Stochastic Modeling and Optimal Control of HIV-1 Infection Dynamics Under Combination Antiretroviral Therapy

Area of Science:

• Mathematical modeling of infectious diseases
• Stochastic differential equations
• Epidemiology and public health

Background:

• Human Immunodeficiency Virus type 1 (HIV-1) infection remains a critical global health issue, with complete viral eradication not yet achievable through current combination antiretroviral therapy (cART).
• Understanding the complex dynamics of HIV-1 infection is crucial for developing more effective treatment strategies.
• Environmental factors and their impact on viral dynamics require further investigation.

Purpose of the Study:

• To develop a novel stochastic differential equation (SDE) model for HIV-1 infection dynamics, incorporating environmental noise.
• To mathematically derive the stochastic basic reproduction number (Rs) and analyze its threshold dynamics for viral clearance or persistence.
• To evaluate the efficacy of different intervention strategies, including cART enhancement, immune modulation, and a combined approach, using optimal control theory.

Main Methods:

• Development of a stochastic differential equation (SDE) model for HIV-1 infection.
• Mathematical derivation of the stochastic basic reproduction number (Rs) and analysis of threshold dynamics.
• Application of optimal control theory to evaluate three distinct intervention strategies for HIV-1 management.

Main Results:

• The derived stochastic basic reproduction number (Rs) predicts viral clearance when Rs < 1 and stochastic persistence when Rs > 1.
• Environmental noise significantly influences HIV-1 infection dynamics, highlighting its importance in modeling.
• A combined intervention strategy (Strategy 3), integrating cART enhancement with immune modulation, demonstrated superior performance in achieving rapid viral suppression.
• The combined strategy proved effective even under cost constraints, suggesting potential for cost-efficient HIV-1 management.

Conclusions:

• The developed SDE model provides a novel theoretical framework for understanding HIV-1 infection dynamics influenced by environmental noise.
• The study reaffirms the critical role of cART in HIV-1 management.
• A combined cART-immune intervention strategy offers significant clinical advantages for rapid viral suppression and cost-effective treatment, emphasizing the importance of cost considerations.