Pulse HIV Vaccination: Feasibility for Virus Eradication and Optimal Vaccination Schedule

We modify the classical virus dynamics model by incorporating an immune response with fixed or fluctuating vaccination frequencies and dosages to obtain a system of impulsive differential equations for the virus dynamics of both the wild-type and mutant strains. This model framework permits us to obtain precise conditions for the virus elimination, which are much more feasible compared with existing results, which require frequent vaccine administration with large dosage. We also consider the corresponding impulsive optimal control problem to describe when and how much of the vaccine should be administered in order to maximize levels of healthy CD4⁺ T cells and immune response cells. A gradient-based optimization method is applied to obtain the optimal schedule numerically. For a case study when the CTL vaccine is administered in a period of one year, our numerical studies support the optimal vaccination schedule consisting of vaccine administration three times, with the first dosage strong (to boost the immune system), followed by a second dosage shortly after (to strengthen the immune response) and then the third and final dosage long after (to ensure the immune system can handle viruses rebound).