Determination of significant immunological timescales from mRNA-LNP-based vaccines in humans.

A compartment model for an in-host liquid nanoparticle delivered mRNA vaccine is presented. Through non-dimensionalisation, five timescales are identified that dictate the lifetime of the vaccine in-host: decay of interferon gamma, antibody priming, autocatalytic growth, antibody peak and decay, and interleukin cessation. Through asymptotic analysis we are able to obtain semi-analytical solutions in each of the time regimes which allows us to predict maximal concentrations and better understand parameter dependence in the model. We compare our model to 22 data sets for the BNT162b2 and mRNA-1273 mRNA vaccines demonstrating good agreement. Using our analysis, we estimate the values for each of the five timescales in each data set and predict maximal concentrations of plasma B-cells, antibody, and interleukin. Through our comparison, we do not observe any discernible differences between vaccine candidates and sex. However, we do identify an age dependence, specifically that vaccine activation takes longer and that peak antibody occurs sooner in patients aged 55 and greater.

Multiple cohort study of hospitalized SARS-CoV-2 in-host infection dynamics: Parameter estimates, identifiability, sensitivity and the eclipse phase profile.

Within-host SARS-CoV-2 modelling studies have been published throughout the COVID-19 pandemic. These studies contain highly variable numbers of individuals and capture varying timescales of pathogen dynamics; some studies capture the time of disease onset, the peak viral load and subsequent heterogeneity in clearance dynamics across individuals, while others capture late-time post-peak dynamics. In this study, we curate multiple previously published SARS-CoV-2 viral load data sets, fit these data with a consistent modelling approach, and estimate the variability of in-host parameters including the basic reproduction number, R0, as well as the best-fit eclipse phase profile. We find that fitted dynamics can be highly variable across data sets, and highly variable within data sets, particularly when key components of the dynamic trajectories (e.g. peak viral load) are not represented in the data. Further, we investigated the role of the eclipse phase time distribution in fitting SARS-CoV-2 viral load data. By varying the shape parameter of an Erlang distribution, we demonstrate that models with either no eclipse phase, or with an exponentially-distributed eclipse phase, offer significantly worse fits to these data, whereas models with less dispersion around the mean eclipse time (shape parameter two or more) offered the best fits to the available data across all data sets used in this work. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

COVID-19 Vaccination and Healthcare Demand.

One of the driving concerns during any epidemic is the strain on the healthcare system. As we have seen many times over the globe with the COVID-19 pandemic, hospitals and ICUs can quickly become overwhelmed by cases. While strict periods of public health mitigation have certainly helped decrease incidence and thus healthcare demand, vaccination is the only clear long-term solution. In this paper, we develop a two-module model to forecast the effects of relaxation of non-pharmaceutical intervention and vaccine uptake on daily incidence, and the cascade effects on healthcare demand. The first module is a simple epidemiological model which incorporates non-pharmaceutical intervention, the relaxation of such measures and vaccination campaigns to predict caseloads into the Fall of 2021. This module is then fed into a healthcare module which can forecast the number of doctor visits, the number of occupied hospital beds, number of occupied ICU beds and any excess demand of these. From this module, we can also estimate the length of stay of individuals in ICU. For model verification and forecasting, we use the four most populous Canadian provinces as a case study.

Mitigating co-circulation of seasonal influenza and COVID-19 pandemic in the presence of vaccination: A mathematical modeling approach.

The co-circulation of two respiratory infections with similar symptoms in a population can significantly overburden a healthcare system by slowing the testing and treatment. The persistent emergence of contagious variants of SARS-CoV-2, along with imperfect vaccines and their waning protections, have increased the likelihood of new COVID-19 outbreaks taking place during a typical flu season. Here, we developed a mathematical model for the co-circulation dynamics of COVID-19 and influenza, under different scenarios of influenza vaccine coverage, COVID-19 vaccine booster coverage and efficacy, and testing capacity. We investigated the required minimal and optimal coverage of COVID-19 booster (third) and fourth doses, in conjunction with the influenza vaccine, to avoid the coincidence of infection peaks for both diseases in a single season. We show that the testing delay brought on by the high number of influenza cases impacts the dynamics of influenza and COVID-19 transmission. The earlier the peak of the flu season and the greater the number of infections with flu-like symptoms, the greater the risk of flu transmission, which slows down COVID-19 testing, resulting in the delay of complete isolation of patients with COVID-19 who have not been isolated before the clinical presentation of symptoms and have been continuing their normal daily activities. Furthermore, our simulations stress the importance of vaccine uptake for preventing infection, severe illness, and hospitalization at the individual level and for disease outbreak control at the population level to avoid putting strain on already weak and overwhelmed healthcare systems. As such, ensuring optimal vaccine coverage for COVID-19 and influenza to reduce the burden of these infections is paramount. We showed that by keeping the influenza vaccine coverage about 35% and increasing the coverage of booster or fourth dose of COVID-19 not only reduces the infections with COVID-19 but also can delay its peak time. If the influenza vaccine coverage is increased to 55%, unexpectedly, it increases the peak size of influenza infections slightly, while it reduces the peak size of COVID-19 as well as significantly delays the peaks of both of these diseases. Mask-wearing coupled with a moderate increase in the vaccine uptake may mitigate COVID-19 and prevent an influenza outbreak.

A mathematical model of protein subunits COVID-19 vaccines.

We consider a general mathematical model for protein subunit vaccine with a focus on the MF59-adjuvanted spike glycoprotein-clamp vaccine for SARS-CoV-2, and use the model to study immunological outcomes in the humoral and cell-mediated arms of the immune response from vaccination. The mathematical model is fit to vaccine clinical trial data. We elucidate the role of Interferon-γ and Interleukin-4 in stimulating the immune response of the host. Model results, and results from a sensitivity analysis, show that a balance between the TH1 and TH2 arms of the immune response is struck, with the TH1 response being dominant. The model predicts that two-doses of the vaccine at 28 days apart will result in approximately 85% humoral immunity loss relative to peak immunity approximately 6 months post dose 1.

Commentary on the use of the reproduction number R during the COVID-19 pandemic.

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

The race to understand immunopathology in COVID-19: Perspectives on the impact of quantitative approaches to understand within-host interactions.

The COVID-19 pandemic has revealed the need for the increased integration of modelling and data analysis to public health, experimental, and clinical studies. Throughout the first two years of the pandemic, there has been a concerted effort to improve our understanding of the within-host immune response to the SARS-CoV-2 virus to provide better predictions of COVID-19 severity, treatment and vaccine development questions, and insights into viral evolution and the impacts of variants on immunopathology. Here we provide perspectives on what has been accomplished using quantitative methods, including predictive modelling, population genetics, machine learning, and dimensionality reduction techniques, in the first 26 months of the COVID-19 pandemic approaches, and where we go from here to improve our responses to this and future pandemics.

Long-term durability of immune responses to the BNT162b2 and mRNA-1273 vaccines based on dosage, age and sex.

The lipid nanoparticle (LNP)-formulated mRNA vaccines BNT162b2 and mRNA-1273 are a widely adopted multi vaccination public health strategy to manage the COVID-19 pandemic. Clinical trial data has described the immunogenicity of the vaccine, albeit within a limited study time frame. Here, we use a within-host mathematical model for LNP-formulated mRNA vaccines, informed by available clinical trial data from 2020 to September 2021, to project a longer term understanding of immunity as a function of vaccine type, dosage amount, age, and sex. We estimate that two standard doses of either mRNA-1273 or BNT162b2, with dosage times separated by the company-mandated intervals, results in individuals losing more than 99% humoral immunity relative to peak immunity by 8 months following the second dose. We predict that within an 8 month period following dose two (corresponding to the original CDC time-frame for administration of a third dose), there exists a period of time longer than 1 month where an individual has lost more than 99% humoral immunity relative to peak immunity, regardless of which vaccine was administered. We further find that age has a strong influence in maintaining humoral immunity; by 8 months following dose two we predict that individuals aged 18-55 have a four-fold humoral advantage compared to aged 56-70 and 70+ individuals. We find that sex has little effect on the immune response and long-term IgG counts. Finally, we find that humoral immunity generated from two low doses of mRNA-1273 decays at a substantially slower rate relative to peak immunity gained compared to two standard doses of either mRNA-1273 or BNT162b2. Our predictions highlight the importance of the recommended third booster dose in order to maintain elevated levels of antibodies.

Estimating the basic reproduction number at the beginning of an outbreak.

We compare several popular methods of estimating the basic reproduction number, R0, focusing on the early stages of an epidemic, and assuming weekly reports of new infecteds. We study the situation when data is generated by one of three standard epidemiological compartmental models: SIR, SEIR, and SEAIR; and examine the sensitivity of the estimators to the model structure. As some methods are developed assuming specific epidemiological models, our work adds a study of their performance in both a well-specified (data generating model and method model are the same) and miss-specified (data generating model and method model differ) settings. We also study R0 estimation using Canadian COVID-19 case report data. In this study we focus on examples of influenza and COVID-19, though the general approach is easily extendable to other scenarios. Our simulation study reveals that some estimation methods tend to work better than others, however, no singular best method was clearly detected. In the discussion, we provide recommendations for practitioners based on our results.

Longitudinal Assessment of SARS-CoV-2-Specific T Cell Cytokine-Producing Responses for 1 Year Reveals Persistence of Multicytokine Proliferative Responses, with Greater Immunity Associated with Disease Severity.

Cell-mediated immunity is critical for long-term protection against most viral infections, including coronaviruses. We studied 23 severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-infected survivors over a 1-year post-symptom onset (PSO) interval by ex vivo cytokine enzyme-linked immunosorbent spot assay (ELISpot) assay. All subjects demonstrated SARS-CoV-2-specific gamma interferon (IFN-γ), interleukin 2 (IL-2), and granzyme B (GzmB) T cell responses at presentation, with greater frequencies in severe disease. Cytokines, mainly produced by CD4+ T cells, targeted all structural proteins (nucleocapsid, membrane, and spike) except envelope, with GzmB and IL-2 greater than IFN-γ. Mathematical modeling predicted that (i) cytokine responses peaked at 6 days for IFN-γ, 36 days for IL-2, and 7 days for GzmB, (ii) severe illness was associated with reduced IFN-γ and GzmB but increased IL-2 production rates, and (iii) males displayed greater production of IFN-γ, whereas females produced more GzmB. Ex vivo responses declined over time, with persistence of IL-2 in 86% and of IFN-γ and GzmB in 70% of subjects at a median of 336 days PSO. The average half-life of SARS-CoV-2-specific cytokine-producing cells was modeled to be 139 days (~4.6 months). Potent T cell proliferative responses persisted throughout observation, were CD4 dominant, and were capable of producing all 3 cytokines. Several immunodominant CD4 and CD8 epitopes identified in this study were shared by seasonal coronaviruses or SARS-CoV-1 in the nucleocapsid and membrane regions. Both SARS-CoV-2-specific CD4+ and CD8+ T cell clones were able to kill target cells, though CD8 tended to be more potent. IMPORTANCE Our findings highlight the relative importance of SARS-CoV-2-specific GzmB-producing T cell responses in SARS-CoV-2 control and shared CD4 and CD8 immunodominant epitopes in seasonal coronaviruses or SARS-CoV-1, and they indicate robust persistence of T cell memory at least 1 year after infection. Our findings should inform future strategies to induce T cell vaccines against SARS-CoV-2 and other coronaviruses.

Modeling waning and boosting of COVID-19 in Canada with vaccination.

SARS-CoV-2, the causative agent of COVID-19, has caused devastating health and economic impacts around the globe since its appearance in late 2019. The advent of effective vaccines leads to open questions on how best to vaccinate the population. To address such questions, we developed a model of COVID-19 infection by age that includes the waning and boosting of immunity against SARS-CoV-2 in the context of infection and vaccination. The model also accounts for changes to infectivity of the virus, such as public health mitigation protocols over time, increases in the transmissibility of variants of concern, changes in compliance to mask wearing and social distancing, and changes in testing rates. The model is employed to study public health mitigation and vaccination of the COVID-19 epidemic in Canada, including different vaccination programs (rollout by age), and delays between doses in a two-dose vaccine. We find that the decision to delay the second dose of vaccine is appropriate in the Canadian context. We also find that the benefits of a COVID-19 vaccination program in terms of reductions in infections is increased if vaccination of 15-19 year olds are included in the vaccine rollout.

A machine learning approach to differentiate between COVID-19 and influenza infection using synthetic infection and immune response data.

Data analysis is widely used to generate new insights into human disease mechanisms and provide better treatment methods. In this work, we used the mechanistic models of viral infection to generate synthetic data of influenza and COVID-19 patients. We then developed and validated a supervised machine learning model that can distinguish between the two infections. Influenza and COVID-19 are contagious respiratory illnesses that are caused by different pathogenic viruses but appeared with similar initial presentations. While having the same primary signs COVID-19 can produce more severe symptoms, illnesses, and higher mortality. The predictive model performance was externally evaluated by the ROC AUC metric (area under the receiver operating characteristic curve) on 100 virtual patients from each cohort and was able to achieve at least AUC = 91% using our multiclass classifier. The current investigation highlighted the ability of machine learning models to accurately identify two different diseases based on major components of viral infection and immune response. The model predicted a dominant role for viral load and productively infected cells through the feature selection process.

Efficacy of a "stay-at-home" policy on SARS-CoV-2 transmission in Toronto, Canada: a mathematical modelling study.

BACKGROUND: Globally, nonpharmaceutical interventions for COVID-19, including stay-at-home policies, limitations on gatherings and closure of public spaces, are being lifted. We explored the effect of lifting a stay-at-home policy on virus resurgence under different conditions. METHODS: Using confirmed case data from Toronto, Canada, between Feb. 24 and June 24, 2020, we ran a compartmental model with household structure to simulate the impact of the stay-at-home policy considering different levels of compliance. We estimated threshold values for the maximum number of contacts, probability of transmission and testing rates required for the safe reopening of the community. RESULTS: After the implementation of the stay-at-home policy, the contact rate outside the household fell by 39% (from 11.58 daily contacts to 7.11). The effective reproductive number decreased from 3.56 (95% confidence interval [CI] 3.02-4.14) on Mar. 12 to 0.84 (95% CI 0.79-0.89) on May 6. Strong adherence to stay-at-home policies appeared to prevent SARS-CoV-2 resurgence, but extending the duration of stay-at-home policies beyond 2 months had little added effect on cumulative cases (25 958 for 65 days of a stay-at-home policy and 23 461 for 95 days, by July 2, 2020) and deaths (1404 for 65 days and 1353 for 95 days). To avoid a resurgence, the average number of contacts per person per day should be kept below 9, with strict nonpharmaceutical interventions in place. INTERPRETATION: Our study demonstrates that the stay-at-home policy implemented in Toronto in March 2020 had a substantial impact on mitigating the spread of SARS-CoV-2. In the context of the early pandemic, before the emergence of variants of concern, reopening schools and workplaces was possible only with other nonpharmaceutical interventions in place.

COVID-19 Seroprevalence in Canada Modelling Waning and Boosting COVID-19 Immunity in Canada a Canadian Immunization Research Network Study.

COVID-19 seroprevalence changes over time, with infection, vaccination, and waning immunity. Seroprevalence estimates are needed to determine when increased COVID-19 vaccination coverage is needed, and when booster doses should be considered, to reduce the spread and disease severity of COVID-19 infection. We use an age-structured model including infection, vaccination and waning immunity to estimate the distribution of immunity to COVID-19 in the Canadian population. This is the first mathematical model to do so. We estimate that 60-80% of the Canadian population has some immunity to COVID-19 by late Summer 2021, depending on specific characteristics of the vaccine and the waning rate of immunity. Models results indicate that increased vaccination uptake in age groups 12-29, and booster doses in age group 50+ are needed to reduce the severity COVID-19 Fall 2021 resurgence.

Modelling COVID-19 transmission in a hemodialysis centre using simulation generated contacts matrices.

The COVID-19 pandemic has been particularly threatening to patients with end-stage kidney disease (ESKD) on intermittent hemodialysis and their care providers. Hemodialysis patients who receive life-sustaining medical therapy in healthcare settings, face unique challenges as they need to be at a dialysis unit three or more times a week, where they are confined to specific settings and tended to by dialysis nurses and staff with physical interaction and in close proximity. Despite the importance and critical situation of the dialysis units, modelling studies of the SARS-CoV-2 spread in these settings are very limited. In this paper, we have used a combination of discrete event and agent-based simulation models, to study the operations of a typical large dialysis unit and generate contact matrices to examine outbreak scenarios. We present the details of the contact matrix generation process and demonstrate how the simulation calculates a micro-scale contact matrix comprising the number and duration of contacts at a micro-scale time step. We have used the contacts matrix in an agent-based model to predict disease transmission under different scenarios. The results show that micro-simulation can be used to estimate contact matrices, which can be used effectively for disease modelling in dialysis and similar settings.

Barrier Gesture Relaxation during Vaccination Campaign in France: Modelling Impact of Waning Immunity

Non-pharmaceutical interventions have been implemented intermittently for more than a year in most countries of the world to mitigate the COVID-19 epidemic. In France, while the vaccination campaign is progressing, the French government has decided to remove many public health restrictions such as business closure, lockdowns, and curfews. Nonetheless, social distancing, mask wearing, and hand washing (also called barrier gestures) are still recommended. We utilize an age-structured compartmental SEIR model that takes into account the SARS-CoV-2 waning immunity, vaccination, and increased transmissibility from variants of concern to estimate if barrier gestures can be relaxed without causing a resurgence of severe infections. This model assumes that the susceptibility to infection is a function of immunity status, which depends on initial infection severity and vaccination status. It is calibrated on confirmed COVID-19 cases from the French surveillance database, and accounts for changes in contact behaviors due to the implementation of nation-wide public health policies. We study the partial and full relaxation of barrier gestures occurring from August to December 2021 under various immunity duration assumptions. Maintaining the application of barrier gestures appears essential to avoid a resurgence of severe infections that would exceed French health care capacities, while surmounting vaccine hesitancy represents the key to consider their relaxation. Immunity duration assumptions significantly influence the short-term dynamic of the epidemic, which should be considered for further modelling.

Analysis of Host Immunological Response of Adenovirus-Based COVID-19 Vaccines.

During the SARS-CoV-2 global pandemic, several vaccines, including mRNA and adenovirus vector approaches, have received emergency or full approval. However, supply chain logistics have hampered global vaccine delivery, which is impacting mass vaccination strategies. Recent studies have identified different strategies for vaccine dose administration so that supply constraints issues are diminished. These include increasing the time between consecutive doses in a two-dose vaccine regimen and reducing the dosage of the second dose. We consider both of these strategies in a mathematical modeling study of a non-replicating viral vector adenovirus vaccine in this work. We investigate the impact of different prime-boost strategies by quantifying their effects on immunological outcomes based on simple system of ordinary differential equations. The boost dose is administered either at a standard dose (SD) of 1000 or at a low dose (LD) of 500 or 250 vaccine particles. Results show dose-dependent immune response activity. Our model predictions show that by stretching the prime-boost interval to 18 or 20, in an SD/SD or SD/LD regimen, the minimum promoted antibody (Nab) response will be comparable with the neutralizing antibody level measured in COVID-19 recovered patients. Results also show that the minimum stimulated antibody in SD/SD regimen is identical with the high level observed in clinical trial data. We conclude that an SD/LD regimen may provide protective capacity, which will allow for conservation of vaccine doses.

Integrated vaccination and non-pharmaceutical interventions based strategies in Ontario, Canada, as a case study: a mathematical modelling study.

Recently, two coronavirus disease 2019 (COVID-19) vaccine products have been authorized in Canada. It is of crucial importance to model an integrated/combined package of non-pharmaceutical (physical/social distancing) and pharmaceutical (immunization) public health control measures. A modified epidemiological, compartmental SIR model was used and fit to the cumulative COVID-19 case data for the province of Ontario, Canada, from 8 September 2020 to 8 December 2020. Different vaccine roll-out strategies were simulated until 75% of the population was vaccinated, including a no-vaccination scenario. We compete these vaccination strategies with relaxation of non-pharmaceutical interventions. Non-pharmaceutical interventions were supposed to remain enforced and began to be relaxed on 31 January, 31 March or 1 May 2021. Based on projections from the data and long-term extrapolation of scenarios, relaxing the public health measures implemented by re-opening too early would cause any benefits of vaccination to be lost by increasing case numbers, increasing the effective reproduction number above 1 and thus increasing the risk of localized outbreaks. If relaxation is, instead, delayed and 75% of the Ontarian population gets vaccinated by the end of the year, re-opening can occur with very little risk. Relaxing non-pharmaceutical interventions by re-opening and vaccine deployment is a careful balancing act. Our combination of model projections from data and simulation of different strategies and scenarios, can equip local public health decision- and policy-makers with projections concerning the COVID-19 epidemiological trend, helping them in the decision-making process.