Abstract
In this paper, a mathematical model has been formulated to describe the population dynamics of human cells pertaining to the HIV/AIDS disease with ART as treatment and is analyzed. The human cells have been divided into four compartments Susceptible – Asymptomatic – Symptomatic – AIDS (SAIV). The well posedness of the four dimensional dynamical system is proved and the steady states of the model are identified. Additionally, parametric expression for the basic reproduction number is constructed following next generation matrix method and analyzed its stability using Routh Hurwitz criterion. From the analytical and numerical simulation studies it is observed that if the basic reproduction is less than one unit then the solution converges to the disease free steady state i.e., disease will wipe out and thus the treatment is said to be successful. On the other hand, if the basic reproduction number is greater than one then the solution converges to endemic equilibrium point and thus the infectious cells continue to replicate i.e., disease will persist and thus the treatment is said to be unsuccessful. Sensitivity analysis of the model parameters is conducted and their impact on the reproduction number is analyzed. Finally, the model of the present study simulated using MATLAB. The results and observations have been included in the text of this paper lucidly.
Highlights
The Human Immunodeficiency Virus Human Immunodeficiency virus (HIV) infects cells of the immune system as well as that of the central nervous system inhuman body
The T-helper lymphocytes are the main type of cells that will be infected by HIV disease
It is well known that the role of these T-helper lymphocytes cells in the immune system is to coordinate with the actions of other immune system cells
Summary
The Human Immunodeficiency Virus HIV infects cells of the immune system as well as that of the central nervous system inhuman body. Few weeks after getting the infection, the infected individuals become highly infectious At this stage there would be a large amount of HIV in the peripheral blood amounting around 106 copies of virus per micro-litter μl of blood. Antibodies and cytotoxic lymphocyte start getting produced in response to the virus which is known as sero-conversion At this stage about 20 percent of people who are HIV positive show symptoms which are not mild. The progression to AIDS can be characterized by CD4+ count which is 200 per ml or below in a patient, while it is around 1000 per ml in a normal person At this stage, the infected individual is likely to develop opportunistic infections in their respiratory system, gastro-intestinal system, central nervous system and on the skin as well.
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