Immune events such as infection, vaccination, and a combination of the two result in distinct time-dependent antibody responses in affected individuals. These responses and event prevalences combine non-trivially to govern antibody levels sampled from a population. Time-dependence and disease prevalence pose considerable modeling challenges that need to be addressed to provide a rigorous mathematical underpinning of the underlying biology. We propose a time-inhomogeneous Markov chain model for event-to-event transitions coupled with a probabilistic framework for anti-body kinetics and demonstrate its use in a setting in which individuals can be infected or vaccinated but not both. We prove the equivalency of this approach to the framework developed in our previous work. Synthetic data are used to demonstrate the modeling process and conduct prevalence estimation via transition probability matrices. This approach is ideal to model sequences of infections and vaccinations, or personal trajectories in a population, making it an important first step towards a mathematical characterization of reinfection, vaccination boosting, and cross-events of infection after vaccination or vice versa.
Effect of antibody levels on the spread of disease in multiple infections
College of Artificial Intelligence, Southwest University（西南大学人工智能学院）；School of Mathematical Sciences, Queen Mary University of London（伦敦大学玛丽女王学院数学科学学院）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Department of Physics, Humboldt University（柏林洪堡大学物理系）
Modeling the effects of tetanus vaccination on chronically infected HIV patients
T细胞活化在HIV-1感染的起始和传播中起关键作用，然而免疫系统的瞬时活化是对免疫的正常应答。在这项研究中，我们扩展了一个简单的艾滋病毒感染模型，包括T细胞激活疫苗接种。然后，我们表明，该模型可以重现Stanley等人观察和报告的破伤风免疫后病毒载量上升的许多但不是全部特征，[N. Engl. J. Med.，334：1222- 1230（1996）]。免疫后最大病毒血症的振幅和大致时间在9/12例中匹配;在具有几乎相等振幅的双峰的患者中，较晚的峰匹配。在病毒血症中具有单个早期峰值的患者最适合具有相对高的抗原清除率常数，而在病毒血症中具有相等或几乎相等幅度的早期和晚期峰值的患者最适合具有低得多的清除率。清除率可能取决于预先存在的抗体水平，而预先存在的抗体水平又可能取决于研究中的个体接受既往破伤风疫苗接种的时间。
Effect of two vaccine doses in the SEIR epidemic model using a stochastic cellular automaton
在这项工作中，为了支持免疫策略的决策，我们建议在SEIR模型中考虑随机元胞自动机包含两种疫苗接种剂量。我们分析了三种不同的疫苗接种方案：$i) unlimited doses, (ii) limited doses into susceptible individuals, and (iii) limited doses randomly distributed overall individuals. Our results suggest that the number of vaccinations and time to start the vaccination is more relevant than the vaccine efficacy, delay between the first and second doses, and delay between vaccinated groups. The scenario (i) shows that the solution can converge early to a disease-free equilibrium for a fraction of individuals vaccinated with the first dose. In the scenario (ii), few two vacci…
