改进的模型数学模型:复杂非线性非线性传染病系统的建模、分离分析和最佳控制研究 (An Improved Mathematical Model of Sepsis: Modeling, Bifurcation Analysis, and Optimal Control Study for Complex Nonlinear Infectious Disease System)

Sepsis is a life-threatening medical emergency, which is a major cause of death worldwide and the second highest cause of mortality in the United States. Researching the optimal control treatment or intervention strategy on the comprehensive sepsis system is key in reducing mortality. For this purpose, first, this paper improves a complex nonlinear sepsis model proposed in our previous work. Then, bifurcation analyses are conducted for each sepsis subsystem to study the model behaviors under some system parameters. The bifurcation analysis results also further indicate the necessity of control treatment and intervention therapy. If the sepsis system is without adding any control under some parameter and initial system value settings, the system will perform persistent inflammation outcomes as time goes by. Therefore, we develop our complex improved nonlinear sepsis model into a sepsis optimal control model, and then use some effective biomarkers recommended in existing clinic practices as optimization objective function to measure the development of sepsis. Besides that, a Bayesian optimization algorithm by combining Recurrent neural network (RNN-BO algorithm) is introduced to predict the optimal control strategy for the studied sepsis optimal control system. The difference between the RNN-BO algorithm from other optimization algorithms is that once given any new initial system value setting (initial value is associated with the initial conditions of patients), the RNN-BO algorithm is capable of quickly predicting a corresponding time-series optimal control based on the historical optimal control data for any new sepsis patient. To demonstrate the effectiveness and efficiency of the RNN-BO algorithm on solving the optimal control solution on the complex nonlinear sepsis system, some numerical simulations are implemented by comparing with other optimization algorithms in this paper.

翻译：塞普西是一个危及生命的医疗紧急情况,这是全世界死亡的一个主要原因,也是造成美国死亡的第二大原因。研究全面败血症系统的最佳控制治疗或干预战略是降低死亡率的关键。为此,首先,本文件改进了我们先前工作中提议的复杂的非线性败血症模型。然后,对每个败血症子系统进行双向分析,以根据某些系统参数研究模型行为。双向分析结果还进一步表明控制治疗和干预治疗的必要性。如果败血症系统在某些参数和初始系统值设置下没有增加任何控制,那么随着时间推移,系统将产生持续的炎症发效应。因此,我们开发了我们复杂的非线性败血症模型,将其改进为一种最优控制模型模型,然后将现有的诊所做法中建议的一些有效的生物标记用作衡量败血症发展情况的优化目标功能。此外,通过将正常神经系统的最佳控制网络(RENN-BA算法)合并,用于预测经研究的Sepsime-最优控制系统的最佳控制战略,一旦通过初步的Sepsiximim 最佳控制系统,则使用其他最优化的Rimal-Rimal-ral oralalalal-revilal 将使用其他最佳控制系统的最佳比率系统进行。