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Nurahmad, Muhammad Fadhil
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Computer Science & IT Mathematics

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A Deterministic Mathematical Model of Meningitis Transmission Dynamics with Vaccination and Screening Amar, Muh Ikhsan; Nisardi, Muhammad Rifki; Nurahmad, Muhammad Fadhil
Jurnal Matematika UNAND Vol 14, No 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.14-30.2025

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
A Deterministic Mathematical Model of Meningitis Transmission Dynamics with Vaccination and Screening Amar, Muh Ikhsan; Nisardi, Muhammad Rifki; Nurahmad, Muhammad Fadhil
Jurnal Matematika UNAND Vol. 14 No. 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.14-30.2025

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
Co-Authors Amar, Muh Ikhsan Muhammad Rifki Nisardi