Flattening the Curve Successfully

Our Projections
The impact of the COVID-19 pandemic is significant and considered to be the most serious public health threat since the A (H1N1) pandemic in 1918, also known as the Spanish flu. In this article, we present the methodology of our epidemiological modeling for the province of Quebec. We are using the official data provided by the INSPQ1 in an attempt to forecast the end of the coronavirus epidemic.

View Our Quebec COVID-19 Projections

Transmission Model
We altered a SEIR Model without vital dynamics that was initially developed to explore and support pandemic influenza planning. This model is superior to the textbook SIR Model because it takes into consideration the incubation period during which individuals have been infected but are not yet infectious. The compartments and equations of the SEIR Model are shown below:

Source: Factor-Based

Clinical Variables
dS/dt = Susceptible = People who are at risk for catching the disease;
dE/dt = Exposed = People who caught the disease or are carrying asymptomatically;
dI/dt = Infectious = People who caught the disease and are experiencing symptoms;
dR/dt = Recovered = People who caught the disease and developed some immunity;
S + E + I + R = Total Population is estimated at 8.5M for the province of Quebec.

Clinical Parameters
Tinf = 1/gamma = Infectious period (in days): 2.3
Based on findings of researchers from Wuhan, a fair estimation for the latent time in which a person becomes infectious is determined at 2.3 days2 in a non-controlled environment.

Tinc = 1/alpha = Incubation period (in days): 5.2
Based on findings of researchers from Wuhan, a person is estimated to be incubating COVID-19 approximately 5.2 days3 (ranging from 2 to 14 days) in a non-controlled environment.

Rt = Basic reproduction number (at time t): 2.6 ← t=0
We examined values between 2.0 and 2.6 and we are settling with a baseline assumption of 2.6 in Quebec at the onset of the epidemic. The province is considered a major flight hub to Europe, with many countries highly infected which is the rationale behind a higher R0.

Intervention Parameters
We consider the impact of nine different non-pharmaceutical interventions (NPI) as they were implemented by the Federal and Provincial governments over the last weeks. In each case, we use a conservative assumption about the impact of the intervention on the reproduction rate of the virus. We assume these measures will stay in place for 3 months and a 10-day lag until the effect becomes apparent.

LabelNon-Pharmaceutical InterventionDateEffectRt Impact
CICase Isolation09-Mar19-Mar8-15%
VQVoluntary Quarantine09-Mar19-Mar8-15%
CSUClosure of Schools & Universities13-Mar23-Mar15-30%
DEHDistancing of Elderlies & Hospitals14-Mar24-Mar15-30%
ITRInternational Travel Restrictions18-Mar28-Mar15-30%
UTRUS Travel Restrictions21-Mar31-Mar15-30%
CNEClosure of Non-Essentials23-Mar02-Apr15-30%
RRARegional Restricted Access28-Mar07-Apr8-15%
PPEPPE Deliveries & Usage04-Apr14-AprGradual
Source: The Gazette, Factor-Based

09-Mar: Case Isolation (CI)
The first presumed case of COVID-19 is confirmed in Quebec on February 28th. The patient, a Montreal-area woman, had returned from Iran that week. A couple of other cases coming from other countries were confirmed the following days and placed in isolation at home.

09-Mar: Voluntary Quarantine (VQ)
Many individuals who travelled outside of the country and are experiencing flu-like symptoms are self-isolating for 14 days as a precaution. Household contact increases during that time but we assume the community contacts are reduced drastically for the containment period.

13-Mar: Closure of Schools & Universities (CSU)
Quebec shuts all daycares, schools, CEGEPs and universities for two weeks. As we are writing this report, this period has now been extended until May 1st. Students are considered to be high transmission vectors so this measure should significantly reduce the spread of the virus.

14-Mar: Distancing of Elderlies & Hospitals (DEH)
Premier François Legault requested all the population over the age of 70 to stay at home to limit the exposure to the virus. At the same time, visits to hospitals and senior residences are banned. This is important as we seen huge clusters in those facilities in the state of Washington.

18-Mar: International Travel Restrictions (ITR)
Prime Minister Justin Trudeau announced that starting Wednesday, all international visitors to Canada will be turned around with the exception of Americans, diplomats and flight crews. This measure came longer than expected as other countries already closed their borders.

21-Mar: US Travel Restrictions (UTR)
Donald Trump announced the US will close its border with Canada to non-essential traffic starting Saturday. Prime Minister Justin Trudeau waited for the US to make the first move to avoid any political tensions. Also, illegal migrants attempting to cross the border irregularly will be turned back.

23-Mar: Closure of Non-Essentials (CNE)
Quebec orders the closure of all non-essential businesses, including construction sites until April 13th. This is a significant measure as many employees are furloughed and will seek government help. However, this measure will greatly lower the transmission as most people are at home.

28-Mar: Regional Restricted Access (RRA)
Deputy Premier Geneviève Guilbault announced that the police would install checkpoints to restrict travel to and from eights regions in Quebec. Only essential travel would be permitted. This will prevent people from infectious regions such as Montreal and Estrie to spread it.

04-Apr: PPE Deliveries & Usage (PPE)
Quebec is expected to receive supplies of medical protective equipment from various suppliers across the world every week. At the same time, the population is becoming more cognizant on wearing artisanal masks outdoor. Usage of PPE like in Asia should mitigate the epidemic.

Epidemiological Outlook
Based on our results, 27K people in Quebec are most likely going to be infected and diagnosed for COVID-19. We are forecasting the official reported numbers from INSPQ. The real number of cases is actually much higher than that considering that 50% of infections are not identified4. This is because people are asymptomatic, with mild cases or under-ascertained.

View Our Quebec COVID-19 Projections

We believe this first wave of COVID-19 to be under control sufficiently in June for the government to reopen progressively non-essential businesses. However cautious is warranted. Drastic interventions to flatten the curve are slowing and extending the progression of the disease to alleviate the hospital system burden. In other words, we might still see cases in the fall.

A takeaway of this article is that the non-pharmaceutical interventions (NPI) are most likely to limit the impact of the pandemic in Quebec. These measures should be successful in reducing the reproduction number in a way that human-to-human transmission becomes mitigated. However, they will have to stay in place and be followed by the population.

Economic Impact
Our research shows non-essential businesses are most likely going to stay closed until the summer. As much as Premier Legault is giving hope to entrepreneurs, we think this measure is going to be extended at least for another month. Also, Valérie Laplante said bars, restaurants and terrases could open in May. We believe this is a wishful thinking and not possible. There will still be too many cases, even if they are declining and we are past the peak.

Looking on the bright side, we believe public listed companies that had a sound business plan before the sanitary crisis will recover as the various measures offered both by the Federal and Provincial governments should partially compensate some of the losses of Revenues. On a competitive level, companies in other countries are also coping with the same situation. Therefore, the impact between the Quebec companies versus their foreign competitors is limited.

Francois Soto, CFA, MBA, FRM, CIM


1. INSPQ. COVID-19 data in Quebec. Last data update as of April 7, 2020, 1pm. Available from: https://www.inspq.qc.ca/covid-19/donnees;

2. Li Q, Guan X, Wu P, et al. Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus– Infected Pneumonia. N Engl J Med 2020; 382:1199-1207. Available from: https://www.nejm.org/doi/pdf/10.1056/NEJMoa2001316?articleTools=true

3. Wu J, Leung K, Leung M, et al. Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. The Lancet 2020; 395: 689-97. Available from:  https://doi.org/10.1016/S0140-6736(20)30260-9  

4. Verity R, Okell LC, Dorigatti I, et al. Estimates of the severity of COVID-19 disease. medRxiv 2020; Available from: https://www.medrxiv.org/content/10.1101/2020.03.09.20033357v1;