Modeling and Analysis of Population Dynamics of Human Cells Pertaining to HIV/AIDS with Treatment

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.

Stochastic Model Analysis of the Impact of Media Campaign on Transmission of Covid – 19 Epidemic.

“…These sociological issues include the lack of palliatives during the lockdown and religious prohibitions on the use of alcohol-based hand sanitizer. Let  be the transmission rate from Susceptible to the Exposed class Based on the information above and earlier research (Stephen et al 2015), (Misra et al 2011,(Kumama andKoya 2019), (He and Libin 2020), (Liu et al 2020), the dynamics of the model are controlled by the following system of non-linear differential equations…”