Stability Analysis of Fixed Points Mathematical Model of Dengue Hemorrhagic Fever Disease Type SEIR
Keywords:
mathematical model, fixed point, fixed point stability analysis.
Abstract
Dengue is one of the infectious diseases transmitted to humans by the bite of Aedes aegypti or Aedes albopictus mosquitoes. Dengue virus infections include dengue fever, dengue hemorrhagic fever and Dengue Shock Syndrome (DSS). The dengue virus has four types of serotypes: DEN_1, DEN_2, DEN_3, DEN_4. In the model, will be studied the dynamics of the spread of dengue hemorrhagic disease type SEIR. From the model then fixed point will be determined, then analyzed the stability of each fixed point by considering the basic reproduction number (R_0 ). The results showed that for fixed point without disease the condition would be stable when R_0<1, while the fixed point of endemic would be stable for condition whenR_0>1.
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References
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van den Driessche, P. 2017. Reproduction numbers of infectious disease models. Infectious Disease Modelling, 2(3): 288–303.
Edelstein-Keshet, L. 1988. Mathematical models in biology. Siam.
Ginanjar, G. 2008. Demam Berdarah. PT Mizan Publika.
Naikteas Bano, E., Sianturi, P. & Jaharuddin 2017. Model Matematika Penyebaran Penyakit Demam Berdarah Dengue Tipe SEIR Iinfeksi Ganda. Repository Institut Pertanian Bogor. Tersedia di https://repository.ipb.ac.id.
Tirtha Chakraborty 2008. Dengue Fever and Other Hemorrhagic Viruses. New York: Chelsea House.
Tu, P.N. 2012. Dynamical systems: an introduction with applications in economics and biology. Springer Science & Business Media.
WHO 2016. Dengue: Immunization, Vaccines and Biologicals. Media Center WHO [Internet]. http://www.who.int/immunization/diseases/dengue
Published
2018-07-31
How to Cite
Bano, E. (2018). Stability Analysis of Fixed Points Mathematical Model of Dengue Hemorrhagic Fever Disease Type SEIR. Jurnal Saintek Lahan Kering, 1(1), 9-10. https://doi.org/https://doi.org/10.32938/slk.v1i1.421
Section
Review article
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