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HIV-1 infection dynamics and optimal control with Crowley-Martin function response.
Computer Methods and Programs in Biomedicine ( IF 6.1 ) Pub Date : 2020-05-04 , DOI: 10.1016/j.cmpb.2020.105503
Muhammad Naeem Jan , Nigar Ali , Gul Zaman , Imtiaz Ahmad , Zahir Shah , Poom Kumam

Background and Objective: As we all know, mathematical models provide very important information for the study of the human immunodeficiency virus type. Mathematical model of human immunodeficiency virus type-1 (HIV-1) infection with contact rate represented by Crowley-Martin function response is taken into account. The aims of this novel study is to checkthe local and global stability of the disease and also prevent the outbreak from the community. Methods: The mathematical model as well as optimal system of nonlinear differential equations are tackled numerically by Runge-Kutta fourth-order method. For global stability we use Lyapunov-LaSalle invariance principle and for the description of optimal control, Pontryagin’s maximum principle is used. Results: Graphical results are depicted and examined with different parameters values versus the basic reproductive number R0 and also the plots with and without control. The density of infected cells continued to increase without treatment, but the concentration of these cells decreased after treatment. The intensity of the pathogenic virus before and after the optimal treatment. This indicates a sharp drop in the rate of pathogenic viruses after treatment. It prevents the production of viruses by preventing cell infection and minimizing side effects. Conclusions: We analysed the model by defining the basic reproductive number, showing the boundedness, positivity and permanence of the solution, and proving the local and global stability of the infection-free state. We show that the threshold quantity R0 < 1, the elimination of HIV-1 infection from the T cell population, is eradicated; while for the threshold quantity R0 > 1, HIV-1 infection remains in the host. When the threshold quantity R0 > 1, then it shows that the steady-state of chronic disease is globally stable. Optimal control strategies are developed with the optimal control pair for the description of optimal control. To reduce the density of infected cells and viruses as well as maximize the density of healthy cells is determined by the objective functional.



中文翻译:

HIV-1感染动力学和克劳利马丁功能反应的最佳控制。

背景与目的:众所周知,数学模型为研究人类免疫缺陷病毒类型提供了非常重要的信息。考虑了以Crowley-Martin功能反应代表的接触率的人类1型免疫缺陷病毒(HIV-1)感染的数学模型。这项新颖的研究的目的是检查疾病的局部和全局稳定性,并防止社区爆发。方法:采用Runge-Kutta四阶方法数值求解非线性微分方程的数学模型和最佳系统。对于全局稳定性,我们使用Lyapunov-LaSalle不变性原理,对于最优控制的描述,使用Pontryagin的最大值原理。结果:R 0以及有和没有控制的图。未经处理的感染细胞密度持续增加,但处理后这些细胞的浓度下降。最佳治疗前后的致病病毒强度。这表明治疗后病原病毒的速度急剧下降。它通过防止细胞感染和最小化副作用来防止病毒的产生。结论:我们通过定义基本生殖数,显示了溶液的有界性,阳性和永久性,并证明了无感染状态的局部和全局稳定性,对模型进行了分析。我们表明阈值量R 0 <1,消除了从T细胞群体中消除HIV-1感染的情况;而对于阈值数量R 0  > 1,宿主中仍保留HIV-1感染。当阈值量R 0  > 1时,表明慢性疾病的稳态是全局稳定的。针对最优控制的描述,开发了带有最优控制对的最优控制策略。降低感染细胞和病毒的密度以及最大化健康细胞的密度是由目标功能决定的。

更新日期:2020-05-04
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