Optimal Control Strategies for Dual-Strain Hepatitis B Dynamics: A Mathematical and Cost-Effectiveness Study

Abstract

This study presents a mathematical model to describe the transmission dynamics of the Hepatitis B Virus (HBV), accounting for two distinct viral strains. The basic reproduction number, R₀, is derived using the next-generation matrix method, and three equilibrium points are identified. Stability analysis reveals that the disease-free equilibrium is locally asymptotically stable when R₀ < 1, the first strain-free equilibrium is stable when R₀₂ > R₀₁, and the endemic equilibrium is stable when R₀ > 1. An optimal control problem is then formulated to evaluate the effectiveness of two intervention strategies: vaccination and treatment. The objective is to minimize infection levels and reduce economic burden. Using Pontryagin's Maximum Principle, the necessary conditions for optimal control are established within a deterministic framework. Numerical simulations, implemented in MATLAB, support the theoretical findings and demonstrate the impact of the proposed controls. Cost-effectiveness analysis indicates that treatment is the most economically efficient strategy. The model offers practical insights for HBV-endemic regions, particularly those with constrained healthcare resources.