Research Article
BibTex RIS Cite

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

Year 2024, Volume: 14 Issue: 1, 390 - 402, 01.03.2024

Cihan Taş Rukiye Kara

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

Abstract

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.

Keywords

Epidemic mathematical model Equilibrium points Stability analysis Numerical simulation Dynamical systems

Supporting Institution

Mimar Sinan Güzel Sanatlar Üniversitesi

Project Number

2021/17

Thanks

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

References

  • 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.

Year 2024, Volume: 14 Issue: 1, 390 - 402, 01.03.2024

Cihan Taş Rukiye Kara

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

Abstract

Project Number

2021/17

References

  • 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.
There are 33 citations in total.

Details

Primary Language English
Subjects Ordinary Differential Equations, Difference Equations and Dynamical Systems
Journal Section Matematik / Mathematics
Authors

Cihan Taş 0000-0002-2670-9427

Rukiye Kara 0000-0002-7588-8337

Project Number 2021/17
Early Pub Date February 20, 2024
Publication Date March 1, 2024
Submission Date October 17, 2023
Acceptance Date December 26, 2023
Published in Issue Year 2024 Volume: 14 Issue: 1

Cite

APA Taş, C., & Kara, R. (2024). Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey. Journal of the Institute of Science and Technology, 14(1), 390-402. https://doi.org/10.21597/jist.1377342
AMA Taş C, Kara R. Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey. J. Inst. Sci. and Tech. March 2024;14(1):390-402. doi:10.21597/jist.1377342
Chicago Taş, Cihan, and Rukiye Kara. “Modeling the Impact of Vaccination on Epidemic Disease Variants With Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey”. Journal of the Institute of Science and Technology 14, no. 1 (March 2024): 390-402. https://doi.org/10.21597/jist.1377342.
EndNote Taş C, Kara R (March 1, 2024) Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey. Journal of the Institute of Science and Technology 14 1 390–402.
IEEE C. Taş and R. Kara, “Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey”, J. Inst. Sci. and Tech., vol. 14, no. 1, pp. 390–402, 2024, doi: 10.21597/jist.1377342.
ISNAD Taş, Cihan - Kara, Rukiye. “Modeling the Impact of Vaccination on Epidemic Disease Variants With Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey”. Journal of the Institute of Science and Technology 14/1 (March 2024), 390-402. https://doi.org/10.21597/jist.1377342.
JAMA Taş C, Kara R. Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey. J. Inst. Sci. and Tech. 2024;14:390–402.
MLA Taş, Cihan and Rukiye Kara. “Modeling the Impact of Vaccination on Epidemic Disease Variants With Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey”. Journal of the Institute of Science and Technology, vol. 14, no. 1, 2024, pp. 390-02, doi:10.21597/jist.1377342.
Vancouver Taş C, Kara R. Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey. J. Inst. Sci. and Tech. 2024;14(1):390-402.
 Download Cover Image