Analisis Sensitivitas Model SEIRV pada Penyebaran Penyakit Covid-19 di Indonesia
Sensitivity Analysis of the SEIRV Model on the Spread of Covid-19 Disease in Indonesia
DOI:
https://doi.org/10.26594/jmpm.v8i1.3438Keywords:
Covid-19, SEIRV, Vaksinasi, Analisis SensitivitasAbstract
Model SEIRV dibentuk dengan melihat pada perlakuan terhadap orang yang terinfeksi di Indonesia dengan pembagian subpopulasi terinfeksi menjadi tiga: subpopulasi terinfeksi dirawat di rumah sakit, terinfeksi tidak teridentifikasi, dan terinfeksi isolasi mandiri. Model ini dianalisis sifat kestabilan titik tetapnya dan menganalisis parameter mana yang paling peka terhadap perubahan simulasi model. Model ini memiliki titik tetap tanpa penyakit yang stabil asimtotik lokal pada kondisi bilangan reproduksi dasar kurang dari satu dan titik tetap endemik stabil asimtotik lokal pada kondisi bilangan reproduksi dasar lebih dari satu. Hasil analisis sensitivitas menunjukkan ada tiga parameter yang memiliki pengaruh besar terhadap model: laju transmisi penyakit dari subpopulasi rentan menjadi terekspos, laju kesembuhan subpopulasi terinfeksi tidak teridentifikasi, dan laju vaksinasi. Hal yang dapat dilakukan ketika menginginkan kondisi dimana tidak ada lagi wabah Covid-19 adalah menekan laju penyebaran Covid-19, meningkatkan laju kesembuhan subpopulasi terinfeksi tidak teridentifikasi, dan meningkatkan laju pemberian vaksinasi terhadap populasi.
References
Adewole MO, Onifade AA, Abdullah FA, Kasali F, Ismail AIM. (2021). Modeling the dynamics of COVID-19 in Nigeria. Int J Appl Comput Math. 2021;7(3):67. doi: 10.1007/s40819-021-01014-5. Epub 2021 Apr 19. PMID: 33898652; PMCID: PMC8053898.
Annas, S., Isbar Pratama, M., Rifandi, M., Sanusi, W., & Side, S. (2020). Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia. Chaos, Solitons and Fractals, 139, 110072. https://doi.org/10.1016/j.chaos.2020.110072
Castillo-Chaves, C., Song, B. (2004). Dynamical models of tuberculosis and their applications. Mathematical Biosciences and Engineering, 1(2):361-404. DOI:10.3934/mbe.2004.1.361.
Chitnis, N, Hyman, JM, Cushing, JM. (2008). Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull. Math. Biol. 70, 1272–1296. ( 10.1007/s11538-008-9299-0)
Diagne, M. L., Rwezaura, H., Techoumi, S. Y., Tchuenche, J. M. (2021). A mathematical model of COVID-19 with vaccination and treatment. Comput Math Methods Med. DOI:10.1155/2021/1250129.
Driessche, P., Watmough, J. (2002). Reproduction number and sub-threahold endemic equilibria for compartemental models of disease transmission. Mathematical Biosciences, 180: 29-48. DOI:10.1016/s0025-5560(02)00108-6.
Edelstein-Keshet, L. (2005). Mathematical Models in Biology. New York (Unites States of Amerika): Random House.
Ivorra, B., Ferrandez, M. R., Vela-Perez, M., and Ramos. (2020). Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the indetected infections. The Case of China. MOMAT Research Group. DOI:10.1016/j.cnsns.2020.105303.
Ndondo, A. M., Kasereka, S. K., Bisuta, S. F., Kyamakya, K., Doungmo, E. F. G., & Ngoie, R. B. M. (2021). Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo. Results in Physics, 24, 104096.
Nuha, A. R., Achmad, N. (2021). Analisis Model Matematika Penyebaran COVID-19 Dengan Intervensi Vaksinasi dan Pengobatan,” Jurnal Matematika UNAND, Vol. 10, No.3. E-ISSN:2721-9410.
Okabe, Y., Shudo, A., (2020). A mathematical model of epidemics- a tutorial for students. Mathematics, 8(7). DOI:10.3390/math8071174.
Sasmita, N. R., Ikhwan, M., Suyanti, S., Chongsuvivatwong, V. (2020). Optimal control on a mathematical model to pattern the progression of coronavirus disease 2019 (COVID-19) in Indonesia. Glob Heal Res Policy. DOI:10.1186/s41256-020-00163-2.
Shakhany, M. Q., Salimifard, K. (2021). Predicting the dynamical behavior of COVID-19 epidemic and the effect of control strategies. ELSEVIER. DOI:10.1016/j.chaos.2021.110823.
Sugiyanto, S., Abrori, M. (2020). A Mathematical Model of the Covid-19 Cases in Indonesia (Under and Without Lockdown Enforcement). Biology, Medicine, & Natural Product Chemistry. 9. 15-19. 10.14421/biomedich.2020.91.15-19.
Susilo, A., Rumende, C. M., Pitoyo, C. W., Santoso, W. D., Yulianti, M., Sinto, R., Singh, G., Nainggolan, L., Nelwan, E. J., Khie, L., Widhani, A., Wijaya, E., Wicaksana, B., Maksum, M., Annisa, F., Jasirwan, O. M., Yunihastuti, E., Penanganan, T., New, I., … Cipto, R. (2020). Coronavirus disease 2019. Tinjauan Literatur Terkini Coronavirus Disease 2019?: Review of Current Literatures. 7(1), 45–67.
Tang, B., Wang, X., Li, Q., Bragazzi, N. L., Tang, S., Xiao, Y., & Wu, J. (2019). Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions. Journal of Clinical Medicine. 1–13. DOI:10.3390/jcm9020462.
Yang, B., Yu, Z., Cai, Y. (2022). The impact of vaccination on the spread of COVID-19: Studying by mathematical model. ELSEVIER. DOI:10.1016/j.physa.2021.126717.
Yavuz, M., Cosar, F. O., Gunay, F., Ozdemir, F. N. (2021). A New mathematical modeling of the COVID-19 pandemic including the vaccination campaign. Scientific Research: An Academic Publisher. DOI:10.4236/ojmsi.2021.93020.
Yuliana. (2020). Corona virus diseases (Covid-19); Sebuah tinjauan literatur. WELLNESS AND HELATHY MAGAZINE, Vol. 2 p. 187 – 192. DOI:10.15408/ppsj.v2i1.15456.
Wachira, C. M., Lawi, G. O., Omondi, L. O. (2022). Sensitivity and optimal control analysis of an extended SEIR COVID-19 mathematical model. J. Math. DOI:10.1155/2022/1475507.
Wali, M., Arsyad, S., Huang, J. (2022). Stability analysis of an extended SEIR covid-19 fractional model with vaccination efficiency. Hindawi, Vol. 2022. DOI:10.1155/2022/3754051.
WHO. (2021). Coronavirus disease (Covid-19). [Online]. Available: https://www.who.int/emergencies/diseases/novel-coronavirus-2019. [Accessed: 18-Aug-2021].
Downloads
Published
Issue
Section
License
Copyright (c) 2023 JMPM: Jurnal Matematika dan Pendidikan Matematika
This work is licensed under a Creative Commons Attribution 4.0 International License.
The formal legal aspect of access to any information and articles contained in this journal website refers to the Creative Commons Attribution 4.0 International (CC BY 4.0) license terms.