A stochastic reaction-diffusion HIV/AIDS model with implications for long-Acting ART.

Area of Science:

• Epidemiology
• Mathematical Biology
• Stochastic Processes

Background:

• Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS) remain significant global health challenges.
• Understanding disease transmission dynamics is crucial for effective public health strategies.

Purpose of the Study:

• To develop a stochastic reaction-diffusion model for HIV/AIDS transmission.
• To analyze disease extinction mechanisms and predict pandemic trajectories.
• To investigate the impact of interventions like long-acting antiretroviral therapy (LA-ART).

Main Methods:

• Application of the Zvonkin transformation for analytical framework.
• Reformulation within reaction-diffusion equations to prove solution existence and uniqueness.
• Lyapunov function construction for disease persistence analysis.
• Derivation of stationary distributions and probability density functions using stochastic modeling theory.

Main Results:

• Sufficient conditions for disease persistence were established.
• Exponential disease extinction was proven under specific parameter regimes and confirmed by simulations.
• Noise was shown to be a factor in exponential disease extinction.
• The asymptomatic stage of AIDS was identified as a critical determinant of the pandemic's trajectory.

Conclusions:

• The developed stochastic model provides insights into HIV/AIDS transmission dynamics.
• While noise can promote extinction, AIDS remains a threat, emphasizing the need for targeted interventions.
• Prioritizing research into the asymptomatic stage is essential for developing effective control strategies.