Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J1P3, Canada.
J Math Biol. 2023 Apr 30;86(5):86. doi: 10.1007/s00285-023-01919-3.
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.
提出了一种用于宿主内液体纳米颗粒递送 mRNA 疫苗的隔间模型。通过无量纲化，确定了决定疫苗在宿主内存活时间的五个时间尺度：干扰素 γ 的衰减、抗体的初始、自催化生长、抗体峰值和衰减以及白细胞介素的停止。通过渐近分析，我们能够在每个时间域中获得半解析解，这使我们能够预测最大浓度并更好地理解模型中的参数依赖性。我们将我们的模型与针对 BNT162b2 和 mRNA-1273 mRNA 疫苗的 22 个数据集进行了比较，证明了良好的一致性。使用我们的分析，我们估计了每个数据集的五个时间尺度中的每个时间尺度的值，并预测了血浆 B 细胞、抗体和白细胞介素的最大浓度。通过我们的比较，我们没有观察到候选疫苗和性别的任何明显差异。然而，我们确实发现了年龄依赖性，具体来说，在 55 岁及以上的患者中，疫苗激活需要更长的时间，并且抗体峰值出现得更早。
