37 million people around the world today live with Human Immunodeficiency Virus (HIV), which is responsible for roughly 1.1 million deaths caused by AIDS-related conditions.
As Naveen Vaidya, a mathematics professor at San Diego State University, explains, "Currently there is no cure for HIV, presumably due to the establishment of latently infected cells that cannot be destroyed by available antiretroviral therapy. Hence, the primary focus of current HIV research has been to destruct HIV latent infections, and as part of this effort, initiation of antiretroviral therapy early in infection to avoid the formation of latently infected cells has been considered as potential means of successful HIV cure."
In a paper publishing this week in the SIAM Journal on Applied Mathematics , Vaidya and Libin Rong, a mathematics professor at the University of Florida, propose a mathematical model that investigates the effects of drug parameters and dosing schedules on HIV latent reservoirs and viral load dynamics.
While previous mathematical models have helped analyze dynamics of latently-infected cells, studies exploring antiretroviral therapy and the resulting pharmacodynamics in latent reservoir dynamics are lacking.
Their model specifically focuses on the impact of antiretroviral therapy early in treatment to control latently infected cells. Using a realistic periodic drug intake scenario to obtain a periodic model system, the authors study local as well as global properties of infection dynamics, described via differential equations. The model takes into account uninfected target cells, productively infected cells, latently infected cells, and free virus concentrations as mutually exclusive compartments.
Variations in specific drug parameters are shown to generate either an infection-free steady state or persistent infection. A viral invasion threshold, derived based on the model, is seen to govern the global stability of the infection-free steady state and viral persistence.
Vaidya's results demonstrate that prophylaxis or very early treatment using drugs with a good pharmacodynamics profile can potentially prevent or postpone establishment of viral infection. Only drugs with proper pharmacodynamic properties given at proper intervals can successfully combat infection. "However, once the latent infection is established, the pharmacodynamic parameters have less effect on the latent reservoir and virus dynamics," Vaidya says. "This is because the latent reservoir can be maintained by hemostasis of latently infected cells or other mechanisms rather than ongoing residual viral replications."
"Mathematical models can be used to analyze and simulate a large number of treatment scenarios, which are often impossible and/or extremely difficult to study in vivo and/or vitro experimental settings," as Vaidya explains. "The results from these models can also provide novel themes for further experiments. For example, our modeling results in this study suggest that the drugs with a larger slope of the drug-response curve, such as protease inhibitors, are more effective in controlling latent infections, and thus such drugs in treatment regimens need to be included in further experimental studies."
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Acknowledgments: Naveen Vaidya's work is funded by NSF grant DMS-1616299 and start-up funds from San Diego State University. Libin Rong is partially supported by the NSF grant DMS-1349939.
Naveen K. Vaidya is an assistant professor in the Department of Mathematics and Statistics at San Diego State University. He can be reached at nvaidya@sdsu.edu . Libin Rong is an associate professor in the Department of Mathematics at the University of Florida. He can be reached at libinrong@ufl.edu .
SIAM Journal on Applied Mathematics