Modeling the transmission dynamics of meningococcal meningitis under hospitalization effects

Iranian Journal of Numerical Analysis and Optimization

مقاله 7، دوره 17، Issue 1 - شماره پیاپی 40، بهار 2027، صفحه 177-216   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2026.98719.1868

نویسندگان

Idowu Oluwarimi Joshua¹؛ Kiruthika K²؛ Mehmet Gümüş³؛ Ali Raza⁴؛ Chandrakumar E⁵؛ Jeeva N^{* 6}

¹Department of Mathematics, University of Benin, Edo State, Nigeria

²Department of Mathematics, K.S.Rangasamy College of Technology, Tiruchengode 637215, Tamil Nadu, India

³Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Türkiye

⁴Department of Mathematics, School of Science, University of Management and Technology, Lahore-54770, Pakistan.

⁵Department of Electrical and Electronics Engineering, K.S.Rangasamy College of Technology, Tiruchengode 637215, Tamil Nadu, India

⁶Department of Mathematics, K.S.Rangasamy College of Technology, Tiruchengode 637215,Tamil Nadu, India

چکیده

Meningococcal meningitis remains a major public health concern owing to its rapid transmission, severe health consequences, and potential to cause recurrent outbreaks. In this study, a deterministic compartmental model is developed to investigate the transmission dynamics of meningococcal meningitis and assess the impact of hospitalization on disease spread. The total population is partitioned into five epidemiological classes: susceptible ($S$), exposed ($E$), infectious ($I$), hospitalized ($H$), and recovered ($R$). The proposed model is shown to be epidemiologically and mathematically well-posed based on the positivity and boundedness of its solutions. The disease-free and endemic equilibrium points are derived, and the basic reproduction number, $\mathcal{R}_0$, is obtained using the next-generation matrix method. It is proved that the disease-free equilibrium is locally and globally asymptotically stable whenever $\mathcal{R}_0<1$, whereas the unique endemic equilibrium is locally and globally asymptotically stable whenever $\mathcal{R}_0>1$. Furthermore, bifurcation analysis based on the center manifold theory of Castillo--Chavez and Song establishes that the model undergoes a forward (supercritical) bifurcation at the critical threshold $\mathcal{R}_0=1$, implying that reducing the basic reproduction number below unity is sufficient for disease eradication. Sensitivity analysis identified the transmission, hospitalization, and recovery rates as the most influential parameters governing disease transmission. Numerical simulations using MATLAB\textsuperscript{\textregistered} supported the analytical results and demonstrated that timely hospitalization, improved recovery, and reduced transmission substantially decreased the number of infectious individuals and shortened the outbreak duration. These findings provide quantitative insights into meningococcal meningitis transmission and offer guidance for designing effective interventions and disease control strategies.

کلیدواژه‌ها

Meningitis modeling؛ Treatment effects؛ Epidemic model؛ Stability analysis؛ Numerical simulation