Age-structured deterministic model for the dynamics of Hepatitis B Virus in Nigeria incorporating vertical and horizontal transmission

सार

This study introduces an age-structured deterministic model for the transmission dynamics of the Hepatitis B Virus (HBV) in Nigeria, accounting for both vertical (mother-to-child) and horizontal (person-to-person) transmission pathways. The population is categorized into children and adults to reflect differences in transmission and intervention effects. Analytical outcomes demon-
strate the non-negativity of solutions and the existence of an invariant region, confirming the model’s biological validity. The disease-free equilibrium (DFE) and the basic reproduction number (R0) were determined using the next generation matrix approach. The local and global stability  of the DFE were assessed using the Jacobian and Castillo–Chavez and Song methods, respectively, while the global stability of the endemic equilibrium was verified through a Lyapunov function. An optimal control problem was developed to examine three intervention strategies: childhood vaccination (u1), adult catch-up vaccination (u2), and birth-dose vaccination (u3). Numerical simulations indicated that increasing childhood vaccination coverage results in an immediate reduction of acute infections among children and a delayed yet significant decline among adults through herd effects. Adult catch-up vaccination leads to a rapid decrease in acute infections and a gradual reduction in chronic cases, although some persistence occurs due to slow clearance and progression rates. Improved birth-dose vaccination demonstrated the most significant impact, preventing vertical transmission and moving the system toward near-elimination levels. Long-term simulations
suggested that HBV reaches an endemic equilibrium under current conditions but could move towards elimination with sustained vaccination efforts. The analysis indicates that age-specific interventions, particularly universal birth-dose and intensified childhood vaccination, represent effective and sustainable strategies for controlling and eventually eliminating HBV in high-endemic regions such as Nigeria