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All Journal Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Isnu Aji Saputro
Department of Mathematics, Jenderal Soedirman University, Indonesia
Mathematics

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DYNAMICAL ANALYSIS OF SVEIR MODEL IN SPREAD OF THE MONKEYPOX DISEASE WITH TIME DELAY Isnu Aji Saputro; Glagah Eskacakra Setyowisnu; Noor Sofiyati; Dian Puspita
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 2 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.2.17707

Abstract

Monkeypox is an infectious disease whose spread is influenced by various epidemiological factors, one of which is the incubation period. This study developed a mathematical model of Monkeypox, SVEIR, by incorporating a time delay in the transition from an exposed individual to an infectious individual, representing the incubation period. Model analysis shows that the system has two equilibrium points: a disease-free state and an endemic state. Based on the simulation results, a threshold value (tau* ) is obtained, which plays a crucial role in disease control. If the incubation period is below the threshold ( tau<tau*), then R0>1 , and the disease will spread endemically. Conversely, if the incubation period exceeds the threshold (tau>tau* ), then R0<1 , and the disease will disappear from the population
ASYMPTOTIC STUDY OF NONLINEAR SPRING OSCILLATION WITH EXTERNAL FORCE USING THE MULTIPLE TIME SCALES METHOD Glagah Eskacakra Setyowisnu; Lilik Muzdalifah; Isnu Aji Saputro
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 2 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.2.18081

Abstract

A nonlinear spring is a type of oscillator that does not follow Hooke's law perfectly. In mathematics, this type of oscillator can be modeled in a nonlinear ordinary differential equation. Of the many discussions on oscillation models, one examines the behavior of the model when disturbed by a parameter with a very small value. In this study, a discussion will be conducted regarding the behavior of the oscillation model with external forces added to the disturbance parameters in the damping and spring stiffness terms. To observe this behavior, one of the techniques in asymptotic analysis called the multiple time scales method is used. The results of this study will show the behavior of the oscillation model with the disturbance parameters caused by the resonance that occurs. To provide a clearer picture, the oscillations that occur are presented in the form of a simulation result graph, containing a comparison between the approximate solution and the numerical solution. Based on the discussion given, it is concluded that the oscillations in the model are strongly influenced by a certain relationship between the natural frequency of the nonlinear spring and the frequency of the external force acting on the model.
Co-Authors Dian Puspita Glagah Eskacakra Setyowisnu Lilik Muzdalifah Noor Sofiyati