A deterministic model for the effects on disease prevalence of the most advanced pre-erythrocytic vaccine against malaria is proposed and studied. The model includes two vaccinated classes that correspond to initially vaccinated and booster dose vaccinated individuals. These two classes are structured by time-since-initial-vaccination (vaccine-age). This structure is a novelty for vector–host models; it allows us to explore the effects of parameters that describe timed and delayed delivery of a booster dose, and immunity waning on disease prevalence. Incorporating two vaccinated classes can predict more accurately threshold vaccination coverages for disease eradication under multi-dose vaccination programs. We derive a vaccine-age-structured control reproduction number [Formula: see text] and establish conditions for the existence and stability of equilibria to the system. The model is bistable when [Formula: see text]. In particular, it exhibits a backward (sub-critical) bifurcation, indicating that [Formula: see text] is no longer the threshold value for disease eradication. Thus, to achieve eradication we must identify and implement control measures that will reduce [Formula: see text] to a value smaller than unity. Therefore, it is crucial to be cautious when using [Formula: see text] to guide public health policy, although it remains a key quantity for decision making. Our results show that if the booster vaccine dose is administered with delay, individuals may not acquire its full protective effect, and that incorporating waning efficacy into the system improves the accuracy of the model outcomes. This study suggests that it is critical to follow vaccination schedules closely, and anticipate the consequences of delays in those schedules.

中文翻译：

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疫苗接种对疟疾流行率的影响：疫苗年龄结构的建模方法

提出并研究了最先进的红细胞前疟疾疫苗对疾病流行影响的确定性模型。该模型包括两个接种类别，对应于最初接种疫苗和加强剂量接种疫苗的个体。这两个类别由自初始疫苗接种的时间（疫苗年龄）构成。这种结构对于载体-宿主模型来说是一种新颖性；它使我们能够探索描述定时和延迟提供加强剂量的参数以及免疫力减弱对疾病流行率的影响。结合两个接种疫苗的类别可以更准确地预测多剂量疫苗接种计划下消灭疾病的疫苗接种覆盖率阈值。我们推导出疫苗年龄结构的控制繁殖数 [公式：见正文] 并为系统平衡的存在和稳定建立条件。当[公式：见正文]时，该模型是双稳态的。特别是它表现出后向（亚临界）分岔，表明[公式：见正文]不再是疾病根除的阈值。因此，为了实现根除，我们必须确定并实施控制措施，将 [公式：见文本] 降低到小于统一的值。因此，在使用[公式：见正文]指导公共卫生政策时要谨慎，尽管它仍然是决策的关键数量。我们的结果表明，如果延迟给予加强疫苗剂量，个体可能无法获得其完全的保护作用，并且将减弱的效力纳入系统可提高模型结果的准确性。