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

BackgroundSince December 2020, public health agencies have implemented a variety of vaccination strategies to curb the spread of SARS-CoV-2, along with pre-existing Nonpharmaceutical Interventions (NPIs). Initial strategy focused on vaccinating the elderly to prevent hospitalizations and deaths. With vaccines becoming available to the broader population, we aimed to determine the optimal strategy to enable the safe lifting of NPIs while avoiding virus resurgence. MethodsWe developed a compartmental deterministic SEIR model to simulate the lifting of NPIs under different vaccination rollout scenarios. Using case and vaccination data from Toronto, Canada between December 28, 2020 and May 19, 2021, we estimated transmission throughout past stages of NPI escalation/relaxation to compare the impact of lifting NPIs on different dates on cases, hospitalizations, and deaths, given varying degrees of vaccine coverages by 20-year age groups, accounting for waning immunity. ResultsWe found that, once coverage among the elderly is high enough (80% with at least one dose), the main age groups to target are 20-39 and 40-59 years, whereby first-dose coverage of at least 70% by mid-June 2021 is needed to minimize the possibility of resurgence if NPIs are to be lifted in the summer. While a resurgence was observed for every scenario of NPI lifting, we also found that under an optimistic vaccination coverage (70% by mid-June, postponing reopening from August 2021 to September 2021can reduce case counts and severe outcomes by roughly 80% by December 31, 2021. ConclusionsOur results suggest that focusing the vaccination strategy on the working-age population can curb the spread of SARS-CoV-2. However, even with high vaccination coverage in adults, lifting NPIs to pre-pandemic levels is not advisable since a resurgence is expected to occur, especially with earlier reopening.

COVID-19 transmission in a theme-park

BackgroundAs COVID-19 vaccination coverage increases, public health and industries are contemplating re-opening measures of public spaces, including theme-parks. To re-open, theme-parks must provide public health mitigation plans. Questions on implementation of public health mitigation strategies such as park cleaning, COVID-19 testing, and enforcement of social distancing and the wearing of personal protective equipment (PPE) in the park remain. MethodsWe have developed a mathematical model of COVID-19 transmission in a theme-park that considers direct human-human and indirect environment-human transmission of the virus. The model thus tracks the changing infection/disease landscape of all visitors, workers, and environmental reservoirs in a theme park setting. FindingsModels results show that theme-park public health mitigation must include mechanisms that reduce virus contamination of the environment to ensure that workers and visitors are protected from COVID-19 transmission in the park. Thus, cleaning rates and mitigation of human-environment contact increases in importance. ConclusionOur findings have important practical implications in terms of public health as policy- and decision-makers are equipped with a mathematical tool that can guide theme-parks in developing public health mitigation strategies for a safe re-opening.

Community structured model for vaccine strategies to control COVID19 spread: a mathematical study

Efforts to mitigate the COVID-19 pandemic have relied heavily on non-pharmaceutical interventions (NPIs), including physical distancing, hand hygiene, and mask-wearing. However, an effective vaccine is essential to containing the spread of the virus. The first doses were distributed at the end of 2020, but the efficacy, period of immunity it will provide, and percentage of coverage still remain unclear. We developed a compartment model to examine different vaccine strategies for controlling the spread of COVID-19. Our framework accounts for testing rates, test-turnaround times, and vaccination waning immunity. Using reported case data from the city of Toronto, Canada between Mar-Dec, 2020 we defined epidemic phases of infection using contact rates, which depend on individuals duration of time spent within the household, workplace/school, or community settings, as well as the probability of transmission upon contact. We investigated the impact of vaccine distribution by comparing different permutations of waning immunity, vaccine coverage and efficacy throughout various stages of NPIs relaxation in terms of cases, deaths, and household transmission, as measured using the basic reproduction number (R0). We observed that widespread vaccine coverage substantially reduced the number of cases and deaths. In order for NPIs to be relaxed 8 months after vaccine distribution, infection spread can be kept under control with either 60% vaccine coverage, no waning immunity, and 70% efficacy, or with 60% coverage with a 12-month waning immunity and 90% vaccine efficacy. Widespread virus resurgence can result when the immunity wanes under 3 months and/or when NPIs are relaxed in concomitance with vaccine distribution. In addition to vaccination, our analysis of R0 showed that the basic reproduction number is reduced by decreasing the tests turnaround time and transmission in the household. While we found that household transmission can decrease following the introduction of a vaccine, public health efforts to reduce test turnaround times remain important for virus containment. Our findings suggest that vaccinating two-thirds of the population with a vaccine that is at least 70% effective may be sufficient for controlling COVID-19 spread, as long as NPIs are not immediately relaxed.

School and community reopening during the COVID-19 pandemic: a mathematical modeling study

BackgroundThe closure of communities, including schools, has been adopted to control the coronavirus disease 2019 (COVID-19) epidemic in most countries. Operating schools safely during the pandemic requires a balance between health risks and the need for in-person learning. We use compartmental models to explore school reopening scenarios. MethodsUsing demographic and epidemiological data between July 31 and November 23, 2020 from the city of Toronto, we developed a Susceptible-Exposed-Asymptomatic-Infectious-Recovered-Hospitalized-Isolated model. Our model with age, household, and community transmission allow us to study the impact of schools open in September 2020. The model mimics the transmission in households, the community, and schools, accounting for differences in infectiousness between adults and children and youth and adults working status. We assessed the extent to which school opening may have contributed to COVID-19 resurgence in the fall and simulated scenarios for the safe reopening of schools up to May 31, 2021. We further considered the impact of the introduction of the new variant of concern. FindingsThough a slight increase in infections among adults (2.8%) and children (5.4%) is anticipated by the end of the year, safe school opening is possible with stringent nonpharmaceutical interventions (NPIs) decreasing the risk of transmission in the community and the household. We found that while school reopening was not the key driver in virus resurgence, but rather it was community spread that determined the outbreak trajectory, brief school closures did reduce infections when transmission risk within the home was low. When considered possible cross-infection amongst households, communities, and schools, we found that home transmission was crucial for mitigating the epidemic and safely operating schools. Simulating the introduction of a new strain with higher infectiousness, we observed substantial increases in infections, even when both schools and communities are closed. InterpretationSchools can open safely under strict maintenance of strict public health measures in the community. The gradual opening of schools and communities can only be achieved by maintaining NPIs and mitigating household transmission risk to avoid the broader escape of infections acquired in schools into the community via households. If the new COVID-19 strain is more infectious for children, public spaces, including schools, should be closed, and additional NPIs, including the use of masks, should be extended to toddlers. FundingThis research was supported by Canadian Institutes of Health Research (CIHR), Natural Sciences and Engineering Research Council of Canada, and York University Research Chair program. Research in contextO_ST_ABSEvidence before this studyC_ST_ABSThe design of a gradual school reopening strategy remains at the heart of decision-making on reopening after shut-downs to control the epidemic. Although available studies have assessed the risk of school reopening by modelling the transmission across schools and communities, it remains unclear whether the risk is due to increased transmission in adults or children and youth.We used GoogleScholar and PubMed searches to identify previous published works. We used te following terms: "school closure", "covid 19 school closure", "reopening schools", "reopening screening school", "school household second wave model". The search of the studies ended in January 2021. Papers in other languages than English and letters were excluded from the search. Two modelling studies examined the effects of screening and delayed school reopening, two other agent-based modelling studies explored the epidemic spread across different age groups. Added-value of this studyWe find that the resurgence of COVID-19 in Toronto in fall 2020 mainly resulted from the increase of contact rate among adults in the community, and that the degree of in-person attendance had the most significant impact on transmission in schools. To our knowledge, our work is the first to investigate the resurgence in infections following school reopening and the impact of risk mitigation measures in schools operation during the pandemic. Our novel and comprehensive model considers the age and household structure, but also considers three different settings, school, household and community. We further examined the effects of self-screening procedures, class size, and schooling days on transmission, which enabled us to compare scenarios of school reopening separately for both adults and children and youth, and model the cross-infection between them to avoid potential underestimation. We found that after schools opened, reducing household transmission was crucial for mitigating the epidemic since it can reduce cross-infection amongst households, communities and schools. Lastly, given the recent report of SARS-CoV-2 variant (VOC202012/01), we investigated the impact of the new variant that may be more infectious in children and youth. Implications of all the available evidenceOur analysis can inform policymakers of planning the safe reopening of schools during COVID-19. We suggest that integrating strict NPIs and school control measures are crucial for safe reopening. When schools are open, reducing transmission risk at home and community is paramount in curbing the spread of COVID-19. Lastly, if children are more susceptible to the new COVID-19 VOC, both schools and community must be closed, the time children spend in essential services locations minimized, and NPIs for those aged less than three years enforced.

Efficacy of stay-at-home policy and transmission of COVID-19 in Toronto, Canada: a mathematical modeling study

BackgroundIn many parts of the world, restrictive non-pharmaceutical interventions (NPI) that aim to reduce contact rates, including stay-at-home orders, limitations on gatherings, and closure of public places, are being lifted, with the possibility that the epidemic resurges if alternative measures are not strong enough. Here we aim to capture the combination of use of NPIs and reopening measures which will prevent an infection rebound. MethodsWe employ an SEAIR model with household structure able to capture the stay-at-home policy (SAHP). To reflect the changes in the SAHP over the course of the epidemic, we vary the SAHP compliance rate, assuming that the time to compliance of all the people requested to stay-at-home follows a Gamma distribution. Using confirmed case data for the City of Toronto, we evaluate basic and instantaneous reproduction numbers and simulate how the average household size, the stay-at-home rate, the efficiency and duration of SAHP implementation, affect the outbreak trajectory. FindingsThe estimated basic reproduction number R_0 was 2.36 (95% CI: 2.28, 2.45) in Toronto. After the implementation of the SAHP, the contact rate outside the household fell by 39%. When people properly respect the SAHP, the outbreak can be quickly controlled, but extending its duration beyond two months (65 days) had little effect. Our findings also suggest that to avoid a large rebound of the epidemic, the average number of contacts per person per day should be kept below nine. This study suggests that fully reopening schools, offices, and other activities, is possible if the use of other NPIs is strictly adhered to. InterpretationOur model confirmed that the SAHP implemented in Toronto had a great impact in controlling the spread of COVID-19. Given the lifting of restrictive NPIs, we estimated the thresholds values of maximum number of contacts, probability of transmission and testing needed to ensure that the reopening will be safe, i.e. maintaining an Rt < 1. Research in contextO_ST_ABSEvidence before this studyC_ST_ABSA survey on published articles was made through PubMed and Google Scholar searches. The search was conducted from March 1 to August 13, 2020 and all papers published until the end of this research were considered. The following terms were used to screen articles on mathematical models: "household structure", "epidemic model", "SARS-CoV-2", "COVID-19", "household SIR epidemic", "household SIS epidemic", "household SEIR epidemic", "quarantine, isolation model", "quarantine model dynamics", "structured model isolation". Any article showing, in the title, application of epidemic models in a specific country/region or infectious diseases rather than SARS-CoV-2 were excluded. Articles in English were considered. Added value of this studyWe develop an epidemic model with household structure to study the effects of SAHP on the infection within households and transmission of COVID-19 in Toronto. The complex model provides interesting insights into the effectiveness of SAHP, if the average number of individuals in a household changes. We found that the SAHP might not be adequate if the size of households is relatively large. We also introduce a new quantity called symptomatic diagnosis completion ratio (d_c). This indicator is defined as the ratio of cumulative reported cases and the cumulative cases by episode date at time t, and it is used in the model to inform the implementation of SAHP. If cases are diagnosed at the time of symptom onset, isolation will be enforced immediately. A delay in detecting cases will lead to a delay in isolation, with subsequent increase in the transmission of the infection. Comparing different scenarios (before and after reopening phases), we were able to identify thresholds of these factors which mainly affect the spread of the infection: the number of daily tests, average number of contacts per individual, and probability of transmission of the virus. Our results show that if any of the three above mentioned factors is reduced, then the other two need to be adjusted to keep a reproduction number below 1. Lifting restrictive closures will require the average number of contacts a person has each day to be less than pre-COVID-19, and a high rate of case detection and tracing of contacts. The thresholds found will inform public health decisions on reopening. Implications of all the available evidenceOur findings provide important information for policymakers when planning the full reopening phase. Our results confirm that prompt implementation of SAHP was crucial in reducing the spread of COVID-19. Also, based on our analyses, we propose public health alternatives to consider in view of a full reopening. For example, for different post-reopening scenarios, the average number of contacts per person needs to be reduced if the symptomatic diagnosis completion ratio is low and the probability of transmission increases. Namely, if fewer tests are completed and the usage of NPIs decreases, then the epidemic can be controlled only if individuals can maintain contact with a maximum average number of 4-5 people per person per day. Different recommendations can be provided by relaxing/strengthening one of the above-mentioned factors.