In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases.

翻译：本文针对一类具有有限年龄跨度的多群体、年龄结构种群模型，提出了一种计算再生数的通用数值逼近方法。为实现出生与转移过程定义的完全灵活性，我们在扩展空间框架内提出了年龄积分状态的等价形式。随后，通过伪谱配点法对出生算子和转移算子进行离散化。文中讨论了该方法在连续及分段连续率下流行病模型中的应用，涵盖了年龄变量（如人口年龄、感染年龄和疾病年龄）及传播项（如水平传播和垂直传播）的不同解释。数值实验表明，该方法可计算包括基础再生数和类型再生数在内的多种再生数，并作为特例纳入框架。