ABSTRACT
The human immunodeficiency virus (HIV) mainly attacks CD4+ T cells in the host. Chronic HIV infection gradually depletes the CD4+ T cell pool, compromising the host’s immunological reaction to invasive infections and ultimately leading to acquired immunodeficiency syndrome (AIDS). The goal of this study is not to provide a qualitative description of the rich dynamic characteristics of the HIV infection model of CD4+ T cells, but to produce accurate analytical solutions to the model using the modified iterative approach. In this research, a new efficient method using the new iterative method (NIM), the coupling of the standard NIM and Laplace transform, called the modified new iterative method (MNIM), has been introduced to resolve the HIV infection model as a class of system of ordinary differential equations (ODEs). A nonlinear HIV infection dynamics model is adopted as an instance to elucidate the identification process and the solution process of MNIM, only two iterations lead to ideal results. In addition, the model has also been solved using NIM and the fourth order Runge–Kutta (RK4) method. The results indicate that the solutions by MNIM match with those of RK4 method to a minimum of eight decimal places, whereas NIM solutions are not accurate enough. Numerical comparisons between the MNIM, NIM, the classical RK4 and other methods reveal that the modified technique has potential as a tool for the nonlinear systems of ODEs.
ABSTRACT
The Coronavirus disease 2019 (COVID-19) outbreak continues to significantly expose the vulnerabilities of healthcare systems around the world. These unprecedented circumstances create an opportunity for improving healthcare services which is desperately needed. This paper proposes a novel framework that distributes the patients across heterogeneous medical facilities (MFs) so that a weighted sum of the expected service time (EST) and service time tail probability (STTP) for all patients is minimized. We propose a model-based and model-free algorithms to schedule patients requests across the MFs. Our algorithms prioritize the patients with severe/critical conditions over others who can tolerate more delay in service. Based on the model-based approach, we formulate an optimization problem as a convex combination of both EST and STTP metrics, and apply an efficient iterative algorithm to solve it. Then, a more practical model-free scheme is proposed by adopting a deep reinforcement learning approach. Our model-free approach does not rely on pre-defined models or assumptions about the environment. Rather, it learns to choose scheduling decisions solely through observations of the resulting performance of past decisions. Our extensive results demonstrate a significant performance improvement of our proposed scheduling schemes when compared with other algorithms and competitive baselines.