Long-term impacts of teleworking policies on occupational health following a pandemic from a private company perspective

Code repository for the MESuRS group project

Model folder

Contains the script for the model.

Equations of the model

We modelled SARS-CoV-2 transmission in a company of $N$ employees using a compartmental model. In this model, employees can be susceptible to the respiratory disease $S$, exposed to the disease but not yet infectious $E$, infectious and asymptomatic $I_A$, exposed to the disease and infectious but presymptomatic $P$, infectious and symptomatic $I_S$, or recovered $R$.

$$\frac{dS}{dt} = - \lambda S$$

$$\frac{dE}{dt} = \lambda S - \sigma E$$

$$\frac{dI_A}{dt} = p_A \sigma E - \gamma_A I_A$$

$$\frac{dP}{dt} = (1 - p_A) \sigma E - \rho P $$

$$\frac{dI_S}{dt} = \rho P - \gamma_S I_S$$

$$\frac{dR}{dt} = \gamma_A I_A + \gamma_S I_S$$

In this compartmental model, infected individuals can develop symptoms with probability $1-p_A$ but their incubation period (here, time from infection to time of the onset of infectiousness) is the same whether they develop symptoms or not and is equal to $\frac{1}{\sigma}$. We also consider that for all individuals there is a pre-symptomatic infectious phase, with a duration equal to $\frac{1}{\rho}$. Infectious and symptomatic individuals are infectious for $\frac{1}{\gamma_S}$ days and are assumed to be on medical leave from their symptom/infectiousness onset to their recovery. Thereby, these individuals do not contribute to the propagation of the epidemic within the company. Infectious and asymptomatic individuals are infectious for $\frac{1}{\gamma_A}$ days and are responsible for the spread of the disease within the company.

The transmission rate $\lambda$ is divided into three terms as follows:

$$\lambda = \frac{5}{7} (1-\alpha) \frac{\beta (\nu I_A + P)}{N-I_S} + \frac{5}{7} \alpha \epsilon \lambda_v + \frac{2}{7} \lambda_v$$

Where $\beta$ is expressed using SARS-CoV-2 $R_0$ that we derived from the next-generation matrix for a frequency-dependent model:

$$\beta = \frac{R_0 \rho \gamma_A}{(1-\alpha) [(1 - p_A) \gamma_A + \rho \nu p_A]}$$

$\alpha$ is the proportion of employees teleworking, $\nu$ is the coefficient of relative infectivity of asymptomatic cases ($I_A$) compared to symptomatic cases ($P$ and $I_S$), $\lambda_v$ is the transmission rate from the community, and $\epsilon$ is a coefficient reducing the transmission from the community on teleworking days.

In addition to the transmission process of the infectious disease, we modelled the number of individuals who will ultimately develop a chronic disease following exposure to teleworking. To do so, we stratified the compartmental model into two populations, one population that will not develop a chronic disease, and a second that will develop a chronic disease. Given the different time scales of occurrence of the chronic disease and the infectious disease, we assume that the two populations mix homogeneously between them.

Parameterization of the model

According to Wu et al., 2022, the pooled incubation period for all SARS-CoV-2 variants is 6.57 days. In this case, $\sigma = \frac{1}{6.57}$.

SARS-CoV-2 variant	Mean incubation period (in days)
Alpha	5.00
Beta	4.50
Delta	4.41
Omicron	3.42

Koelle et al., 2022 have reviewed how our understanding of the transmission of SARS-CoV-2 has changed over the pandemic mostly using modelling studies. The first studies in Wuhan estimated that the $R_0$ lied between 2 and 4 before the lockdown. In their review, Dhungel et al., 2022 have estimated a pooled $R_0$ of 2.66 from studies published in the early months of the pandemic.

Buitrago-Garcia et al., 2020 estimated that the proportion of asymptomatic cases is on average equal to 20%. This would lead to $p_A = 0.20$. They also estimated that asymptomatic cases are less infectious than symptomatic cases by 65% leading to $\nu = 0.35$.

Need to find estimates for $\gamma_A$ and $\gamma_S$.

Analysis folder

Contains scripts used to run the model and generate figures.

Figures folder