As widely known, the basic reproduction number plays a key role in weighing birth/infection and death/recovery processes in several models of population dynamics. In this general setting, its characterization as the spectral radius of next generation operators is rather elegant, but simultaneously poses serious obstacles to its practical determination. In this work we address the problem numerically by reducing the relevant operators to matrices through a pseudospectral collocation, eventually computing the sought quantity by solving finite-dimensional eigenvalue problems. The approach is illustrated for two classes of models, respectively from ecology and epidemiology. Several numerical tests demonstrate experimentally important features of the method, like fast convergence and influence of the smoothness of the models’ coefficients. Examples of robust analysis of instances of specific models are also presented to show potentialities and ease of application.

众所周知，在多种种群动态模型中，基本再生数在衡量出生/感染和死亡/恢复过程中起着关键作用。在这种一般设置下，其作为下一代算子的谱半径的表征相当优雅，但同时对其实际确定造成了严重障碍。在这项工作中，我们通过伪谱搭配将相关算子简化为矩阵，以数值方式解决该问题，最终通过解决有限维特征值问题来计算所需的量。该方法针对两类模型进行了说明，分别来自生态学和流行病学。几个数值测试证明了该方法的实验重要特征，例如快速收敛和模型系数平滑度的影响。还提供了对特定模型实例进行稳健分析的示例，以显示应用的潜力和易用性。