DYNAMICS OF A SIRV MODEL FOR THE SPREAD OF COVID-19 IN MALUKU PROVINCE
COVID-19 (Coronavirus Disease 2019) is caused by the SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2) coronavirus spreading around the world. In this study, the SIRV model was used, which is an epidemic model carried out by grouping the population into four subpopulations, namely the subpopulation of susceptible individuals who can be infected (Susceptible), the subpopulation of infected individuals (Infected), the subpopulation of individuals who recover from illness (Recovered), and the subpopulation of individuals who have been vaccinated (Vaccination). Based on the dynamic system analysis conducted, two equilibrium points were obtained, namely the disease-free equilibrium point and the endemic equilibrium point. In addition, based on data processing and model simulation results obtained, was obtained so that it can be concluded that the higher the number of vaccinated populations, the lower the level of Covid-19 spread, which means that vaccines can suppress cases of Covid-19 spread in Maluku Province
R. Teguh, A. Sagit, and F. F. Adjic, “PEMODELAN PENYEBARAN INFEKSI COVID-19 DI KALIMANTAN, 2020,” Jurnal Teknologi Informasi , vol. 14, no. 2, pp. 171–178, Aug. 2020.
“Analisis Data Covid-19 Indonesia update per November 30, 2022 [Covid-19 Data Analysis Indonesia update as of November 30, 2022],” Covid-19 Handling Task Force Team, Nov. 2022.
Y. Liu, S. Jian, and J. Gao, “Dynamics analysis and optimal control of SIVR epidemic model with incomplete immunity,” Advances in Continuous and Discrete Models, vol. 2022, no. 1, Dec. 2022, doi: 10.1186/s13662-022-03723-7.
W. O. Kermack and A. G. Mckendrick, “A Contribution to the Mathematical Theory of Epidemics,” 1927.
R. Resmawan, A. R. Nuha, and L. Yahya, “Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina,” Jambura Journal of Mathematics, vol. 3, no. 1, pp. 66–79, Jan. 2021, doi: 10.34312/jjom.v3i1.8699.
S. Annas, Muh. Isbar Pratama, Muh. Rifandi, W. Sanusi, and S. Side, “Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia,” Chaos Solitons Fractals, vol. 139, p. 110072, Oct. 2020, doi: 10.1016/j.chaos.2020.110072.
R. Resmawan, L. Yahya, R. S. Pakaya, H. S. Panigoro, and A. R. Nuha, “Analisis Dinamik Model Penyebaran COVID-19 dengan Vaksinasi,” Jambura Journal of Biomathematics (JJBM), vol. 3, no. 1, Jul. 2022, doi: 10.34312/jjbm.v3i1.13176.
Z. Zhang, “A novel covid-19 mathematical model with fractional derivatives: Singular and nonsingular kernels,” Chaos Solitons Fractals, vol. 139, p. 110060, Oct. 2020, doi: 10.1016/j.chaos.2020.110060.
A. S. Bhadauria, R. Pathak, and M. Chaudhary, “A SIQ mathematical model on COVID-19 investigating the lockdown effect,” Infect Dis Model, vol. 6, pp. 244–257, Jan. 2021, doi: 10.1016/j.idm.2020.12.010.
Y. Li and Q. Zhang, “The balanced implicit method of preserving positivity for the stochastic SIQS epidemic model,” Physica A: Statistical Mechanics and its Applications, vol. 538, p. 122972, Jan. 2020, doi: 10.1016/j.physa.2019.122972.
M. Higazy, “Novel fractional order SIDARTHE mathematical model of COVID-19 pandemic,” Chaos Solitons Fractals, vol. 138, p. 110007, Sep. 2020, doi: 10.1016/j.chaos.2020.110007.
A. M. Ramos, M. R. Ferrández, M. Vela-Pérez, A. B. Kubik, and B. Ivorra, “A simple but complex enough θ -SIR type model to be used with COVID-19 real data. Application to the case of Italy,” Physica D, vol. 421, p. 132839, Jul. 2021, doi: 10.1016/j.physd.2020.132839.
K. S. Nisar, S. Ahmad, A. Ullah, K. Shah, H. Alrabaiah, and M. Arfan, “Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data,” Results Phys, vol. 21, p. 103772, Feb. 2021, doi: 10.1016/j.rinp.2020.103772.
C. M. Batistela, D. P. F. Correa, Á. M. Bueno, and J. R. C. Piqueira, “SIRSi compartmental model for COVID-19 pandemic with immunity loss,” Chaos Solitons Fractals, vol. 142, p. 110388, Jan. 2021, doi: 10.1016/j.chaos.2020.110388.
P. E. Paré, C. L. Beck, and T. Başar, “Modeling, estimation, and analysis of epidemics over networks: An overview,” Annu Rev Control, vol. 50, pp. 345–360, 2020, doi: 10.1016/j.arcontrol.2020.09.003.
C.-C. Zhu and J. Zhu, “Dynamic analysis of a delayed COVID-19 epidemic with home quarantine in temporal-spatial heterogeneous via global exponential attractor method,” Chaos Solitons Fractals, vol. 143, p. 110546, Feb. 2021, doi: 10.1016/j.chaos.2020.110546.
H. Wei, Y. Jiang, X. Song, G. H. Su, and S. Z. Qiu, “Global attractivity and permanence of a SVEIR epidemic model with pulse vaccination and time delay,” J Comput Appl Math, vol. 229, no. 1, pp. 302–312, Jul. 2009, doi: 10.1016/j.cam.2008.10.046.
S. İğret Araz, “Analysis of a Covid-19 model: Optimal control, stability and simulations,” Alexandria Engineering Journal, vol. 60, no. 1, pp. 647–658, Feb. 2021, doi: 10.1016/j.aej.2020.09.058.
A. E. S. Almocera, G. Quiroz, and E. A. Hernandez-Vargas, “Stability analysis in COVID-19 within-host model with immune response,” Commun Nonlinear Sci Numer Simul, vol. 95, p. 105584, Apr. 2021, doi: 10.1016/j.cnsns.2020.105584.
S. Sharma and G. P. Samanta, “Dynamical Behaviour of an HIV/AIDS Epidemic Model,” Differ Equ Dyn Syst, vol. 22, no. 4, pp. 369–395, Oct. 2014, doi: 10.1007/s12591-013-0173-7.
U. Avila-Ponce de León, Á. G. C. Pérez, and E. Avila-Vales, “An SEIARD epidemic model for COVID-19 in Mexico: Mathematical analysis and state-level forecast,” Chaos Solitons Fractals, vol. 140, p. 110165, Nov. 2020, doi: 10.1016/j.chaos.2020.110165.
H. M. Youssef, N. A. Alghamdi, M. A. Ezzat, A. A. El-Bary, and A. M. Shawky, “A new dynamical modeling SEIR with global analysis applied to the real data of spreading COVID-19 in Saudi Arabia,” Mathematical Biosciences and Engineering, vol. 17, no. 6, pp. 7018–7044, 2020, doi: 10.3934/mbe.2020362.
R. Carli, G. Cavone, N. Epicoco, P. Scarabaggio, and M. Dotoli, “Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario,” Annu Rev Control, vol. 50, pp. 373–393, 2020, doi: 10.1016/j.arcontrol.2020.09.005.
Z. A. Leleury, M. E. Rijoly, and F. M. Risamena, “ANALISIS STABILITAS MODEL SIR (SUSCEPTIBLES, INFECTED, RECOVERED) PADA PENYEBARAN VIRUS COVID-19 DI KOTA AMBON,” J. Ris. & Ap. Mat, vol. 06, no. 02, pp. 159–169, 2022.
Statistics Agency of Maluku Province, “ Life Expectancy at Birth in 2022 in Maluku Province.,” 2023.
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