Memory-driven modeling of herpes simplex virus type-1 and type-2 dynamics with neural network optimization

Herpes Simplex Virus Types 1 and 2 (HSV-1 and HSV-2) are chronic viral infections with widespread prevalence and lasting health effects, including neurological and oncological complications. Traditional epidemiological models often fail to capture memory-dependent dynamics inherent in such infections. This study develops a novel modeling framework that incorporates memory effects to better understand HSV dynamics and evaluate intervention strategies.

We constructed a fractional-order compartmental model using the Caputo derivative to describe HSV-1 and HSV-2 transmission. The population is divided into susceptible (with and without health education), infected (type-1 and type-2), and recovered groups. We examined the model's qualitative properties, including existence, uniqueness, and stability. The basic reproduction number was derived, and sensitivity analysis was performed using the Latin Hypercube Sampling-Partial Rank Correlation Coefficient method. Numerical simulations were conducted via the Adams-Bashforth-Moulton predictor-corrector scheme. Additionally, a deep neural network was implemented to approximate the model's behavior.

Our findings show that fractional-order dynamics substantially influence infection persistence, with lower fractional orders prolonging infectious periods. Sensitivity analysis identified transmission rates and public awareness as the most impactful parameters. Recovery rates were negatively correlated with the basic reproduction number. Simulations demonstrated that increased awareness reduces infection levels. The neural network achieved high predictive accuracy (R≈1) across all compartments, effectively modeling both peak and recovery phases.

The incorporation of fractional derivatives improves model realism by capturing memory effects critical to HSV progression. Combining this with deep learning enables accurate simulation and real-time assessment of interventions. This integrated framework is a powerful tool for public health planning, particularly in optimizing awareness and treatment strategies for HSV-1 and HSV-2 control.