Mathematical model studying the effect of vaccination rate on the spreading of respiratory system virus

Jaafar, Mohanad N.; Mohammed, Areej Salah; Huisen, Reem Waleed

doi:10.47974/JIM-1581

Open Access Research Article

Mathematical model studying the effect of vaccination rate on the spreading of respiratory system virus

^*Mohanad N. JaafarCorresponding authormuhanned.n.j@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BagdadBaghdad, IraqView full profile → , Areej Salah Mohammedareej.s.m@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BagdadBaghdad, IraqView full profile → , Reem Waleed Huisenreem.w.h@ihcoedu.uobaghdad.edu.iqDepartment of MathematicsCollege of Education for Pure Science (Ibn Al-Haitham)University of BagdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1563–1569Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1581XML

Published Online:: 01 Nov 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1581
Pages:: 1563–1569

Abstract

This research try to study how vaccination rate and vaccine efficiency can affect the infection by respiratory system viruses using dynamical system. Depending on epidemiological state of the study community we divided it into four group : S (healthy),V (who get vaccine), I (who get infection) and Q (who attended to health quarantine). By solving all the equations of system we can found that the system has two equilibrium point. On the other hand the system was locally analyzed. And the numerical analysis of the system showed that rapid increase in infection rate when we have low vaccination rate and decrease in infection rate when increase vaccination rate and also explain how vaccine efficiency effect on development and spreading of disease.

Keywords

Dynamical system Covid-19 Respiratory system viruses Vaccine rate Vaccine efficiency SVIQ model

Subject Classifications

00A7103C10

References

[1] Peter, J. O.; Qureshi, S.; Yusuf, A. and AL-Shomrani, M. : A new mathematical model of COVID-19 using real data from Pakistan. Results in Physics 24 (2021).
[2] Angelia, M.; Neofotistosa ,G.; Mattheakisa, M. and Kaxirasa, E. : Modeling the effect of the vaccination campaign on the Covid-19 pandemic (2021). arXiv:2108.13908v1 [q-bio.PE].
[3] Vishnu Vytla, V.; Ramakuri, S. K.; Peddi, A.; Srinivas, K. and Ragav, N. N. : Mathematical Models for Predicting Covid-19 Pandemic. Journal of Physics (2021). doi:10.1088/1742-6596/1797/1/012009.
[4] Ahmed, I.; Modu, G. U.; Yusuf, A.; Kumam, P. and Yusuf, I. : A mathematical model of Coronavirus Disease (COVID-19) containing asymptomatic and symptomatic classes. Results in Physics. 21. 103776 (2021).
[5] Al-Hilfi RA, Majeed YY, Ali SS, Shanan B, Banoosh AK, Muften AB.COVID-19 Situation Report Nos. 5. Ministry of Health. Directorate General of Public Health, Field Epidemiology Training Programe. Baghdad (May 18, 2020).
[6] Omran, S.; Habib, O. S.; Jassim, H. A.; Alshihaby, W. Aand Mohammed, M. : The Dynamics of COVID-19 Epidemic in Basrah-Second Report. The Medical Journal of Basrah University. 38(1) (2020).
[7] Mahmoud A. Ibrahim, M. A. and Al-Najafi, A. : Modeling, Control, and Prediction of the Spread of COVID-19 Using Compartmental, Logistic, and Gauss Models: A Case Study in Iraq and Egypt.
MDPI., 8, 1400 (2020); doi:10.3390/pr8111400.
[8] Yavuz, M.; Coşar, F. Ö.; Günay, F. and Özdemir, F. N. : A New Mathematical Modeling of the COVID-19 Pandemic Including the Vaccination Campaign. Open Journal of Modelling and Simulation. 9 : 299-321 (2021).
[9] Hirscs M. W., and Smale, S., Differential Equation, Dynamical System, and Linear Algebra. Academic Press, Inc., New York. 169-170 (1974).
[10] Lial M. L., precalculus et. al., Adison-wesly, New York (2001).
[11] May R. M., Stability and Complexity in model ecosystem, Princeton, New Jersey : Princeton University press (1973).
[12] Negi, S. S.; Sharma, N. and Rana, S. P. A SEIAR mathematical model to analyse the effect of COVID-19 pandemic over the crowded and dense populatedregions. Journal of Interdisciplinary Mathematics. 27:2063-2071 (2022).
[13] Modi, K., Umate L., Makade, K., Dubey, S. R. and Agarwal, A. Simulation based study for estimation of COVID-19 spread in India using SEIR model. Journal of Interdisciplinary Mathematics. 24 : 245-258 (2021).
[14] Radhi, A. : Early stage prediction of COVID-19 Using machine learning model. Wasit Journal of Computer and Mathematics Sciences, 2(1), 46-61 (2023).‏

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