Effects of periodic intake of drugs of abuse (morphine) on HIV dynamics: Mathematical model and analysis

Drugs of abuse, such as opiates, have been widely associated with diminishing host-immune responses, including suppression of HIV-specific antibody responses. In particular, periodic intake of the drugs of abuse can result in time-varying periodic antibody level within HIV-infected individuals, consequently altering the HIV dynamics. In this study, we develop a mathematical model to analyze the effects of periodic intake of morphine, a widely used opiate. We consider two routes of morphine intake, namely, intravenous morphine (IVM) and slow-release oral morphine (SROM), and integrate several morphine pharmacodynamic parameters into HIV dynamics model. Using our non-autonomous model system we formulate the infection threshold, R-t, for global stability of infection-free equilibrium, which provides a condition for avoiding viral infection in a host. We demonstrate that the infection threshold highly depends on the morphine pharmacodynamic parameters. Such information can be useful in the design of antibody-based vaccines. In addition, we also thoroughly evaluate how alteration of the antibody level due to periodic intake of morphine can affect the viral load and the CD4 count in HIV infected drug abusers.