Objectives

The network will develop novel mathematical methodologies, as well as work in concert with other experts, to address mathematical issues that arise in the modelling of SARSCoV-2 variants. Three instances of novel methodologies are the real-time contact-mixing quantification, transmission properties of viral genotypes, and the integration of ventilation design in affecting transmission dynamics in public spaces. An instance of working in concert with other experts is participation in the VOC testing group with microbiologists, epidemiologists and clinicians to quickly develop the first transmission model of B.1.1.7 in Ontario and in making regular forecasts of frequency of the new variants.

Real-time contact-mixing quantification

This has been developed at the Laboratory for Industrial and Applied Mathematics (LIAM) at York University to quantify the contact-mixing during a rapid evolving pandemic when public health interventions modify the social mixing so rapidly that time and resources are not available to conduct survey studies. This methodology was used to identify age- and setting (workplace, household, school and community)- specific contact mixing patterns, and to quantify the shifts of contacts due to social distancing measures escalated in Ontario to manage the first COVD-19 wave. The LIAM group is currently using this methodology to identify shifts of contact mixing during the second wave in Ontario, and this work is important to identify the contacts in the school (schools were closed in the first wave, so the early study did not give information about school contacts under different social distancing guidelines), and hence could be used to inform the significance of school transmission, and evaluate different school-based interventions including asymptomatic testing. This group is in an excellent position to expand its work to use the updated incidence data, by ages and strains, to provide real-time assessment of the community transmission and to provide nowcasting of the transmission trend when the VOC strains become the dominating ones. This work will also allow us to inform strain-specific and age-specific transmissibility and severity (in terms of hospitalization and mortality), and to derive optimal reopening strategy (time and mode for switching to different stages of re-opening) by integrating their model with their developed stochastic optimization techniques. This optimal reopening strategy includes mass vaccination prioritization.

Transmission properties of viral genotypes

The emergence of variants of concern like B1.1.7 point to a need for the development of methods that can distinguish between viral genotypes that have enhanced transmission from those that are merely part of the background noise. Day (Queen’s University) proposes this be done is by using information contained in the shape of the epidemiological curve. For example, before a significant level of herd immunity occurs, the growth in daily case cases is expected to be linear on a log scale because of constant per capita growth (i.e., exponential growth). This is only true, however, if there is a single variant present. If variants are present with different transmission rates, then this curve should accelerate (bend upward) as the most transmissible variants come to dominate. Thus, there is information in the shape of these epidemiological curves about whether significant differences in transmission rate exist among currently circulating viral genotypes. Day’s goal will be to develop methods that can extract this information from these epidemiological curves. Preliminary results demonstrate that the “curvature" of these epidemiological data are, in fact, equal to the genetic variance in transmission rate in the viral population.

Integration of ventilation design

Of great interest is to study the role of ventilation in a safe reopening of public places. A model of S. Chaudhuri (Aerospace Studies, University of Toronto) mechanistically shows how the basic reproduction number from a particular expiratory event varies with the viral load and the infectious dose required for 99% probability of infection. One of the major pressing emerging questions of the present pandemic is how the overall reproduction number will change with new variants. We propose to address this by first including other major expiratory pathways (like breathing and speaking) to yield a comprehensive model from the flow physics of disease transmission. Next, the higher infectivity of the newer variants (for e.g., B.1.1.7 or B.1.351) will be incorporated in the model with correspondingly estimated lower MIDs (minimum infectious dose or infectious dose required for 99% probability of infection). For each variant, a probability density function (PDF) of the basic reproduction number will be calculated. The mode will correspond to average viral load while a suitably chosen higher moment will be given by the maximum viral load with the PDF connecting them. Individual PDF of R0 will be obtained for each variant, MID pair. From the available data on the fractions of each variant under circulation, the R0 PDFs for each variant will be appropriately weighted to obtain one comprehensive PDF. The first moment of this comprehensive PDF will provide the average basic reproduction number while the higher moments of the PDF will yield its overall superspreading potential.

Team Memebers

• Kumar Murty - The Fields Institute & University of Toronto

• Troy Day - Queen’s University

• Samira Mubareka - Sunnybrook Research Institute

• Beate Sander - UHN and University of Toronto

• Jianhong Wu - York University

• Swetaprovo Chaudhuri - Institute for Aerospace Studies & University of Toronto