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The stochasticity in adherence to nonpharmaceutical interventions and booster doses and the mitigation of COVID-19

  • *Corresponding author: Huaiping Zhu

    *Corresponding author: Huaiping Zhu

Dedicate to Professor Jibin Li on the occasion of his 80th birthday.
†These authors contributed equally to this work.

The first author is supported by [Chinese Scholarship Council]

Abstract Full Text(HTML) Figure(9) / Table(5) Related Papers Cited by
  • Facing the more contagious COVID-19 variant, Omicron, nonpharmaceutical interventions (NPIs) were still in place and booster doses were proposed to mitigate the epidemic. However, the uncertainty and stochasticity in individuals' behaviours toward the NPIs and booster dose increase, and how this randomness affects the transmission remains poorly understood. We present a model framework to incorporate demographic stochasticity and two kinds of environmental stochasticity (notably variations in adherence to NPIs and booster dose acceptance) to analyze the effects of different forms of stochasticity on transmission. The model is calibrated using the data from December 31, 2021, to March 8, 2022, on daily reported cases and hospitalizations, cumulative cases, deaths and vaccinations for booster doses in Toronto, Canada. An approximate Bayesian computational (ABC) method is used for calibration. We observe that demographic stochasticity could dramatically worsen the outbreak with more incidence compared with the results of the corresponding deterministic model. We found that large variations in adherence to NPIs increase infections. The randomness in booster dose acceptance will not affect the number of reported cases significantly and it is acceptable in the mitigation of COVID-19. The stochasticity in adherence to NPIs needs more attention compared to booster dose hesitancy.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

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  • Figure 1.  Flow diagram of COVID-19 transmission dynamics with third dose vaccination processes. All individuals are in different states, $ S $ (Susceptible), $ E $ (Latently infected), $ I_1 $ (Unreported infected), $ I_2 $ (Reported mild infected), $ H $ (Hospitalized), $ D $ (Deceased), $ R $ (Recovered), $ V $ (Vaccinated with booster doses)

    Figure 2.  Fitting results of daily infections and hospitalizations, cumulative cases, deaths and vaccinations for booster doses in Toronto from December 31, 2021, to March 8, 2022. Circles represent observed data. Lines represent calibration results which are the average of 1,000 runs. Shaded areas with color represent the 95% confidence interval of predictions

    Figure S1.  MCMC simulation. Chains of 1,000,000 samples are drawn with first 20,000 burn-in samples in every chain. We can see that the chains are well-mixed, implying the convergence of the sampling

    Figure S2.  MCMC simulation. Posterior distributions of the parameters

    Figure 3.  Effects of stochasticity in NPI adherence on the outbreak. Average results of reported cases and total cases under different volatility of the transmission rate with 1,000 simulations are shown, given two different means of transmission rate (0.17 and 0.27)

    Figure 4.  Comparisons of the effect of demographic stochasticity and environmental stochasticity in adherence to NPIs on the outbreak under a reopening or closing strategy. Average results of daily reported cases under stepwise volatility of transmission rate are shown when lifting control measures with time (a) or intensifying control measures with time (b) with 1,000 simulations. The inner plots show the cumulative reported cases. Results for ODE model, stochastic model with demographic stochasticity, and stochastic model with demographic and environmental stochasticity are shown. For the model with demographic and environmental stochasticity, we assume volatility of transmission rate is time-dependent, and volatility of vaccination rate takes the estimated value. Used values of mean and volatility of transmission rate in figures see Table 5. The volatility in the figure legend refers to volatility of transmission rate, and DS represents demographic stochasticity

    Figure 5.  Effects of stochasticity in vaccine acceptance on the outbreak. Average results of vaccinations and total cases under different volatility (a) and the speed of variation (b) of vaccination rate with 1,000 simulations are shown

    Figure 6.  Comparisons of the effect of demographic stochasticity and environmental stochasticity in vaccines on the outbreak under a reopening strategy. Average results of daily reported cases under stepwise volatility of vaccination rate when lifting control measures with 1,000 simulations are shown. The inner plot shows cumulative reported cases. Results for ODE model, stochastic model with demographic stochasticity, and stochastic model with demographic and environmental stochasticity are shown. For the model with demographic and environmental stochasticity, we assume volatility of vaccine rate is time-dependent, and volatility of transmission rate takes the estimated value. Used values of mean and volatility of vaccination rate in the figure see Table 5. The volatility in the figure legend refers to volatility of vaccination rate, and DS represents demographic stochasticity

    Figure 7.  Comparisons of the effect of variations in vaccination rate and transmission rate on the outbreak. Average results of cumulative vaccinations (a) and total cases (b) are shown under different mean and volatility of transmission rate, as well as the speed of variation and volatility of vaccination rate with 1,000 simulations

    Table 1.  Model assumptions

    Notation Description
    Testing/Reporting A proportion of symptomatic infections get a PCR test and confirmed, then included in the report.
    Severe Outcomes Only severe infected individuals will be admitted to hospitals; Only hospitalized individuals die in ICUs will count as death from the infection.
    Vaccination Due to low efficacy of the first two doses and waning immunity, the vaccine compartment reflects the individuals protected by dose 3. We only include the booster dose efficacy against infections.
     | Show Table
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    Table 2.  Model variables and fixed parameters

    Variables and their initial values
    Descriptions Values
    Notation Description Initial Value
    $ S(t) $ Number of susceptible individuals at day $ t $ Estimated
    $ E(t) $ Number of exposed individuals at day $ t $ Estimated
    $ I_1(t) $ Number of unreported individuals who are asymptomatic or symptomatic mild infectious at day $ t $ Estimated
    $ I_2(t) $ Number of reported individuals who are symptomatic mild infectious at day $ t $ Estimated
    $ H(t) $ Number of severe patients that need hospital care 230
    $ D(t) $ Number of deceased individuals at day $ t $ 3,730
    $ R(t) $ Number of recovered individuals at day $ t $ 222,279
    $ V(t) $ Number of effectively protected individuals from booster doses at day $ t $ 552,800
    $ log(\lambda(t)) $ Logarithm of the daily vaccination rate for booster dose at day $ t $ Estimated
    Fixed parameters for Omicron transmission in Toronto
    Stages Values in stages
    $ N $ Population size in Toronto 2,974,293 [7]
    $ 1/\alpha $ Length of days between exposure and case report 5 [41,48]
    $ \tau $ Latent period 1.5 [48,22]
    $ \rho $ Proportion of infected people who will develop symptoms 0.632 [23]
    $ \gamma_1 $ Recovery rate of unreported infectious individuals 1/8.5 [51,41,48,22]
    $ \gamma_2 $ Recovery rate of reported infectious individuals 1/5 [51]
    $ 1/ \gamma_h $ Length of days for mildly infected individuals developing severe symptoms and being admitted into hospital 8 [41,49]
    $ \gamma_{hr} $ Recovery rate of hospitalized individuals 1/5.5 [11]
    $ 1/\gamma_{d} $ Length of stay for patients in hospital before died 8 [15]
    $ \epsilon $ Efficacy booster dose 70% [36]
     | Show Table
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    Table 3.  Estimated initial values and parameters

    Notation Description Prior distributions Estimated mean value 95% CI
    $ E(t_0) $ Number of exposed individuals at day $ t_0 $ $ \mathbb{N}(18000, 0.5) $ 19545 $ [8133, 44304] $
    $ I_1(t_0) $ Number of unreported individuals who are asymptomatic or symptomatic mild infectious at day $ t_0 $ $ \mathbb{N}(42233, 0.5) $ 47043 $ [26351, 50883] $
    $ I_2(t_0) $ Number of reported individuals who are symptomatic mild infectious at day $ t_0 $ $ \mathbb{N}(18670, 0.5) $ 17160 $ [8368, 20081] $
    $ log(\lambda(t_0) $ Logarithm of daily vaccination rate for booster dose at day $ t_0 $ $ \mathbb{N}(log(0.0093), 0.5) $ $ log(0.0097) $ [$ log(0.0047), log(0.0214) $]
    $ p_2 $ Proportion of infected people who will conduct PCR test $ \mathbb{N}(0.8, 0.5) $ 0.7803 $ [0.3475, 1.2846] $
    $ p_h $ Proportion of mildly infected individuals develop severe symptoms and need hospital care in stages Stage1: $ \mathbb{N}(0.032, 0.5) $; Stage2: $ \mathbb{N}(0.097, 0.5) $ Stage1: 0.0399; Stage2: 0.1059 Stage1: [0.0254, 0.0672]; Stage2: [0.0605, 0.2114]
    $ p_d $ Proportion of hospitalized patients died $ t_0 $ $ \mathbb{N}(0.159, 0.5) $ 0.1555 $ [0.0860, 0.2591] $
    $ \bar{\beta} $ Mean transmission rate $ \mathbb{N}(0.17, 0.5) $ 0.1654 $ [0.0915, 0.3662] $
    $ \sigma_{\beta} $ Volatility of transmission rate $ \mathbb{N}(0.2, 0.5) $ 0.2 $ [0.0936, 0.3948] $
    $ log(\bar{\lambda}) $ Logarithm of mean vaccination rate $ \mathbb{N}(log(0.00056), 0.5) $ $ log(0.0005) $ [$ log(0.00024), log(0.001) $]
    $ r_{\lambda} $ Speed of variation of the vaccination rate for third doses $ \mathbb{N}(0.01, 0.5) $ 0.0081 $ [0.0040, 0.0271] $
    $ \sigma_{\lambda} $ Volatility of vaccination rate for booster doses $ \mathbb{N}(0.153, 0.5) $ 0.1517 $ [0.0916, 0.1828] $
     | Show Table
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    Table 4.  Summary of possible changes on the process for the epidemic model when $ \Delta t $ is small

    Possible change Probability
    $ [-1, 0, 0, 0, 0, 0, 0, +1] $ $ \lambda \epsilon S \Delta t = P_{c1} \Delta t $
    $ [-1, +1, 0, 0, 0, 0, 0, 0] $ $ \beta S I_1 \Delta t /N = P_{c2} \Delta t $
    $ [0, -1, +1, 0, 0, 0, 0, 0] $ $ \frac{1-\rho} {\tau} E\Delta t + \frac{\rho (1-p_2)}{ \tau} E \Delta t = P_{c3} \Delta t $
    $ [0, 0, -1, 0, 0, 0, +1, 0] $ $ \gamma_1 I_1 \Delta t = P_{c4} \Delta t $
    $ [0, -1, 0, +1, 0, 0, 0, 0] $ $ \rho p_2 \alpha E \Delta t = P_{c5} \Delta t $
    $ [0, 0, 0, -1, 0, 0, 0, 0] $ $ (1-p_h) \gamma_2 I_2 \Delta t = P_{c6} \Delta t $
    $ [0, 0, 0, -1, +1, 0, 0, 0] $ $ p_h \gamma_h I_2 \Delta t = P_{c7}\Delta t $
    $ [0, 0, 0, 0, -1, 0, +1, 0] $ $ (1-p_d) \gamma_{hr} H \Delta t = P_{c8} \Delta t $
    $ [0, 0, 0, 0, -1, +1, 0, 0] $ $ p_d \gamma_d H \Delta t = P_{c9} \Delta t $
     | Show Table
    DownLoad: CSV

    Table 5.  List of scenarios related to partial/total reopening, and values of the mean transmission rate, the volatility of transmission rate, and the volatility of vaccination rate used to project cases in the investigation

    Mean transmission rate
    Descriptions Values
    Baseline Limit capacity of social gatherings and indoor public settings & events venues Estimated mean transmission rate using the data between December 31, 2021, and March 8, 2022
    Partial opening Lift mask mandates Increase the baseline value by 127%$ ^{\circledast} $
    Total reopening Remove all control measures, directives and orders Increase the partial opening value by 70%
    Case 1: lift control measures over time
    Stages Mean transmission rate
    Stage 1: Jan 1, 2022 - Mar 20, 2022[45] Baseline value
    Stage 2: Mar 21, 2022 - Apr 26, 2022[46] Partial opening value
    Stage 3: Apr 27, 2022 – Dec 31, 2022 Total reopening value
    Case 2: strengthen control measures over time
    Stages Mean transmission rate
    Stage 1: Jan 1, 2022 - Jan 10, 2022 Total reopening value
    Stage 2: Jan 11, 2022 - Jan 20, 2022 Partial opening value
    Stage 3: Jan 21, 2022 - Mar 29, 2022 Baseline value
    Volatility of transmission rate
    Stages Values in stages
    Gradually increased $ 1.3 \quad \quad 1.6 \quad 1.9$
    Gradually decreased $1.3 \quad \quad 0.9 \quad 0.5$
    Fixed $1.3 \quad\quad 1.3 \quad 1.3$
    Zero $\;0 \quad\; \quad 0 \quad\quad 0$
    Volatility of vaccination rate
    Descriptions Values in stages
    Gradually increased $0.1 \quad \quad 0.3 \quad 0.5$
    Gradually decreased $0.5 \quad \quad 0.3 \quad 0.1$
    Fixed $0.5 \quad\quad 0.5 \quad 0.5$
    Zero $0 \quad\; \quad 0 \quad\quad 0$
    $ ^{\circledast}$ Assumed a 70% reduced risk of acquiring infection for persons wearing masks [47], and 80% of populations adhere to mask mandates. Then transmission rate for partial opening can be calculated by the formula: baseline /(1-0.7*0.8) [35].
     | Show Table
    DownLoad: CSV
  • [1] O. Alagoz, A. K. Sethi, B. W. Patterson, M. Churpek, G. Alhanaee, E. Scaria, et al., The impact of vaccination to control COVID-19 burden in the United States: A simulation modeling approach, PLoS One, 16 (2021), e0254456. doi: 10.1371/journal.pone.0254456.
    [2] E. Allen, Modeling with Ito Stochastic Differential Equations, Springer Science and Business Media, Berlin, 2007.
    [3] E. Allen, Environmental variability and mean-reverting processes, Discrete Continuous Dyn. Syst. Ser. B., 21 (2016), 2073-2089.  doi: 10.3934/dcdsb.2016037.
    [4] E. J. AllenL. J. S. AllenA. Arciniega and P. E. Greenwood, Construction of equivalent stochastic differential equation models, Stoch. Anal. Appl., 26 (2008), 274-297.  doi: 10.1080/07362990701857129.
    [5] E. J. AllenL. J. S. Allen and H. L. Smith, On real-valued SDE and nonnegative-valued SDE population models with demographic variability, J. Math. Biol., 81 (2020), 487-515.  doi: 10.1007/s00285-020-01516-8.
    [6] L. J. S. Allen and X. Wang, Stochastic models of infectious diseases in a periodic environment with application to cholera epidemics, J. Math. Biol., 82 (2021), Paper No. 48, 26 pp. doi: 10.1007/s00285-021-01603-4.
    [7] A. J. ArenasG. González-Parra and J. A. Moraño, Stochastic modeling of the transmission of respiratory syncytial virus (RSV) in the region of Valencia, Spain, Biosystems, 96 (2009), 206-212.  doi: 10.1016/j.biosystems.2009.01.007.
    [8] E. Aruffo, P. Yuan, Y. Tan, E. Gatov, E. Gournis, S. Collier, et al., Community structured model for vaccine strategies to control COVID19 spread: A mathematical study, PLoS One, 17 (2022), e0258648. doi: 10.1371/journal.pone.0258648.
    [9] E. Aruffo, P. Yuan, Y. Tan, E. Gatov, I. Moyles, J. Bélair, et al., Mathematical modelling of vaccination rollout and NPIs lifting on COVID-19 transmission with VOC: A case study in Toronto, BMC Public Health, 22 (2022), Article number: 1349, 12 pp. doi: 10.1186/s12889-022-13597-9.
    [10] J. CaoX. HuW. ChengL. YuW.-J. Tu and Q. Liu, Clinical features and short-term outcomes of 18 patients with corona virus disease 2019 in intensive care unit, Intensive Care Med., 46 (2020), 851-853.  doi: 10.1007/s00134-020-05987-7.
    [11] C. Carvalho-Schneider, E. Laurent, A. Lemaignen, E. Beaufils, C. Bourbao-Tournois, S. Laribi, et al., Follow-up of adults with noncritical COVID-19 two months after symptom onset, Clin. Microbiol. Infect., 27 (2021), 258-263. doi: 10.1016/j.cmi.2020.09.052.
    [12] B. CazellesC. ChampagneB. Nguyen-Van-YenC. ComiskeyE. Vergu and B. Roche, A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic, PLoS Comput. Biol., 17 (2021), e1009211.  doi: 10.1371/journal.pcbi.1009211.
    [13] A. L. Chanu and R. K. B. Singh, Stochastic approach to study control strategies of COVID-19 pandemic in India, Epidemiol. Infect., 148 (2020), e200.  doi: 10.1017/S0950268820001946.
    [14] P. CzupponE. SchertzerF. Blanquart and F. Débarre, The stochastic dynamics of early epidemics: Probability of establishment, initial growth rate, and infection cluster size at first detection, J. R. Soc. Interface, 18 (2021), 20210575.  doi: 10.1098/rsif.2021.0575.
    [15] A. Danielle Iuliano, J. M. Brunkard, T. K. Boehmer, E. Peterson, S. Adjei, A. M. Binder, et al., Trends in disease severity and health care utilization during the early Omicron variant period compared with previous SARS-CoV-2 high transmission periods—United States, December 2020–January 2022, Morb. Mortal. Wkly. Rep., 71 (2022), 146-152. doi: 10.15585/mmwr.mm7104e4.
    [16] G. Giordano, M. Colaneri, A. Di Filippo, F. Blanchini, P. Bolzern, G. De Nicolao, et al., Modeling vaccination rollouts, SARS-CoV-2 variants and the requirement for non-pharmaceutical interventions in Italy, Nat. Med., 27 (2021), 993-998. doi: 10.1038/s41591-021-01334-5.
    [17] Y. Goldberg, M. Mandel, Y. M. Bar-On, O. Bodenheimer, L. Freedman, E. J. Haas, et al., Waning immunity after the BNT162b2 vaccine in Israel, N. Engl. J. Med., 385 (2021), e85. doi: 10.1056/NEJMoa2114228.
    [18] A. GrayD. GreenhalghL. HuX. Mao and J. Pan, A stochastic differential equation SIS epidemic model, SIAM J. Appl. Math., 71 (2011), 876-902.  doi: 10.1137/10081856X.
    [19] S. HeY. Peng and K. Sun, SEIR modeling of the COVID-19 and its dynamics, Nonlinear Dynamics, 101 (2020), 1667-1680.  doi: 10.1007/s11071-020-05743-y.
    [20] X. Hou, S. Gao, Q. Li, Y. Kang, N. Chen, K. Chen, et al., Intracounty modeling of COVID-19 infection with human mobility: Assessing spatial heterogeneity with business traffic, age, and race, Proc. Natl. Acad. Sci. U. S. A., 118 (2021), e2020524118. doi: 10.1073/pnas.2020524118.
    [21] G. Hussain, T. Khan, A. Khan, M. Inc, G. Zaman, K. S. Nisar, et al., Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model, Alex. Eng. J., 60 (2021), 4121-4130. doi: 10.1016/j.aej.2021.02.036.
    [22] L. Jansen, B. Tegomoh, K. Lange, K. Showalter, J. Figliomeni, B. Abdalhamid, et al., Investigation of a SARS-CoV-2 B. 1.1. 529 (omicron) variant cluster—Nebraska, November–December 2021, Morb. Mortal. Wkly. Rep., 70 (2021), 1782-1784. doi: 10.15585/mmwr.mm705152e3.
    [23] M. Kang, H. Xin, J. Yuan, S. T. Ali, Z. Liang, J. Zhang, et al., Transmission dynamics and epidemiological characteristics of SARS-CoV-2 Delta variant infections in Guangdong, China, May to June 2021, Eurosurveillance, 27 (2022), 2100815. doi: 10.2807/1560-7917.ES.2022.27.10.2100815.
    [24] A. J. Kucharski, T. W. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk, et al., Early dynamics of transmission and control of COVID-19: A mathematical modelling study, Lancet Infect. Dis., 20 (2020), 553-558. doi: 10.1016/S1473-3099(20)30144-4.
    [25] S. Lambert, P. Ezanno, M. Garel and E. Gilot-Fromont, Demographic stochasticity drives epidemiological patterns in wildlife with implications for diseases and population management, Sci. Rep., 8 (2018), Article number: 16846, 14 pp. doi: 10.1038/s41598-018-34623-0.
    [26] E. G. Levin, Y. Lustig, C. Cohen, R. Fluss, V. Indenbaum, S. Amit, et al., Waning immune humoral response to BNT162b2 Covid-19 vaccine over 6 months, N. Engl. J. Med., 385 (2021), e84. doi: 10.1056/NEJMoa2114583.
    [27] L. G. McCoy, J. Smith, K. Anchuri, I. Berry, J. Pineda, V. Harish, et al., Characterizing early Canadian federal, provincial, territorial and municipal nonpharmaceutical interventions in response to COVID-19: A descriptive analysis, Can. Med. Assoc. J., 8 (2020), E545-E553. doi: 10.9778/cmajo.20200100.
    [28] D. Nino-TorresA. Ríos-GutiérrezV. ArunachalamC. Ohajunwa and P. Seshaiyer, Stochastic modeling, analysis, and simulation of the COVID-19 pandemic with explicit behavioral changes in Bogotá: A case study, Infect. Dis. Model., 7 (2022), 199-211.  doi: 10.1016/j.idm.2021.12.008.
    [29] K. F. Nipa, S. R.-J. Jang and L. J. S. Allen, The effect of demographic and environmental variability on disease outbreak for a dengue model with a seasonally varying vector population, Math. Biosci., 331 (2021), 108516, Paper No. 108516, 18 pp. doi: 10.1016/j.mbs.2020.108516.
    [30] O. M. Otunuga, Time-dependent probability distribution for number of infection in a stochastic SIS model: Case study COVID-19, Chaos Solit. Fractals, 147 (2021), 110983, 20 pp. doi: 10.1016/j.chaos.2021.110983.
    [31] O. M. Otunuga and M. O. Ogunsolu, Qualitative analysis of a stochastic SEITR epidemic model with multiple stages of infection and treatment, Infect. Dis. Model., 5 (2020), 61-90.  doi: 10.1016/j.idm.2019.12.003.
    [32] U. Picchini, Inference for SDE models via approximate Bayesian computation, J. Comput. Graph. Stat., 23 (2014), 1080-1100.  doi: 10.1080/10618600.2013.866048.
    [33] L. Pinky, G. Gonzalez-Parra and H. M. Dobrovolny, Effect of stochasticity on coinfection dynamics of respiratory viruses, BMC Bioinform., 20 (2019), Article number: 191, 12 pp. doi: 10.1186/s12859-019-2793-6.
    [34] N. Shakiba, C. J. Edholm, B. O. Emerenini, A. L. Murillo, A. Peace, O. Saucedo, et al., Effects of environmental variability on superspreading transmission events in stochastic epidemic models, Infect. Dis. Model., 6 (2021), 560-583. doi: 10.1016/j.idm.2021.03.001.
    [35] A. K. SrivastavP. K. TiwariP. K. SrivastavaM. Ghosh and Y. Kang, A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: Deterministic vs. stochastic, Math. Biosci. Eng., 18 (2021), 182-213.  doi: 10.3934/mbe.2021010.
    [36] S. Y. Tartof, J. M. Slezak, L. Puzniak, V. Hong, T. B. Frankland, B. K. Ackerson, et al., Effectiveness of a third dose of BNT162b2 mRNA COVID-19 vaccine in a large US health system: A retrospective cohort study, Lancet Reg. Health-Am., 9 (2022), 100198. doi: 10.1016/j.lana.2022.100198.
    [37] J. Thaker and S. Ganchoudhuri, The role of attitudes, norms, and efficacy on shifting COVID-19 vaccine Intentions: A longitudinal study of COVID-19 vaccination intentions in New Zealand, Vaccines, 9 (2021), 1132.  doi: 10.3390/vaccines9101132.
    [38] G. T. TilahunS. Demie and A. Eyob, Stochastic model of measles transmission dynamics with double dose vaccination, Infect. Dis. Model., 5 (2020), 478-494.  doi: 10.1016/j.idm.2020.06.003.
    [39] Vaccine Hesitancy Plunges to Three per cent, but One-tenth of Population Remain Unwilling to be Jabbed, Angusreid Institute, 2021. Available from: https://angusreid.org/canada-astrazeneca-herd-immunity/.
    [40] Changing Attitudes to Vaccination after the Covid-19 Pandemic Could Increase Adult Vaccination Rates, Improving Health Outcomes over the Longer Term, GSK, 2021. Available from: https://www.gsk.com/en-gb/media/press-releases/changing-attitudes-to-vaccination-after-the-covid-19-pandemic-could-increase-adult-vaccination-rates-improving-health-outcomes-over-the-longer-term/.
    [41] Covid-19: Monitoring Dashboard Share, City of Toronto, 2022. Available from: https://www.toronto.ca/home/covid-19/covid-19-pandemic-data/covid-19-monitoring-dashboard-data/.
    [42] Ontario Now Distinguishing between People Admitted to Hospital 'with' or 'for' COVID-19, Cp24, 2022. Available from: https://www.cp24.com/news/ontario-now-distinguishing-between-people-admitted-to-hospital-with-or-for-covid-19-1.5736010?cache = %2F7.381763.
    [43] Matlab for Artificial Intelligence, Math Works, 2022. Available from: https://www.mathworks.com.
    [44] Datagraph, Datagraph, 2022. Available from: https://www.visualdatatools.com/DataGraph/.
    [45] Ontario to Drop Most Mask Mandates on March 21, 2022, all Measures on April 27, DLA Piper, 2022. Available from: https://www.dlapiper.com/en-ca/insights/publications/2022/03/ontario-to-drop-mask-mandates.
    [46] Here's a Look at Ontario's Timeline for Lifting all COVID Measures by April 27, Toronto Star, 2022. Available from: https://www.thestar.com/news/canada/2022/03/09/heres-a-look-at-ontarios-timeline-for-lifting-all-covid-measures-by-april-27.html.
    [47] Use of Masks to Control the Spread of SARS-CoV-2, Centers for Disease Control and Prevention, 2021. Available from: https://www.cdc.gov/coronavirus/2019-ncov/science/science-briefs/masking-science-sars-cov2.html.
    [48] 2021 Census: Population and Dwelling Counts, City of Toronto, 2022. Available from: https://www.toronto.ca/wp-content/uploads/2022/02/92e3-City-Planning-2021-Census-Backgrounder-Population-Dwellings-Backgrounder.pdf.
    [49] Covid-19 Cases with Lineage b.1.1.529 (omicron) or S-Gene Target Failure (sgtf) in Ontario: October 31, 2021 to December 29, 2021. 2022, Government of Ontario, 2022. Available from: https://www.publichealthontario.ca/-/media/documents/ncov/epi/covid-19-omicron-weekly-epi-summary.pdf?sc_lang = en.
    [50] P. Yuan, E. Aruffo, E. Gatov, Y. Tan, Q. Li, N. Ogden, et al., School and community reopening during the COVID-19 pandemic: A mathematical modelling study, R. Soc. Open Sci., 9 (2022), 211883. doi: 10.1098/rsos.211883.
    [51] P. YuanE. AruffoY. TanL. YangN. H. OgdenA. Fazil and H. Zhu, Projections of the transmission of the Omicron variant for Toronto, Ontario, and Canada using surveillance data following recent changes in testing policies, Infect. Dis. Model., 7 (2022), 83-93.  doi: 10.1016/j.idm.2022.03.004.
    [52] P. Yuan, J. Li, E. Aruffo, E. Gatov, Q. Li, T. Zheng, et al., Efficacy of 'Stay-at-Home' policy and transmission of COVID-19 in Toronto, CMAJ Open, 10 (2022), E367-E378. doi: 10.9778/cmajo.20200242.
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