A Deterministic Mathematical Model of Meningitis Transmission Dynamics with Vaccination and Screening

Authors

DOI:

https://doi.org/10.25077/jmua.14.1.14-30.2025

Keywords:

Basic Reproduction Number, Meningitis Modelling Disease, Routh-Hurwitz Criterion

Abstract

This study aims to examine the mathematical model of meningitis transmission as a deterministic model. The model includes five compartments: susceptible (S), carrier (C), infected (I), treatment (T), and recovered (R). We also consider vaccination and screening as interventions in disease transmission. In this work, we obtained two equilibrium points: disease-free equilibrium point and endemic equilibrium point. The next generation matrix is employed to compute the basic reproduction numbers ($R_0$). We also analyzed the sensitivity of parameters concerning $R_0$. If $R_0 < 1$, then the disease-free equilibrium point exists and is locally stable, whereas the endemic equilibrium point exists when $R_0 > 1$ and is locally stable if the Routh-Hurwitz criterion is satisfied. We use the Runge-Kutta 4th order method to confirm the stability properties of the equilibrium points and also show that vaccination and screening affect the transmission dynamics of Meningitis

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Author Biographies

Muh Ikhsan Amar, Insitut Teknologi Bacharuddin Jusuf Habibie

Ilmu Komputer

Muhammad Rifki Nisardi, Insitut Teknologi Bacharuddin Jusuf Habibie

Teknik Metalurgi

Muhammad Fadhil Nurahmad, Insitut Teknologi Bacharuddin Jusuf Habibie

Matematika

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Published

31-01-2025

How to Cite

Amar, M. I., Nisardi, M. R., & Nurahmad, M. F. (2025). A Deterministic Mathematical Model of Meningitis Transmission Dynamics with Vaccination and Screening. Jurnal Matematika UNAND, 14(1), 14–30. https://doi.org/10.25077/jmua.14.1.14-30.2025

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Vol. 14 No. 1 (2025)

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