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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Biomathematics (JJBM)
Nugrahani, Endar H.
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Computer Science & IT Decision Sciences, Operations Research & Management Mathematics

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Dynamics System in the SEIR-SI Model of the Spread of Malaria with Recurrence Ahkrizal, Afdhal; Jaharuddin, Jaharuddin; Nugrahani, Endar H.
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.18754

Abstract

Mathematical model is used to describe the dynamics of the spread of malaria in human and mosquito populations. The model used is the SEIR-SI model. This study discusses the stability of the equilibrium point, parameter sensitivity, and numerical simulation of the spread of malaria. The analysis shows that the model has two equilibrium points, namely the disease-free and endemic equilibrium points, each of which is locally asymptotically stable. Numerical simulations show that the occurrence of disease cure in exposed humans causes the rate of malaria spread to decrease. Meanwhile, the presence of disease recurrence causes the spread of malaria to increase.
The Effect of Susceptible Immigrants in a System Dynamic on the Spread of Malaria in Indonesia Aprianti, Euis; Jaharuddin, Jaharuddin; Nugrahani, Endar H.
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8630

Abstract

The spread of malaria is a serious public health problem, including in Indonesia. The mathematical model is formulated to describe the dynamic nature of the spread of malaria. The model used in this article is the SIR-SI model. This article discusses the stability of the fixed point analyzed using the Jacobian matrix and Routh-Hurwitz criteria, bifurcation analysis using the Castillo-Chaves and Song Theorem, and numerical simulation of the effect of the rate of susceptible immigrants on the dynamics of the malaria by using data on malaria cases in Indonesia. The results of the analysis show that the stability of the fixed point is related to the basic reproduction number determined by the next-generation matrix, and bifurcation occurs when the basic reproduction number is equal to one. The results of numerical simulations show that in order to suppress the spread of malaria, it is necessary to reduce the rate of susceptible immigrants. 
Co-Authors Ahkrizal, Afdhal Aprianti, Euis Jaharuddin, Jaharuddin