# Methods

Described below is a brief description of methods, data and model parameters used at 613covid.ca. More detailed information can be found in the accompanying references.

## Projection models

All data used to create projection models can be accessed at Open Ottawa. See ’COVID-19 cases and deaths`.

1. Covid-19 short-term projections are created using the Bayesian EpiNow2 model developed by the EpiForecasts team.

• Projections are based on observed covid-19 cases by reporting date, which is, in turn, estimated using reported incubation period and consideration for reporting delays. Future updates on 613covid.ca will consider observed episode date for Ottawa cases.
2. Covid-19 case projections created using the Bayesian SEIR model developed by Simon Fraser University.

• Projections are based on observed covid-19 cases by episode date. Episode date reflects the date closest to the onset of symptoms. Projections exclude the most recent week of cases, reflecting a lag time in detecting and reporting recent covid-19 infections.

• Covid-19 transmission is estimated within the SEIR model.

3. Hospital projections created using the Bayesian extension to the CHIME model developed by the University of Pennsylvania Health System.

• Projections are based on the observed covid-19 hospitalization census for each day for the five Ottawa hospitals who treat covid-19 patients.

• Hospitalization is used to estimate covid-19 transmission in Ottawa population that results in hospitalization.

• Model parameters other than Ottawa hospital use are aligned with other models, described below.

## Wastewater covid-19 surveillance

Ottawa’s wastewater data is available here.

See Ottawa Public Health webiste for an overview of the wastewater surveillance program and its role in covid-19 surveillance. Detail laboratory methods are published here. The surveillance program is under development. Results and interpretation are publicly-presented for discussion.

Wastewater samples are from the Robert O. Pickard Environmental Centre (ROPEC) which collects and treats wastewater from ~91.6% of Ottawa’s population. Samples for covid-19 surveillance are collected hourly for a period of 24 hours, five days a week from sludge (directly from the primary clarifiers). The assay method has been validated in a national cross-laboratory study. Two viral regions of SARS-CoV-2 (N1 and N2) are assayed and standardized using the viral levels of Pepper Mild Mottle Virus (PMMoV). The reported measure is the sample mean of N1 + N2 copies per copy of PMMoV. A peer-reviewed study describes the methods in more detail. The pre-print is published here.

## The importance of physical distancing

The trend of COVID-19 cases and hospital use is summarized as “doubling time.” Doubling time — and the weekly change in doubling time — are the most important parameters in COVID-19 projections that vary between communities.

An exponential growth in covid-19 cases and hospitalization (doubling time of less than 4 days) will occur unless one of two situations occurs:

1. The number of people susceptible to infection decreases. As an epidemic progresses, there will be fewer people left in the community who can become infected. However, as of Oct 18, 2021 only a small proportion of people living in Ottawa are currently infected or are recovered from COVID-19 – likely less than 5%. This means that the current reduction in susceptible people has a negligible effect effect on changes to hospital infection doubling times.

2. Preventive measures slow the spread of infection.

The first situation — how doubling time decreases as the number of susceptible people decreases — can be easily modelled using mathematical formulas.

The second situation — the effectiveness of preventive measures — is more difficult to estimate accurately. Prevention and control measures depend not only on what measures are in place over the last 2-4 weeks, but also how well people follow the measures.

## How physical distancing affects COVID-19 projections

The projections of hospital cases uses an $$SIR$$ model ($$S$$ = susceptible, $$I$$ = infected, $$R$$ = recovered people). Within an SIR model, new infections at time ($$t+1$$) are equal to:

$I_{t+1} = \beta S_t I_t$ Where $$\beta$$ is commonly referred as the “force of infection” because it describes how quickly a disease can move through a population. $$\beta$$ is a probability or risk that ranges from 0 to 1. $$\beta$$ value = 0.5 means 50% of susceptible people ($$S_t$$) who are in contact with an infected person ($$I_t$$) will become infected ($$I_{t+1}$$).

Physical distancing is a ‘control measure’ to reduce the effective force of infection, $$\beta$$. A control measure, $$\lambda$$ reduces new infections, where $$\lambda = 1$$ results in a complete disruption in new infections (conversely, $$\lambda = 0$$ has no effect for reducing new infections). The projections presented on this website assume physical distancing is directly related to effective control. This means 50% physical distancing is the same as $$\lambda = 0.5$$. Daughton et al. (2017)

Note that $$\beta$$ is related to the epidemiology measure $$R_0$$ - the basic reproductive number that describes the expected number of people who become infected with from each person with COVID-19 at the beginning of an outbreak. $$R_0 = \frac{\beta}{\gamma}$$, where $$\gamma$$ is the reciprocal of the infectious period ($$\psi$$).

## Calculating physical distancing effectiveness

Physical distancing effectiveness is equal to $$\lambda$$, for the calculations on this website. In practice, contract tracing and isolation is the other main control measure. The effect of contract tracing was not separated from physical distancing.

Physical distancing effectiveness, $$\lambda$$:

$\lambda = 1 - \frac{(g + \gamma)}{\beta_0}$ Where,

$$g$$ is the observed growth rate, expressed the rate of new COVID-19 cases each day. $$\beta_0$$ is the force of infection at the beginning of the outbreak. $$\beta_0 = 0.332$$ when doubling time $$D_t = 4$$ days (or growth rate at the beginning of the outbreak, $$g_0 = 0.189$$). In turn, $$g_0$$ is derived from a basic reproduction number ($$R_0$$) of 2.32 and mean generation interval ($$T_c$$) of 7 days, where,

$g_0 = \frac{R_0 - 1}{T_c}$ or,

$g_0 = 2^\frac{1}{T_d} - 1$ or,

$g_0 = \beta_0 - \gamma$

## Input parameters

Parameter estimates for hospital projections are based on covid-19 patients from the Ottawa Hospital and from the COVID-19-MC and Tuite, Fisman, et al. models, with updates based on Verity et al. (Lancet, March 20, 2020)* and Ferguson et al. (March 16, 2020).

## Data used to plot visualizations

### References

Daughton, Ashlynn R, Nicholas Generous, Reid Priedhorsky, and Alina Deshpande. 2017. “An Approach to and Web-Based Tool for Infectious Disease Outbreak Intervention Analysis.” Scientific Reports 7: 46076.