Vaccines against varicella-zoster virus (VZV) are under introduction in Hungary into the routine vaccination schedule, hence it is important to understand the current transmission dynamics and to estimate the key parameters of the disease. Mathematical models can be greatly useful in advising public health policy decision making by comparing predictions for different scenarios. First we consider a simple compartmental model that includes key features of VZV such as latency and reactivation of the virus as zoster, and exogeneous boosting of immunity. After deriving the basic reproduction number $R_{0}$, the model is analysed mathematically and the threshold dynamics is proven: if $R_{0}\leq 1$ then the virus will be eradicated, while if $R_{0}>1$ then an endemic equilibrium exists and the virus uniformly persists in the population. Then we extend the model to include seasonality, and fit it to monthly incidence data from Hungary. It is shown that besides the seasonality, the disease dynamics has intrinsic multi-annual periodicity. We also investigate the sensitivity of the model outputs to the system parameters and the underreporting ratio, and provide estimates for $R_{0}$.

中文翻译：

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在匈牙利模拟水痘的传播动力学

在匈牙利，针对水痘带状疱疹病毒（VZV）的疫苗正在引入常规疫苗接种时间表，因此，了解当前的传播动态并评估该疾病的关键参数非常重要。通过比较不同情景的预测，数学模型在建议公共卫生政策决策中非常有用。首先，我们考虑一个简单的隔离模型，该模型包括VZV的关键特征，例如潜伏期和带状疱疹病毒的重新激活以及免疫的外源性增强。在得出基本复制数$ R_ {0} $之后，对该模型进行数学分析并证明阈值动态：如果$ R_ {0} \ leq 1 $，则病毒将被清除，而如果$ R_ {0}> 1美元，则存在地方均衡，病毒在种群中均匀地持续存在。然后，我们将模型扩展为包括季节性，并将其与匈牙利的月度发病率数据拟合。结果表明，除季节性外，疾病动态还具有固有的多年周期性。我们还研究了模型输出对系统参数和报告不足率的敏感性，并提供了$ R_ {0} $的估计值。