Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures

Area of Science:

• Epidemiology
• Mathematical Modeling
• Public Health

Background:

• Infectious disease control relies on vaccination and treatment to manage transmission and reduce mortality.
• Bacterial meningitis remains a significant public health concern, particularly in specific regions and environments.

Purpose of the Study:

• To develop and analyze a mathematical model for bacterial meningitis dynamics.
• To identify optimal control strategies for minimizing infection, illness, and control costs.

Main Methods:

• A nonlinear deterministic model with time-dependent controls was formulated.
• The model's equilibria and bifurcation at the effective reproduction number (ℛ_VT) were analyzed.
• An optimal control problem was set up to minimize a Lagrangian function.

Main Results:

• The model demonstrates a unique disease-free equilibrium (ℰ₀) when ℛ_VT ≤ 1 and an endemic equilibrium (ℰ₁) when ℛ_VT > 1.
• Carriers were identified as having a higher transmission potential than individuals with clinical symptoms.
• Numerical simulations indicated that combining vaccination with treatment and education is the optimal control strategy.

Conclusions:

• Integrated control strategies, including vaccination, treatment, and public health education, are crucial for managing bacterial meningitis.
• Targeted vaccine and antibiotic production and distribution are recommended for high-risk areas like Sub-Saharan Africa.
• Individuals in warm, humid environments should prioritize vaccination against bacterial meningitis.