An attempt at the computer-aided management of HIV infection

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Abstract

The immune system is a complex and diverse system in the human body and HIV virus disrupts and destroys it through extremely complicated but surprisingly logical process. The purpose of this paper is to make an attempt to present a method for the computer-aided management of HIV infection process by means of a mathematical model describing the dynamics of the host pathogen interaction with HIV-1. Treatments for the AIDS disease must be changed to more efficient ones in accordance with the disease progression and the status of the immune system. The level of progression and the status are represented by parameters which are governed by our mathematical model. It is then exhibited that our model is numerically stable and uniquely solvable. With this knowledge, our mathematical model for HIV disease progression is formulated and physiological interpretations are provided. The results of our numerical simulations are visualized, and it is seen that our results agree with medical aspects from the point of view of antiretroviral therapy. It is then expected that our approach will take to address practical clinical issues and will be applied to the computer-aided management of antiretroviral therapies.

MSC

37M05
65M06
65M50
65M55
92B05
92C05
92C30
92C35
92C45
92C50

Keywords

Mathematical model
Time-dependent evolution equation
Immune system
Semi-implicit product formula
Continuous model
Numerical model
HIV infection process
Antiretroviral therapy
Computer-aided management

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Partially supported by a Grant-in-Aid for Research Project from the Institute of Science and Engineering, Chuo University.