论文标题
结构化种群的基本繁殖编号的有效数值计算
Efficient numerical computation of the basic reproduction number for structured populations
论文作者
论文摘要
众所周知，基本的繁殖数在称量出生/感染和死亡/恢复过程中起着关键作用，在几种人口动态模型中。在这种一般环境中，它作为下一代操作员的光谱半径的表征相当优雅，但同时构成了严重的障碍。在这项工作中，我们通过将相关的运算符通过伪谱搭配减少到矩阵来解决该问题，最终通过求解有限维度特征值问题来计算所寻求的数量。分别从生态学和流行病学分别说明了两类模型的方法。几项数值测试表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。还提出了对特定模型实例的强大分析示例，以显示潜力和易于应用。
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.
