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Fig. 1 | BMC Public Health

Fig. 1

From: Mathematical modelling of vaccination rollout and NPIs lifting on COVID-19 transmission with VOC: a case study in Toronto, Canada

Fig. 1

Flow diagram of COVID-19 transmission dynamics with two vaccination processes. Acronyms: i  {1–6}Age groups: 0–9 (unvaccinated), 10–19, 20–39, 40–59, 60–79, 80+ ; In Age group i: Si (Susceptible), Li (Latently infected), Ai (Asymptomatic infected), Imi (Symptomatic mild infected), Hi (Hospitalized), Di (Deceased), Ri (Recovered), V1i (Vaccinated with first dose), V2i (Vaccinated with second dose). To capture the different infection severities coming from VOC or wildtype variant, each disease-state progression is variant-dependent (* = wildtype or VOC). Red arrows: vaccination process. Dashed lines: waning process. Model assumptions:

• Only susceptible individuals, aged 10+ years, will receive the vaccine. Vaccine reduces susceptibility. Partially vaccinated people can become infected and infectious if the vaccine is not efficient.

• Immunity follows two steps: partial (receiving 1 dose) and full (receiving 2 doses), with the second dose given after 112 days (in some predictive scenarios after 50 or 21 days). Immunity from one dose wanes in 120 days and from two doses after 365 days. Vaccination continues until 80% of the entire population receive at least one dose.

• Vaccine efficacy is age-dependent (higher for teenagers and adults, 10% lower for elderly) and is the same against wildtype variant and VOC (all non-wildtype cases are assumed to be B.1.1.7 variant).

• VOC and wildtype are both included in the transmission process, assuming that the proportion of VOC cases increases over time following a sigmoidal function, with transmission from VOC 1.5 times higher than wildtype.

• Only individuals hospitalized might die from the infection.  \({\beta }^{O}, {\beta }^{N}\):

• probability of transmission; \({c}_{ij}\): contacts rate between individuals in age group i and individuals in age group j; \(\xi\): proportion of infectious individuals not respecting isolation; \(\lambda\): daily vaccine doses; \({\omega }_{1}, {\omega }_{2}\): waning rates, after one or two doses; \(\sigma\): average time between doses; \(\rho\): proportion of individuals developing symptoms; \({\gamma }_{H}\): hospitalization rate; \({\mu }_{H}\): death rate; \({\gamma }_{aR}, {\gamma }_{mR}, {\gamma }_{HR}\): recovery rate of asymptomatic, infectious and hospitalized individuals

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