Analysis of Dynamics of HIV-1 Associated Kaposi Sarcoma during HAART and ACI

Aims: To formulate, analyze, and perform investigative computer simulations for clinically plausible mathematical model depicting the patho-physiodynamics of HIV-1 associated Kaposi Sarcoma (KS) during Highly Active Anti-Retroviral Therapy (HAART) of AIDS and Adoptive Cellular Immunotherapy (ACI). The basic principle of digital combination therapy involving HAART and ACI is exhibited in the computer simulations.

Study Design: The mathematical model proposed in the current research is based on the results of the state-of-the-art data published in peer-reviewed journals relating to HAART, KS, and ACI. Using Dynamic Systems Theory, the clinical data is reformulated into a system of non-linear deterministic differential equations involving six model variables: non-HIV-1 infected CD4+ T lymphocytes, HIV-1 infected lymphocytes, free HIV-1 virions in the blood plasma, HIV-1 specific cytotoxic CD8+ T lymphocytes/ex-vivointerleukin-2 (IL-2) incubated CD8+ T cells, HAART drug molecules, and the KS cancer cells. The model incorporates all appropriate stoichiometric interaction rate coefficients, apoptotic rate constants, rate constants for viral recruitment from latent reservoirs, and other relevant parameters. The role of CD4+ T cell-induced syncytia in modulating the outcome of HAART and ACI is exhibited in the computer simulations using clinically plausible hypothetic patient physiological parametric configurations.

Place and Duration of Study: This research was conducted at Fayetteville State University (FSU), Fayetteville, North Carolina, USA. The digital version of the model was initiated in the summer of 2015 under the HBCU Graduate STEM Summer Grant in 2015.

Methodology: The equilibrium points, also known as the physiological outcomes were computed and the local stability at these points were analyzed utilizing the Hartman-Grobman theory, the principles of linearized stability, Banach space techniques, and Lozinskii matrix based stability. The clinically desirable physiological outcomes are further analyzed to obtain plausible robust criteria under which the HIV-1 virions, HIV-1 infected CD4+ lymphocytes and KS cells are annihilated. In particular, some scenarios of therapeutic failure are also discussed.

Results: Theoretical digital criteria for remission and possible cure of KS and AIDS are derived in terms of biophysically measurable parameters. The model simulations incorporate scenarios with and without HIV-1 induced syncytia. The digital prognosis of KS and the associated HIV-1 AIDS are exhibited in terms of biophysically measurable mathematical criteria. In particular, the computer simulations use hypothetical patient parametric configurations to elucidate the quantitative dynamics of KS and associated HIV-1 AIDS during HAART and ACI.

Conclusion: This research has demonstrated that under certain patient parametric configurations, a higher density of syncytia prevents reconstitution of CD4+ T cells at various doses of HAART drug cocktail. It also establishes theoretically it is possible for HAART to annihilate HIV-1 infected CD4+ T cells and HIV-1 virions without necessarily eliminating KS.