Stability Analysis of Mathematical Model of Spread of Covid19 SEIRS Type with Constant Birth Rate
Abstract
The Covid19 case dated 11 November 2021 recorded that the human population died from Covid19 (143,595 people) with confirmed cases (4,249,323 cases) and active cases (9,537 cases). Based on these data, it can be concluded that COVID-19 is an acute and deadly disease. In addition to deaths, due to Covid-19, namely the increase in divorce cases, decreased income in the economy and tourism. In this study, the author made a mathematical modeling of Covid19 type as an effort to prevent the spread of Covid19. In the modeling there are human populations susceptible to Covid19 , human populations have been vaccinated , human populations have not been vaccinated , human populations are exposed , human populations are infected with Covid19 , and human populations recovered from Covid19 . The research objectives are 1) to build a mathematical model of Covid19, 2) to determine the fixed point and basic reproduction numbers, and 3) to analyze the stability of the fixed point. This type of research includes applied science research. The research procedure is 1) observing real phenomena, 2) searching literature, 3) determining variables, parameters, and assumptions in mathematical modeling, 4) building a mathematical model of Covid19, 5) analyzing the Covid19 mathematical model in the form of fixed points, basic reproduction numbers, and fixed point stability. The results of the analysis 1) the mathematical model type has a fixed point without disease and an endemic fixed point, 2) a fixed point without disease is stable for the condition , and the endemic fixed point is stable for the condition .
Downloads
References
Abdy, M., Side, S., Annas, S., Nur, W., & Sanusi, W. (2021). An SIR epidemic model for Covid-19 spread with fuzzy parameter: the case of Indonesia. Advances in Difference Equations, 2021(1). https://doi.org/10.1186/s13662-021-03263-6.
Afwan, M. I. (2021). Mathematical modeling of the spread of Covid-19 disease using the SIRSe model. 4(2), 34–40.
Alrabaiah, H., Arfan, M., Shah, K., Mahariq, I., & Ullah, A. (2021). A comparative study of spreading of novel corona virus disease by ussing fractional order modified SEIR model. Alexandria Engineering Journal, 60(1), 573–585. https://doi.org/10.1016/j.aej.2020.09.036.
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 & Fractals, 139, 110072. https://doi.org/10.1016/j.chaos.2020.110072.
Apriliani, V., Jaharuddin, & Sianturi, P. (2016). Mathematical model of tuberculosis spread within two groups of infected population. Applied Mathematical Sciences, 10(41–44), 2131–2140. https://doi.org/10.12988/ams.2016.63130.
Hanum, F., Nugrahani, E. H., & Susanti, S. (2015). Utilization of renewable natural resources in the economic lease model. Journal of Mathematics and Its Applications, 14(2), 57. https://doi.org/10.29244/jmap.14.2.57-69.
Ministry of Health of the Republic of Indonesia. (2021). Current situation of developments (Covid-19). Ministry of Health, September.
Resmawan, R., Sianturi, P., & Nugrahani, E. H. (2017). The analysis of SEIRS-SEI epidemic models on malaria with regard to human recovery rate. Aceh International Journal of Science and Technology, 6(3), 132–140. https://doi.org/10.13170/aijst.6.3.9303.
Rifandy, M., Rahmawati, & Side, S. (2021). Mathematical modelling for event occurrence rainbow secondary. Journal of Physics: Conference Series, 1752(1). https://doi.org/10.1088/1742-6596/1752/1/012006.
Sari, S. P., & Arfi, E. (2021). Dynamic Analysis of the SIR Model in the Case of the Spread of Corona Virus Disease-19 (Covid-19). Indonesian Journal of Applied Mathematics, 1(2). https://doi.org/10.35472/indojam.v1i2.354.
Side, S. (2020). Analysis and Simulation of SIRI Model for Dengue Fever Transmission. Indian Journal of Science and Technology, 13(3), 340–351. https://doi.org/10.17485/ijst/2020/v13i03/147852.
Teguh, R., Sahay, A. S., & Adji, F. F. (2020). Modeling the Spread of Covid-19 Infection in Kalimantan, 2020. Journal of Information Technology: A Journal of Science and Application in Informatics Engineering, 14(2). https://doi.org/10.47111/jti.v14i2.1229.
Zhou, T., Liu, Q., Yang, Z., Liao, J., Yang, K., Bai, W., Lu, X., & Zhang, W. (2020). Preliminary prediction of the basic reproduction number of the Wuhan novel coronavirus 2019-nCoV. Journal of Evidence-Based Medicine, 13(1). https://doi.org/10.1111/jebm.12376.
