Time-dependent vaccine efficacy estimation quantified by a mathematical model (original) (raw)
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Estimation of the time-dependent vaccine efficacy from a measles epidemic
Statistics in Medicine, 2002
We present a method to estimate the time-dependent vaccine efficacy from the cohort-specific vaccination coverage and from data on the vaccination status of cases and apply it to a measles epidemic in Germany which involved 529 cases, 88 of whom were vaccinated and 370 unvaccinated (for the remaining 71 cases the vaccination status is unknown). Our epidemiological model takes into account that maternal antibodies prevent successful vaccination and that vaccine immunity may be lost over time. Model parameters are estimated from the data using maximum likelihood. Vaccination coverage, as determined in school surveys, ranged from 27.6 per cent for the cohort born in 1974 to 85 per cent for the 1986 cohort, which is far too low to prevent measles transmission. Cohorts for which no school surveys were performed are omitted from analysis. Thus, sufficient data are available for only 282 cases, 69 of whom are vaccinated. According to our estimates, measles vaccinations provided no immunity before 1978 (95 per cent CI: 0 to 47 per cent), for the period 1978-1982, the estimated vaccine efficacy was 80per cent (95 per cent CI: 67 to 89 per cent), and for 1982–1990 it was 97 per cent (95 per cent CI: 93 to 99 per cent). After 1990, the estimated value dropped to 89 per cent, but its confidence interval widely overlaps with that of the previous period (95 per cent CI: 74 to 97 per cent). Loss of immunity was estimated to be zero (95 per cent CI: 0 to 0.003/year). Several sensitivity analyses were performed with respect to the model assumptions. A modified model which assumed constant efficacy at all vaccination times yielded a high estimate of 96 per cent (95 per cent CI: 92 to 98 per cent) for primary vaccine efficacy but also a high loss rate of immunity of 0.007/year (95 per cent CI: 0.001 to 0.012) to explain the high fraction of vaccinated cases among older individuals. The likelihood score value is however significantly inferior compared to the score value of the model with time-dependent vaccine efficacy. Copyright © 2002 John Wiley & Sons, Ltd.
An sveir model for assessing potential impact of an imperfect anti-sars vaccine
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The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number (Rv). If Rv ≤ 1, the disease will be eliminated from the community; whereas an epidemic occurs if Rv > 1. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming R 0 = 4). Numerical simulations are used to explore the severity of outbreaks when Rv > 1. 2000 Mathematics Subject Classification. 92D30.
PLOS Computational Biology
The SARS-CoV-2 pandemic is a major concern all over the world and, as vaccines became available at the end of 2020, optimal vaccination strategies were subjected to intense investigation. Considering their critical role in reducing disease burden, the increasing demand outpacing production, and that most currently approved vaccines follow a two-dose regimen, the cost-effectiveness of delaying the second dose to increment the coverage of the population receiving the first dose is often debated. Finding the best solution is complex due to the trade-off between vaccinating more people with lower level of protection and guaranteeing higher protection to a fewer number of individuals. Here we present a novel extended age-structured SEIR mathematical model that includes a two-dose vaccination schedule with a between-doses delay modelled through delay differential equations and linear optimization of vaccination rates. By maintaining the minimum stock of vaccines under a given production r...
2021
The SARS-CoV-2 pandemic is a major concern all over the world and, as vaccines became available at the end of 2020, optimal vaccination strategies were subjected to intense investigation. Considering their critical role in reducing disease burden, the increasing demand outpacing production, and that most currently approved vaccines follow a two-dose regimen, the cost-effectiveness of delaying the second dose to increment the coverage of the population receiving the first dose is often debated. Finding the best solution is complex due to the trade-off between vaccinating more people with lower level of protection and guaranteeing higher protection to a fewer number of individuals.Here we present a novel extended age-structured SEIR mathematical model that includes a two-dose vaccination schedule with a between-doses delay modelled through delay differential equations and linear optimization of vaccination rates. Simulations for each time window and for different types of vaccines and...
2021
With the development of high-efficacy vaccines against SARS-CoV-2, an urgent open question is whether currently available vaccines protect with similar efficacy against infection with SARS-CoV-2 variants of concern (VOC). Recent reports quantifying the extent by which VOC can evade vaccine immunity resulted in a range of estimates for the same VOC, which makes them difficult to interpret. One possible explanation for the discrepancies between different studies is an inconsistency in terms of the time post-vaccination of the sampled population. Here we present a model based on the observed correlation between antibody neutralization levels and vaccine efficacy, which demonstrates the impact of time post-vaccination on the comparison of the vaccine efficacy for VOC versus non-VOC infections. Our model predicts and exemplifies several possible consequences for vaccine efficacy in VOC infections: 1) a delay in the onset of vaccine efficacy against VOC; 2) a transient increase in suscept...