论文标题
下一代矩阵提供了流行病的开始和结尾阶段吗？ - 重新审视药物敏感和抗性结核病模型
Are the beginning and ending phases of epidemics provided by next generation matrices? -- Revisiting drug sensitive and resistant tuberculosis model
论文作者
论文摘要
在流行病学模型中，在微不足道平衡下评估的下一代基质的光谱半径被认为是基本的繁殖数。同样，琐碎平衡点的全局稳定性由与该下一代矩阵相关的左侧向量确定。最近，还从下一代矩阵中获得了易感个体的比例。通过重新审视药物敏感和抗性结核病模型，计算了易感个体的总繁殖数和比例。因此，下一代矩阵将动力学的演变浮出水面：通过繁殖数和通过易感个体的渐近分数到达流行病水平的流行病的开始。
In epidemiological modelings, the spectral radius of the next generation matrix evaluated at the trivial equilibrium was considered as the basic reproduction number. Also, the global stability of the trivial equilibrium point was determined by the left eigenvector associated to that next generation matrix. More recently, the fraction of susceptible individuals was also obtained from the next generation matrix. By revisiting drug sensitive and resistant tuberculosis model, the gross reproduction number and the fraction of susceptible individuals are calculated. Hence, the next generation matrices shed light to the evolution of the dynamics: the beginning of the epidemics via the reproduction number and the approaching to the epidemics level via the asymptotic fraction of susceptible individuals.
