A Novel Model for Transmission Dynamics of Bacterial Meningitis Incorporating Vaccination and Treatment Using Counterfeit and Non-Counterfeit Drugs

• Published in: Journal of Advances in Mathematics and Computer Science Vol. 40; no. 8; pp. 105 - 129
• Main Authors: Ngari, CharlesWanjohi, Kilonzi, Jeremiah Savali
• Format: Journal Article
• Language: English
• Published: Journal of Advances in Mathematics and Computer Science 09.08.2025
• Subjects: Mathematics
• ISSN: 2456-9968; 2456-9968
• DOI: 10.9734/jamcs/2025/v40i82035

The protective membranes around the brain and spinal cord become inflamed or swollen when meningitis occurs. The original mode of transmission for bacterial meningitis was from animal to human, but it can now spread from person to person through contaminated surfaces, saliva, respiratory secretions, and aerosol droplets. This study analyzes bacterial meningitis using counterfeit and non-counterfeit drugs. Numerous mathematical representations regarding bacterial meningitis transmission formerly been put up and examined, finding out what happen when you subject infected individuals to medication with counterfeit and non-counterfeit drugs is our objectives. According to the model analysis, the endemic equilibrium is only locally asymptotically stable when the basic reproduction number is smaller than unity, while the disease-free equilibrium is asymptotically stable both locally and globally. When counterfeit drugs find themselves on health facilities and are then administered to infected individuals they will have devastating effect on these individuals as most of them never recover leading to high mortality case. Areas with weaker systems and less regulatory control usually face challenges in ensuring that all patients receive genuine medications. MATLAB software is utilized to do numerical simulations that illustrate the influence of counterfeit and non-counterfeit drugs resulting to severe illness on areas prone to counterfeit drugs. The model exhibits forward bifurcation where R0 < 1. Sensitivity has shown that the parameter ϕ,ω,η1 and η2 to be positive and hence increasing the basic reproduction number hence the right intervention should be put in place to reduce them. As bacterial meningitis have been shown to have devastating effect on an individual a coordinated effort among governments, healthcare providers, pharmaceutical companies, and the public where each stakeholder has a role to play in ensuring the integrity of the drug supply chain to stop the effect seen in patients particularly bacterial meningitis.