Optimum Control of SEIR Model on COVID-19 Spread with Delay Time and Vaccination Effect in South Sulawesi Province
The increasing number of cases and the development of new variants of the Covid-19 virus globally including the territory of Indonesia, especially in the province of South Sulawesi are increasingly worrying and need to be prevented. Therefore, this study aims to develop a SEIR model on the spread of Covid-19 with vaccination control, optimal control analysis, stability analysis and numerical simulation of the SEIR model on the spread of Covid-19 in South Sulawesi. This study uses the SEIR epidemic model to predict the spread of Covid-19 in South Sulawesi Province with parameters such as birth rate, cure rate, mortality rate, interaction rate and vaccination. The SEIR model was chosen because it is one of the basic methods in the epidemiological model. The method used to build the model is a time delay model by considering the vaccination factor as a model parameter, model analysis using the next generation matrix method to determine the basic reproduction number and stability of the Covid-19 distribution model in South Sulawesi. Numerical model simulation using secondary data on the number of Covid-19 cases in South Sulawesi starting in 2021 which was obtained from the South Sulawesi Provincial Health Office. The results obtained are model analysis provides evidence of the existence of optimal control in the model. Based on the results obtained, it can also be seen that vaccination greatly influences the spread of Covid-19 in South Sulawesi, so that awareness is needed for the people of South Sulawesi to follow the government's recommendation to vaccinate to prevent or reduce the rate of transmission of Covid-19 in South Sulawesi.
pandemic covid-19 spread in indonesia. Chaos, Solitons & Fractals, 139:110072.
Annas, S., Side, S., Padjalangi, A., Syahrul, N. F., and Arradiah, L. (2021). Using sapr model for solution of social poverty problem
due to covid-19 in makassar city. Jurnal Varian, 5(1):47–58.
Apenteng, O. O. and Ismail, N. A. (2017). Modelling the spread of hiv and aids epidemic trends in male and female populations.
World Journal of Modelling and Simulation, 13(3):183–192.
Demirci, E., Unal, A., et al. (2011). A fractional order seir model with density dependent death rate. Hacettepe Journal of Mathematics and Statistics, 40(2):287–295.
Diekmann, O., Heesterbeek, J., and Roberts, M. G. (2010). The construction of next-generation matrices for compartmental epidemic
models. Journal of the royal society interface, 7(47):873–885.
Dontwi, I., Obeng-Denteh, W., Andam, E., and Obiri-Apraku, L. (2014). A mathematical model to predict the prevalence and
transmission dynamics of tuberculosis in amansie west district, ghana. British Journal of Mathematics & Computer Science,
Egonmwan, A. and Okuonghae, D. (2019). Analysis of a mathematical model for tuberculosis with diagnosis. Journal of Applied
Mathematics and Computing, 59(1):129–162.
Kementerian Kesehatan RI (2018). Pedoman Pencegahan dan Pengendalian Coronavirus Disease (Coviid 19).
Rangkuti, Y. M., Side, S., and Noorani, M. S. M. (2014). Numerical analytic solution of sir model of dengue fever disease in
south sulawesi using homotopy perturbation method and variational iteration method. Journal of Mathematical and Fundamental
Rundle, C. W., Presley, C. L., Militello, M., Barber, C., Powell, D. L., Jacob, S. E., Atwater, A. R., Watsky, K. L., Yu, J., and
Dunnick, C. A. (2020). Hand hygiene during covid-19: recommendations from the american contact dermatitis society. Journal
of the American Academy of Dermatology, 83(6):1730–1737.
Rusliza, A. and Budin, H. (2012). Stability analysis of mutualism population model with time delay. Int J Math Comput Phys Electr
Comput Eng, 6(2):151–155.
Side, S. (2015). A susceptible-infected-recovered model and simulation for transmission of tuberculosis. Advanced Science Letters,
Side, S., Hulinggi, P. K. M., Syam, H. K., Irfan, M., and Taufik, A. G. P. (2021). The effectiveness of vaccination against the spread
of covid-19 with seir mathematical modeling in gowa district. Jurnal Varian, 5(1):17–28.
Side, S., Mulbar, U., Sidjara, S., and Sanusi, W. (2017). A seir model for transmission of tuberculosis. In AIP conference proceedings,
volume 1830, page 020004. AIP Publishing LLC.
Spencer, J. A., Shutt, D. P., Moser, S. K., Clegg, H., Wearing, H. J., Mukundan, H., and Manore, C. A. (2020). Epidemiological parameter review and comparative dynamics of influenza, respiratory syncytial virus, rhinovirus, human coronavirus, and adenovirus.
Syafruddin, S. and Noorani, M. S. M. (2013). Lyapunov function of sir and seir model for transmission of dengue fever disease. Int.
J. Simul. Process. Model., 8(2/3):177–184.
Tanto, T. and Handayani, H. (2022). Literature review: Determinan kepatuhan terhadap protokol kesehatan covid-19 di indonesia.
Jurnal Ilmu Kesehatan Masyarakat, 11(02):127–136.
Wahyuni, W. and Kurniawidjaja, M. (2022). Kepatuhan perilaku cuci tangan tenaga kesehatan pada masa pandemi covid-19: A
systematic review. PREPOTIF: Jurnal Kesehatan Masyarakat, 6(1):268–277.
Waziri, A. S., Massawe, E. S., and Makinde, O. D. (2012). Mathematical modelling of hiv/aids dynamics with treatment and vertical
transmission. Appl. Math, 2(3):77–89.
WHO (2021). HeaIth and Care Worker Deaths during Covid-19. https://www.who.int/news/item/20-10-2021-heaIth-and-careworker-deaths-during-Covid-19.
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