New algorithms for solving high-dimensional time-dependent optimal control problems and their applications in infectious disease models

Abstract

Infectious diseases have been the primary cause of human death worldwide nowadays. The optimal control strategy for infectious disease has attracted increasing attention, becoming a significant issue in the healthcare domain. Optimal control of diseases can affect the progression of diseases and achieve high-quality healthcare. In previous studies, massive efforts on the optimal control of diseases have been made. However, some infectious diseases' mortality is still high and even developed into the second highest cause of mortality in the US. According to the limitations in existing research, this research aims to study the optimal control strategy via some industrial engineering techniques such as mathematical modeling, optimization algorithm, analysis, and numerical simulation. To better understand the optimal control strategy, two infectious disease models (epidemic disease, sepsis) are studied. Complex nonlinear time-series and high-dimensional infectious disease control models are developed to study the transmission and optimal control of deterministic SEIR or stochastic SIS epidemic diseases. In addition, a stochastic sepsis control model is introduced to study the progression and optimal control for sepsis system considering possible medical measurement errors or system uncertainty. Moreover, an improved complex nonlinear sepsis model is presented to more accurately study the sepsis progression and optimal control for sepsis system. In this dissertation, some analysis methods such as stability analysis, bifurcation analysis, and sensitivity analysis are utilized to help reader better understand the model behavior and the effectiveness of the optimal control. The significant contributions of this dissertation are developing or improving nonlinear complex disease optimal control models and proposing several effective and efficient optimization algorithms to solve the optimal control in those researched disease models, such as an optimization algorithm combining machine learning (EBOC), an improved Bayesian Optimization algorithm (IBO algorithm), a novel high-dimensional Bayesian Optimization algorithm combining dimension reduction and dimension fill-in (DR-DF BO algorithm), and a high-dimensional Bayesian Optimization algorithm combining Recurrent Neural Network (RNN-BO algorithm). Those algorithms can solve the optimal control solution for complex nonlinear time-series and high-dimensional systems. On top of that, numerical simulation is used to demonstrate the effectiveness and efficiency of the proposed algorithms.