In epidemiological modeling, the basic reproduction number is usually defined as being the spectral radius of the next-generation matrix evaluated at the trivial equilibrium. The global stability of the trivial equilibrium point was determined by the left eigenvector associated with that next-generation matrix. More recently, the fraction of susceptible individuals was also obtained from the next generation matrix. The gross reproduction number and the fraction of susceptible individuals were calculated by revisiting the drug-sensitive and resistant tuberculosis model. Hence, the next-generation matrices shed light on the evolution of the dynamics: the beginning of the epidemic via the basic reproduction number and approaching the epidemic’s steady-state via the susceptible individuals’ asymptotic fraction.

中文翻译：

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下一代矩阵是否以流行病的开始和结束阶段为特征？– 药物敏感和耐药结核病模型的案例研究

在流行病学建模中，基本再生数通常定义为在平凡平衡下评估的下一代矩阵的光谱半径。平凡平衡点的全局稳定性由与该下一代矩阵相关的左特征向量确定。最近，易感个体的比例也从下一代矩阵中获得。通过重新审视药物敏感和耐药结核病模型，计算了总繁殖数和易感个体的比例。因此，下一代矩阵揭示了动力学的演变：通过基本繁殖数开始流行病，通过易感个体的渐近分数接近流行病的稳态。