Analisis Kestabilan Lokal Model Transmisi Demam Berdarah Dengue

Arista Fitri Diana; Muhammad Ibnu Hajar; Zakaria Bani Ikhtiyar; Lathifatul Aulia

doi:10.21580/square.2024.6.1.21018

Analisis Kestabilan Lokal Model Transmisi Demam Berdarah Dengue

* - Institut Teknologi Statistika dan Bisnis Muhammadiyah Semarang, Indonesia

- Institut Teknologi Statistika dan Bisnis Muhammadiyah Semarang, Indonesia

(*) Corresponding Author

DOI: 10.21580/square.2024.6.1.21018

Abstract
References
Licensing
How to cite

Dengue fever transmission in Indonesia has an advanced amount. In this article, dynamic model of interaction between human and Aedes aegypti mosquitos is learned. The SEIRRD (Susceptible, Exposed, Infected, Recovered, Deceased) model is used in this article. The prurpose in this model is to describe the stability of dengue transmission, so that we can analyze the developed of epidemic model in mathemtic field. Using NGM method to analyze basic reproduction number and applying Routh-Hurwitz criteria method to show the local stability of model. Then, two equilibrium points, called endemic and non-endemic equilibrium points, are obtained. The result of basic reproduction number is described the stability analysis. If basic reproduction number less then one, the endemic equilibrium point is locally asymptotically stable and otherwise. Local stability analysis at the equilibrium point is determined through parameter analysis. Furthermore, numerical simulations are carried out by fitting the data to obtaine the result of the parameters. The results of numerical simulations explaine the spread of dengue transmission

Keywords: Dynamic Model, Epidemic Model, Equilibrium Point, Local Stability, Routh Hurwitz

A. pardi Agustina anjel. (2023). Analisis Model Sir-Asi Pada Penyakit Demam Berdarah Dengue.
B. Wang, X, et al. (2023). Threshold dynamics and optimal control of a dengue epidemic model with time delay and saturated incidence. J. Appl. Math. Comput., vol. 69, no. 1, pp. 871–893.
C. Xu, Y. Yu, G. Ren, Y. Sun, and X. Si. (2023). Stability analysis and optimal control of a fractional-order generalized SEIR model for the COVID-19 pandemic. Appl. Math. Comput., vol. 457, p. 128210.
F. Nurbaya and J. Pertiwi. (2019). Analisis Penanggulangan Demam Berdarah Dengue (Dbd) Di Kabupaten Sragen. J. Manaj. Inf. dan Adm. Kesehat., vol. 2, no. 2.
G. C. D. Podung, S. N. N. Tatura, and M. F. J. Mantik. (2021). Faktor Risiko Terjadinya Sindroma Syok Dengue pada Demam Berdarah Dengue. J. Biomedik, vol. 13, no. 2, p. 161.
H. R. Pandey, G. R. Phaijoo, and D. B. Gurung. (2023). Analysis of dengue infection transmission dynamics in Nepal using fractional order mathematical modeling. Chaos, Solitons Fractals X, vol. 11.
J. Z. Ndendya, L. Leandry, and A. M. Kipingu. (2023). A next-generation matrix approach using Routh–Hurwitz criterion and quadratic Lyapunov function for modeling animal rabies with infective immigrants. Healthc. Anal., vol. 4, p. 100260.
M. Faid and D. D. Purwanto. (2019). Desain Sistem Pakar Untuk Mendiagnosa Penyakit Demam Berdarah Dengue (DBD). J. Inf. Syst. Hosp. Technol., vol. 1, no. 01, pp. 25–29.
N. Anandika. (2020). Demam Berdarah. p. 38;64.
N. R. Dewi. (2015). Demam Berdarah Dengue. Bul. Jendela Epidemiol., vol. 2, p. 48, 2015,
P. R. Murugadoss, et al. (2023). Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays. Front. Biosci. Landmark, vol. 28, no. 6.