Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey

Yıl 2024, Cilt: 14 Sayı: 1, 390 - 402, 01.03.2024

Cihan Taş Rukiye Kara

https://doi.org/10.21597/jist.1377342

Öz

The stability analysis of an epidemic model that takes into account the impact of vaccination and hospitalization is investigated in this study. Disease-free and endemic equilibrium points are obtained for the stability analysis. The necessary conditions for analyzing local stability at equilibrium points as well as global stability at the disease-free equilibrium point are also defined. Using data from three different periods corresponding to the emergence of three different variants of the COVID-19 outbreak in Turkey, the numerical simulation with graph fitting for the model is also taken into account. The analysis considers the efficacy of vaccination in restricting the virus's spread.

Anahtar Kelimeler

Epidemic mathematical model, Equilibrium points, Stability analysis, Numerical simulation, Dynamical systems

Destekleyen Kurum

Mimar Sinan Güzel Sanatlar Üniversitesi

Proje Numarası

2021/17

Teşekkür

This work was supported by Scientific Research Projects (BAP) Coordination Unit of Mimar Sinan Fine Arts University. Project No. 2021/17

Kaynakça

• Ahmad, S., Owyed, S., Abdel-Aty, A. H., Mahmoud, E. E., Shah, K., & Alrabaiah, H. (2021). Mathematical analysis of COVID-19 via new mathematical model. Chaos, Solitons & Fractals, 143, 110585.
• Ahmed, N., Elsonbaty, A., Raza, A., Rafiq, M., & Adel, W. (2021a). Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model. Nonlinear Dynamics, 106, 1293-1310.
• Ahmed, I., Modu, G. U., Yusuf, A., Kumam, P., & Yusuf, I. (2021b). A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes. Results in physics, 21, 103776.
• Al-Asuoad, N., Rong, L., Alaswad, S., & Shillor, M. (2016). Mathematical model and simulations of MERS outbreak: Predictions and implications for control measures. Biomath, 5(2), ID-1612141.
• Anderson, R. M., & May, R. M. (1991). Infectious diseases of humans: dynamics and control. Oxford university press.
• Baleanu, D., Shekari, P., Torkzadeh, L., Ranjbar, H., Jajarmi, A., & Nouri, K. (2023). Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study. Chaos, Solitons & Fractals, 166, 112990.
• Biswas, S. K., Ghosh, J. K., Sarkar, S., & Ghosh, U. (2020). COVID-19 pandemic in India: a mathematical model study. Nonlinear dynamics, 102, 537-553.
• Budhwar, N., & Daniel, S. (2017). Stability analysis of a human-mosquito model of malaria with infective immigrants. International Journal of Mathematical and Computational Sciences, 11(2), 85-89.
• Bugalia, S., Bajiya, V. P., Tripathi, J. P., Li, M. T., & Sun, G. Q. (2020). Mathematical modeling of COVID-19 transmission: the roles of intervention strategies and lockdown. Math. Biosci. Eng, 17(5), 5961-5986.
• Castillo-Garsow, C. W., & Castillo-Chavez, C. (2020). A Tour of the Basic Reproductive Number and the Next Generation of Researchers. An Introduction to Undergraduate Research in Computational and Mathematical Biology: From Birdsongs to Viscosities, 87–124.
• Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. (1990). On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of mathematical biology, 28, 365-382.
• Gu, Y., Khan, M., Zarin, R., Khan, A., Yusuf, A., & Humphries, U. W. (2023). Mathematical analysis of a new nonlinear dengue epidemic model via deterministic and fractional approach. Alexandria Engineering Journal, 67, 1-21. Halloran, M. E., Longini Jr, I. M., Nizam, A., & Yang, Y. (2002). Containing bioterrorist smallpox. Science, 298(5597), 1428-1432.
• He, S., Peng, Y., & Sun, K. (2020). SEIR modeling of the COVID-19 and its dynamics. Nonlinear dynamics, 101, 1667-1680.
• Iboi, E., Sharomi, O. O., Ngonghala, C., & Gumel, A. B. (2020). Mathematical modeling and analysis of COVID-19 pandemic in Nigeria. medRxiv. Preprint posted online July, 31.
• Ivorra, B., Ferrández, M. R., Vela-Pérez, M., & Ramos, A. M. (2020). Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China. Communications in nonlinear science and numerical simulation, 88, 105303.
• Keeling, M. J., & Eames, K. T. (2005). Networks and epidemic models. Journal of the royal society interface, 2(4), 295-307.
• Khalaf, S. L., Kadhim, M. S., & Khudair, A. R. (2023). Studying of COVID-19 fractional model: Stability analysis. Partial Differential Equations in Applied Mathematics, 7, 100470.
• Kim, K. S., Ejima, K., Iwanami, S., Fujita, Y., Ohashi, H., Koizumi, Y., ... & Iwami, S. (2021). A quantitative model used to compare within-host SARS-CoV-2, MERS-CoV, and SARS-CoV dynamics provides insights into the pathogenesis and treatment of SARS-CoV-2. PLoS biology, 19(3), e3001128.
• Li, B., & Eskandari, Z. (2023). Dynamical analysis of a discrete-time SIR epidemic model. Journal of the Franklin Institute, 360(12), 7989-8007
• Liu, J., & Zhang, T. (2011). Global stability for a tuberculosis model. Mathematical and Computer Modelling, 54(1-2), 836-845.
• Mahata, A., Paul, S., Mukherjee, S., & Roy, B. (2022). Stability analysis and Hopf bifurcation in fractional order SEIRV epidemic model with a time delay in infected individuals. Partial Differential Equations in Applied Mathematics, 5, 100282.
• Marghitu, D. B. (2001). Mechanical engineer's handbook. Elsevier.
• Meltzer, M. I., Damon, I., LeDuc, J. W., & Millar, J. D. (2001). Modeling potential responses to smallpox as a bioterrorist weapon. Emerging infectious diseases, 7(6), 959.
• Ndaïrou, F., Area, I., Nieto, J. J., & Torres, D. F. (2020). Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan. Chaos, Solitons & Fractals, 135, 109846.
• Newman, M. E., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical review E, 69(2), 026113.
• Ottaviano, S., Sensi, M., & Sottile, S. (2022). Global stability of SAIRS epidemic models. Nonlinear Analysis: Real World Applications, 65, 103501.
• Rahman, S. A., Vaidya, N. K., & Zou, X. (2016). Impact of early treatment programs on HIV epidemics: an immunity-based mathematical model. Mathematical biosciences, 280, 38-49.
• Paul, S., Mahata, A., Mukherjee, S., & Roy, B. (2022). Dynamics of SIQR epidemic model with fractional order derivative. Partial Differential Equations in Applied Mathematics, 5, 100216.
• Samui, P., Mondal, J., & Khajanchi, S. (2020). A mathematical model for COVID-19 transmission dynamics with a case study of India. Chaos, Solitons & Fractals, 140, 110173.
• Singh, H., Srivastava, H. M., Hammouch, Z., & Nisar, K. S. (2021). Numerical simulation and stability analysis for the fractional-order dynamics of COVID-19. Results in physics, 20, 103722.
• Sorensen, S. W., Sansom, S. L., Brooks, J. T., Marks, G., Begier, E. M., Buchacz, K., ... & Kilmarx, P. H. (2012). A mathematical model of comprehensive test-and-treat services and HIV incidence among men who have sex with men in the United States. PloS one, 7(2), e29098.
• Yavuz, M., Coşar, F. Ö., Günay, F., & Özdemir, F. N. (2021). A new mathematical modeling of the COVID-19 pandemic including the vaccination campaign. Open Journal of Modelling and Simulation, 9(3), 299-321.
• Zeb, A., Alzahrani, E., Erturk, V. S., & Zaman, G. (2020). Mathematical model for coronavirus disease 2019 (COVID-19) containing isolation class. BioMed research international, 2020.