Kendali Optimal Penyebaran Penyakit Influenza H1N1 Tiga Strain dengan Vaksinasi dan Pengobatan
Kata Kunci:
Influenza H1N1, Kontrol Optimal, Prinsip Minimum Pontryagin,, Runge Kutta Forward Backward SweepAbstrak
H1N1 influenza is a respiratory tract infection with common symptoms, namely fever, headache, coughing, and sore throat. H1N1 influenza has several strains known to infect humans, birds, and pigs. Some efforts to overcome the infection of the H1N1 influenza virus are vaccination and treatment. This Research discusses the optimal control in the form of vaccination and treatment applied to the model H1N1 Influenza disease spread. The method used to solve this optimal control problem is the Pontryagin Minimum Principle followed by searching numerical solutions using the Runge-Kutta Forward-Backward Sweep method. Numerical simulations were conducted to compare the spread of H1N1 Influenza before and after optimal control efforts were given. Based on the simulation result, it was shown that giving optimal control in the form of vaccination to susceptible individuals and treatment in individuals infected with three strains could reduce the number of individuals infected with H1N1 Influenza disease .
Unduhan
Referensi
R. Casagrandi, L. Bolzoni, S. A. Levin, and V. Andreasen, “The SIRC Model and Influenza A,” Math. Biosci., vol. 200, no. 2, pp. 152–169, 2006.
World Health Organization, “Managing Epidemics - Key Facts about Major Deadly Diseases,” 2018. https://www.who.int/emergencies/diseases/managing-epidemics/en/.
D. Natalia, T. Bakhtiar, and J. Jaharuddin, “Model Pengendalian Influenza H1N1 Dua Strain dengan Vaksinasi dan Pengobatan,” J. Math. Its Appl., vol. 17, pp. 1–16, 2018.
T. Syafriati, “Mengenal Penyakit Influenza Babi,” Lokakarya Nas. Penyakit Zoonosis Bogor, 2014.
World Health Organization, “CDC Protocol of Realtime RTPCR for Influenza A (H1N1),” 2009. https://www.who.int/csr/resources/publications/swineflu/realtimeptpcr/en/.
I. A. Baba and E. Hincal, “A Model for Influenza with Vaccination and Awareness,” Chaos, Solitons & Fractals, vol. 106, pp. 49–55, 2018.
D. S. Naidu, Optimal Control System. Pocatello, Idaho, USA: CRC Press, 2003.
R. L. Burden and J. D. Faires, Numerical Analysis, Ninth Edit. Richard Stratton, 2010.
Supriyanto, “Runge-Kutta Orde Empat,” Dep. Fis. Univ. Indones., 2006.
S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models. Chapman & Hall/CRC, Taylor & Francis Group, 2007.
