Analisis dinamik dan simulasi numerik model SIRV untuk penyebaran COVID-19

Authors

  • M. Rafi Prima Yoga Program Studi Matematika, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Keywords:

COVID-19, modeling, numerical, SIRV, vaccination

Abstract

The COVID-19 pandemic has encouraged the use of mathematical modeling to understand transmission dynamics and evaluate public health interventions. This study develops an SIRV epidemiological model by extending the classical SIR framework through the inclusion of a vaccination compartment. Vaccination is modeled as a single effective immunization process that transfers individuals from susceptible or recovered classes into a vaccinated class with permanent immunity. The model analysis includes the determination of equilibrium points, derivation of the basic reproduction number, and local stability analysis of the disease-free equilibrium. Numerical simulations are performed using the fourth-order Runge–Kutta method with explicit specification of time step and simulation horizon. The results demonstrate that increasing vaccination rates significantly reduces infection peaks and accelerates convergence toward a disease-free state. Sensitivity analysis shows that the transmission rate is the most influential parameter, followed by vaccination and recovery rates, emphasizing the importance of combining vaccination strategies with contact reduction policies.

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Published

2026-11-02

How to Cite

Yoga, M. R. P. (2026). Analisis dinamik dan simulasi numerik model SIRV untuk penyebaran COVID-19. Maliki Interdisciplinary Journal, 4(11), 2384–2398. Retrieved from https://urj.uin-malang.ac.id/index.php/mij/article/view/33767

Issue

Vol. 4 No. 11 (2026): NOVEMBER

Section

Articles

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Copyright (c) 2026 M. Rafi Prima Yoga

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