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.

Lytic viruses infect and kill host cells, producing a large number of viral copies. Temperate viruses, in contrast, are able to integrate viral genetic material into the host cell DNA, leaving a viable host cell. The evolutionary advantage of this strategy, lysogeny, has been demonstrated in complex environments that include spatial structure, oscillating population dynamics, or periodic environmental collapse. Here, we examine the evolutionary stability of the lysis–lysogeny decision, that is, we predict the long‐term outcome of the evolution of lysogeny rates. We demonstrate that viruses with high rates of lysogeny are stable against invasion by more virulent viral strains even in simple environments, as long as the pool of susceptible hosts is not unlimited. This mirrors well‐known results in both r‐K selection theory and virulence evolution: although virulent viruses have a faster potential growth rate, temperate strains are able to maintain positive growth on a lower density of the limiting resource, susceptible hosts. We then outline scenarios in which the rate of lysogeny is predicted to evolve either toward full lysogeny or full lysis. Finally, we demonstrate conditions under which intermediate rates of lysogeny, as observed in temperate viruses in nature, can be sustained long‐term. In general, intermediate lysogeny rates persist when the coupling between susceptible host density and virus density is relaxed.

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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.

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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.

Background. The lipid nanoparticle (LNP)-formulated mRNA vaccines are a widely adopted two-dose vaccination public health strategy to manage the COVID-19 pandemic. Clinical trial data has described the immunogeneicity of the vaccine, albeit within a limited study time frame. Our aims were to use a within-host mathematical model for LNP-formulated mRNA vaccines, informed by available clinical trial data, to project a longer term understanding of humoral immunity as a function of vaccine type, dosage amount, age, and sex. Methods. We developed a mathematical model describing the immunization process of LNP-formulated mRNA vaccines, and fit our model to twenty-two clinical humoral and cytokine BNT162b2 or mRNA-1273 human two-dose vaccination data sets. We incorporated multi-dose effects in our model to specify whether the dosage is standard or low-dose. We further specify the age groups 18-55, 56-70, and 70+ in our fits for two-standard doses of mRNA-1273, and sex in our fits for two-standard doses of BNT162b2. We used non-linear mixed effect models to fit to all similar data types (e.g. standard two-dose BNT162b2 or mRNA-1273, or two low-dose mRNA-1273). Therefore, in our fits all estimated parameters are statistically correlated, which allowed us to determine the underlying 'population-dynamics' structure common to a data type. We therefore made accurate long-term predictions informed by all clinical data used in this study. Findings. We estimate that two standard doses of either mRNA-1273 or BNT162b2, with dosage times separated by the company-mandated intervals, results in individuals loosing more than 99% humoral immunity relative to peak immunity by eight months following the second dose. We predict that within an eight month period following dose two (corresponding to the CDC time-frame for administration of a third dose), there exists a period of time longer than one month where an individual has less then 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 eight 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 vaccine uptake and long-term IgG counts. Finally, we find that humoral immunity generated from two low doses of mRNA-1273 decays substantially slower relative to peak immunity gained than compared to two standard doses of either mRNA-1273 or BNT162b2. Interpretation. For the two dose mRNA vaccines, our predictions highlight the importance of the recommended third booster dose in order to maintain elevated levels of antibodies. We further show that age plays a critical role in determining the antibody levels. Hence, a third booster dose may confer an immuno-protective advantage in older individuals.

Reconstructing the early dynamics of the HIV-1 pandemic can provide crucial insights into the socioeconomic drivers of emerging infectious diseases in human populations, including the roles of urbanization and transportation networks. Current evidence indicates that the global pandemic comprising almost entirely of HIV-1/M originated around the 1920s in central Africa. However, these estimates are based on molecular clock estimates that are assumed to apply uniformly across the virus genome. There is growing evidence that recombination has played a significant role in the early history of the HIV-1 pandemic, such that different regions of the HIV-1 genome have different evolutionary histories. In this study, we have conducted a dated-tip analysis of all near full-length HIV-1/M genome sequences that were published in the GenBank database. We used a sliding window approach similar to the ‘bootscanning’ method for detecting breakpoints in inter-subtype recombinant sequences. We found evidence of substantial variation in estimated root dates among windows, with an estimated mean time to the most recent common ancestor of 1922. Estimates were significantly autocorrelated, which was more consistent with an early recombination event than with stochastic error variation in phylogenetic reconstruction and dating analyses. A piecewise regression analysis supported the existence of at least one recombination breakpoint in the HIV-1/M genome with interval-specific means around 1929 and 1913, respectively. This analysis demonstrates that a sliding window approach can accommodate early recombination events outside the established nomenclature of HIV-1/M subtypes, although it is difficult to incorporate the earliest available samples due to their limited genome coverage.