论文标题

在霍林型III型饱和医学治疗的存在下,关于Covid-19的年龄结构建模的最佳控制研究

Optimal Control Studies on Age Structural Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

论文作者

Chhetri, Bishal, Vamsi, D. K. K, Sanjeevi, Carani B

论文摘要

最初,我们提出了一个年龄结构化模型,并计算平衡点和基本繁殖数。后来,我们提出了一个最佳控制问题,以了解治疗在控制流行病中的作用。从稳定性分析中,我们可以看到,每当$ r_0 <1 $且AS $ r_0 $跨越统一时,无感染平衡保持渐近稳定,我们就具有稳定的感染平衡。从灵敏度分析参数$ u_ {11} $,$ b_1 $,$β_1$,$ d_1 $和$μ$很敏感。最佳控制研究的发现表明,考虑到第二个控制$ u_ {12} $,成年人口(年龄$ \ geq 30)$的感染最少是最少的。当考虑第二个对照之后,累积感染的人群降低了最大值,同时考虑了两个对照。控制$ u_ {12} $对于轻度流行$(R_0 \ in(1,2))$有效,而控制$ u_ {11} $在流行病是严重的$(R_0 \ in(2,7)$的age Group $(\ leq 30)$时,发现$ u_ {11} $是非常有效的。而对于年龄组$(\ geq 30)$控制$ u_ {12} $对于整个基本复制编号的范围非常有效。还在数值上探讨了饱和水平在治疗中的影响。

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.

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