Holling型III饱和药物作用下COVID-19年龄结构模型的最优控制研究
Optimal Control Studies on Age Structural Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III
摘要：
在本研究中，我们首先提出一个年龄结构模型，并计算出平衡点和基本再生产数。后来，我们提出了一个最优控制问题，以了解治疗在控制流行病中的作用。从稳定性分析中，我们看到，无论何时$R_0 < 1$，无感染平衡都保持渐近稳定，并且当$R_0 < 1$穿过1时，我们有感染平衡是稳定的。从敏感性分析参数$u_{11}$，$b_1$，$β_1$，$d_1$和$μ$被认为是敏感的。最优控制研究的结果表明，考虑到第二种对照$u_{12}$，成年人群（年龄$\geq 30)$）中的感染最小，而当同时考虑对照$u_{11}$和$u_{12}$时，年轻人群（年龄$ \leq 30$）中的感染最小。当考虑第二个对照，然后同时考虑两个对照时，累积感染群体减少了最大值。对照$u_{12}$对轻度流行性$(R_0 \in(1, 2))$有效，而对照$u_{11}$在流行性为重度$(R_0 \in(2, 7))$时对年龄组$(\leq 30)$人群高度有效。而对于年龄组$(\geq 30)$，对照$u_{12}$对整个基本繁殖数范围都非常有效。饱和度在处理中的效果也进行了数值研究。
英文摘要：
In this study initially, we propose an age structured model and calculate the equilibrium points and basic reproduction number. Later we propose an optimal control problem to understand the roles of treatment in controlling the epidemic. From the Stability analysis we see that the infection free equilibrium remains asymptotically stable whenever $R_0 < 1$ and as $R_0$ crosses unity we have the infected equilibrium to be stable. From the sensitivity analysis parameters $u_{11}$, $b_1$, $β_1$, $d_1$ and $μ$ were found to be sensitive. Findings from the Optimal Control studies suggests that the infection among the adult population(age $\geq 30)$ is least considering the second control $u_{12}$ whereas, when both the controls $u_{11}$ and $u_{12}$ are considered together the infectives is minimum in case of young populations(age $ \leq 30$). The cumulative infected population reduced the maximum when the second control was considered followed by considering both the controls together. The control $u_{12}$ was effective for mild epidemic $(R_0 \in(1, 2))$ whereas control $u_{11}$ was found to be highly effective when epidemic was severe $(R_0 \in(2, 7))$ for the population of age group $(\leq 30)$. Whereas for age group $(\geq 30)$ the control $u_{12}$ was highly effective for the entire range of basic reproduction number. The effect of saturation level in treatment is also explored numerically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
