazer, M.; Xiao, Y.; Heffernan, J.M.; Asgary, A.; Ogden, N.H.; Wu, J.
De-Escalation by Reversing the Escalation with a Stronger Synergistic Package of Contact Tracing, Quarantine, Isolation and Personal Protection: Feasibility of Preventing a COVID-19 Rebound in Ontario, Canada, as a Case Study. *Biology* **2020**, *9*, 100.
https://doi.org/10.3390/biology9050100

**AMA Style**

Tang B, Scarabel F, Bragazzi NL, McCarthy Z, Glazer M, Xiao Y, Heffernan JM, Asgary A, Ogden NH, Wu J.
De-Escalation by Reversing the Escalation with a Stronger Synergistic Package of Contact Tracing, Quarantine, Isolation and Personal Protection: Feasibility of Preventing a COVID-19 Rebound in Ontario, Canada, as a Case Study. *Biology*. 2020; 9(5):100.
https://doi.org/10.3390/biology9050100

**Chicago/Turabian Style**

Tang, Biao, Francesca Scarabel, Nicola Luigi Bragazzi, Zachary McCarthy, Michael Glazer, Yanyu Xiao, Jane M. Heffernan, Ali Asgary, Nicholas Hume Ogden, and Jianhong Wu.
2020. "De-Escalation by Reversing the Escalation with a Stronger Synergistic Package of Contact Tracing, Quarantine, Isolation and Personal Protection: Feasibility of Preventing a COVID-19 Rebound in Ontario, Canada, as a Case Study" *Biology* 9, no. 5: 100.
https://doi.org/10.3390/biology9050100