A comparison of deterministic and stochastic model on the dynamics of HIV and CD4+ T-cells interactions

Abstract

This study aims to present a comparison of deterministic and stochastic approaches on the interaction of HIV and CD4⁺ T-cells with effects of HAART treatment. A three-dimensional nonlinear model is formulated with randomness that is considered as a Brownian motion coming from the uncertainty of the death rate of cells and viruses. We establish sufficient conditions for stability of endemic and nonendemic solutions that associate with an early reproductive threshold value of HIV infection which is linearly negative depending on the HAART treatment parameters. Non-negative stochastic solutions are also analysed. Numerical simulations show that HAART parameters have a significant effect in reducing HIV infection. The smaller value of treatment parameter, the more infected cells, which is also indicated by a threshold value that is greater than one. It also results in high fluctuations in the stochastic solutions. If the treatment parameter increases due to regular treatment, the number of infected cells and viruses decreases. It also reduces high fluctuations in the stochastic solutions which on average follow the decreasing trend of deterministic solutions. These results provide an overview of the intervals of the number of viruses and infected cells produced before and after being given treatment.