Simulasi Numerik Model Vaksinasi Transmisi Virus Influenza dengan Incidence Rate
DOI:
https://doi.org/10.14421/fourier.2023.121.41-50Keywords:
KriteriaBendixson-Dulac, Maple, Model Vaksinasi Transmisi Virus Influenza dengan Incidence Rate, Nilai Parameter.Abstract
Model Vaksinasi Transmisi Virus Influenza dengan Incidence Rate ini merupakan model vaksinasi [1] yang ditambahkan asumsi laju tingkat jenuh (Incidence Rate) . Analisis terhadap eksistensi solusi periodik menunjukkan bahwa tidak memuat orbit periodik pada himpunan positif kelas yang divaksin. Simulasi diberikan dengan nilai parameter yang berbeda terhadap nilai laju individu yang divaksin terinfeksi dan laju kontak yang berbeda. Kemudian simulasi dan potret phase yang diperoleh diinterpretasikan dan dibandingkan dengan model sebelumnya. Hasil menunjukkan bahwa dengan adanya laju tingkat jenuh (Incidence Rate), kejadian individu terinfeksi baru sedikit daripada model sebelumnya.
Downloads
References
D. J. D. Earn, J. Dushoff, and S. A. Levin, “Ecology and evolution of the flu,” Trends Ecol. Evol., vol. 17, no. 7, pp. 334–340, 2002.
R. A. Lamb, “Genes and Proteins of the Influenza Viruses,” Influ. Viruses, pp. 1–87, 1989, doi: 10.1007/978-1-4613-0811-9_1.
R.G. Webster and B.R. Murphy, “Orthomyxoviruses, in Fields Virology, 3rd ed., B. N. Fields D.M.Knipe, P. M. Howley,et.al.,eds,” Lippincott-Raven Publ., pp. 1397–1445, 1996.
S. F. Regan and C. Fowler, “Influenza. Past, present, and future.,” J. Gerontol. Nurs., vol. 28, no. 11, pp. 30–37; quiz 52, 2002.
I. Grotto et al., “Influenza vaccine efficacy in young, healthy adults,” Clin. Infect. Dis., vol. 26, no. 4, pp. 913–917, 1998, doi: 10.1086/513934.
V. Andreasen, J. Lin, and S. A. Levin, “The dynamics of cocirculating influenza strains conferring partial cross-immunity.,” J. Math. Biol., vol. 35, no. 7, pp. 825–842, 1997, doi: 10.1007/s002850050079.
H. W. Hethcote, “The Mathematics of Infectious,” Society, vol. 42, no. 4, pp. 599–653, 2000.
S. M. Moghadas, “Modelling the effect of imperfect vaccines on disease epidemiology,” Discret. Contin. Dyn. Syst. - Ser. B, vol. 4, no. 4, pp. 999–1012, 2004, doi: 10.3934/dcdsb.2004.4.999.
M. E. Alexander, C. Bowman, S. M. Moghadas, R. Summers, A. B. Gumel, and B. M. Sahai, “A vaccination model for transmission dynamics of influenza,” SIAM J. Appl. Dyn. Syst., vol. 3, no. 4, pp. 503–524, 2004, doi: 10.1137/030600370.
G. J. Olsder, Mathematical System Theory. Delftse Uitgevers Maatschappij, CW Delft, Netherlands, 1994.
O. Osuna and G. Villaseñor, “On the Dulac functions,” Qual. Theory Dyn. Syst., vol. 10, no. 1, pp. 43–49, 2011, doi: 10.1007/s12346-011-0036-y.
S. Balamuralitharan and M. Radha, “Bifurcation analysis in SIR epidemic model with treatment,” J. Phys. Conf. Ser., vol. 1000, no. 1, 2018, doi: 10.1088/1742-6596/1000/1/012169.
A. D. Anggoro, “Pemodelan SIRPS untuk Penyakit Influenza dengan Vaksinasi pada Populsi Konstan,” Universitas Negeri Semarang, 2013.
W. Hahn, Stability of Motion. Springer-Verlag, 1967.
L. Perko, Differential Equations and Dynamical Systems, Third Edit. Springer, 2009.
S. Balamuralitharan and M. Radha, “Bifurcation analysis in SIR epidemic model with treatment,” J. Phys. Conf. Ser., vol. 1000, no. 1, 2018, doi: 10.1088/1742-6596/1000/1/012169.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Irma Suryani
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
