Modelling Optimal Control of In-Host HIV Dynamics Using Different Control Strategies

Area of Science:

• Mathematical modeling
• Epidemiology
• Public Health

Background:

• Human Immunodeficiency Virus (HIV) remains a leading cause of mortality, particularly in Sub-Saharan Africa.
• Effective treatment strategies are crucial for managing HIV infection and reducing transmission rates.

Purpose of the Study:

• To develop and analyze an in vivo deterministic model for HIV dynamics.
• To apply optimal control theory to identify effective HIV treatment strategies.
• To investigate the role of different drug regimens, including protease inhibitors, in controlling HIV.

Main Methods:

• Utilized a deterministic model of differential equations to simulate HIV dynamics.
• Applied optimal control theory, specifically Pontryagin's Maximum Principle, to determine optimal treatment strategies.
• Employed a numerical approach using the Runge-Kutta fourth-order scheme for solving the model.

Main Results:

• Optimal controlled treatment strategies demonstrated a significant reduction in viral load.
• The model indicated a substantial decrease in HIV transmission rates under optimal control.
• Protease inhibitors were identified as playing a key role in virus suppression, especially when used in combination therapy.

Conclusions:

• An optimal treatment strategy combining multiple drug regimens can effectively suppress HIV.
• Mathematical modeling and optimal control theory provide valuable insights into designing effective HIV interventions.
• Integrated treatment approaches are essential for maximizing the impact of HIV therapy and reducing disease burden.