Analysis Approximate with Using Sumudu Adomian Decomposition Method for Solving SEIVR Epidemic Model
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Abstract
Whenever a mathematical model is suggested to classing COVID-19. The population must be divided into several groups and our model has five groups namely S(t), E(t), I(t), V(t) and R(t) which represent susceptible, exposed, inflected, vaccinated and recovered individuals respectively. This model is a continuous dynamical system where the derivative is in fractional form. An analysis solution evaluates the positivity of the functions S(t), E(t), I(t), V(t) and R(t) as solutions of the system. The uniformity of the solutions of the system under consideration is also proved. And finding the equilibrium points. To get acceptable results one needs the solutions. Some of the solutions are points called equilibrium points and the other are functions. and studying their stability fractional differential system orders are checked locally and globally. The basic reproduction number is used to prove the stability of all equilibrium points as well as the method of the nature of the eigenvalues of the Jacobian at each equilibrium point. And then studied the local bifurcation to the asymptotically stable and stable equilibrium points. And evaluated approximately. These solutions must satisfy the nature of the problem under consideration for example under certain conditions some of the equilibrium points are stable. Also, the approximate solution must give results close to the real situation. All these demands are shown in this paper. Approximate and Numerical simulation is given through a tables and graphs which shows the efficiency of the method, using the MATLAP to all the figures.
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Allman, E.S. and Rhodes, J.A., 2004. Mathematical models in biology: An introduction, Thesis of Cambridge University, England.
Aslam, M. and Alkhaldi, A.H., 2015. A novel method of audio steganography using advanced encryption standard. Nonlinear Engineering, 4(3), pp. 155-159. https://doi.org/10.1515/nleng-2015-0018.
Assessment M.E., 2005. Ecosystems and human well-being: Our human planet-summary for decision-makers. https://wedocs.unep.org/20.500.11822/28979.
Al-Yasiri, H.A., 2004. A new protocol to design cellular systems with variable spreading factors. Journal of Engineering, 10(1), pp.1-12. https://doi.org/10.31026/j.eng.2004.01.01.
Al-Azaiza N and Al-Azzawi S.N., 2023. Using differential transform method for solving COVID-19 model. In 2023 Second International Conference on Advanced Computer Applications (ACA) Feb 27 (pp. 200-204). IEEE. https://doi.org/10.1109/ACA57612.2023.10346954.
AL-Azzawi S.N., Shihab F.A. and Al-Sayyid M. M. 2017. Solution of modified Kuznetsov model with mixed therapy. Global J Pure Appl Math.;13(9):6269-88.
Binuyo A. O., Odejide S. A. and Aregbesola Y.A., 2014. Numerical study of a SEIVR epidemic model among Infants with vaccination and temporary immune protection. Computing J. of Math.; 3(151), P. 2. http://dx.doi.org/10.4172/2168-9679.1000151.
Frölich, M. and Vazquez‐Alvarez, R., 2009. HIV/AIDS knowledge and behavior have information campaigns reduced HIV infection? The case of Kenya. African Development Review, 21(1), pp.86-146. https://doi.org/10.1111/j.1467-8268.2009.00205.x.
Gao, D.P., Huang, N.J., Kang, S.M. and Zhang, C., 2018. Global stability analysis of an SVEIR epidemic model with general incidence rate. Boundary Value Problems, 2018(1), p.42. https://doi.org/10.1186/s13661-018-0961-7.
Ge, F., Zhang, D., Wu, L. and Mu, H., 2020. Predicting psychological state among Chinese undergraduate students in the COVID-19 epidemic: a longitudinal study using a machine learning. Neuropsychiatric disease and treatment, pp.2111-2118. https://doi.org/10.2147/NDT.S262004.
Ghadeer, E.T. and Mohammed, M.A., 2022. Applying a suitable approximate-simulation technique of an epidemic model with random parameters. International Journal of Nonlinear Analysis and Applications, 13(2), pp.963-970. https://doi.org/10.22075/ijnaa.2022.6398.
Ghosh, J.K., Biswas, S.K., Sarkar, S. and Ghosh, U., 2022. Mathematical modelling of COVID-19: A case study of Italy. Mathematics and Computers in Simulation, 194, pp.1-18. https://doi.org/10.1016/j.matcom.2021.11.008.
Heffernan J.M., Smith R.J. and Wahl L.M., 2005. Perspectives on the basic reproductive ratio. Journal of the Royal Society Interface, 2(4), pp.281-293. https://doi.org/10.1098%2Frsif.2005.0042.
Heffernan, J.M., Smith, R.J. and Wahl, L.M., 2006. Perspectives on the basic reproductive ratio. Journal of the Royal Society Interface, 2(4), pp.281-293. https://doi.org/10.1098%2Frsif.2005.0042.
Hu, X., Hu, Z., Xu, T., Zhang, K., Lu, H.H., Zhao, J., Boerwinkle, E., Jin, L. and Xiong, M., 2024. Equilibrium points and their stability of COVID-19 ithe US. Scientific Reports, 14(1), p.1628. https://doi.org/10.1038/s41598-024-51729-w.
Ibraheem, R.G. and Hummady, L.Z., 2023. Powell-eyring fluid peristaltic transfer in an asymmetric channel and a porous medium under the influence of a rotation and an inclined magnetic field. Iraqi Journal of Science, pp. 6431-6444.
James W., 2021. The Basic Reproduction number, fields-CQAM thematic program on integrative modelling of EID, fields institute, Thesis of University of New Brunswick, Canada.
Kadhim, M.O. and Hummady, L.Z., 2024. Effect of the magnetic field and rotation on peristaltic flow of a Bingham fluid in asymmetric channel with porous medium. Iraqi Journal of Science, 65(3), P.1578.
Kapur, J.N., 1985. Mathematical models in biology and medicine. Affiliated East-West Press.15. OCLC Number / Unique Identifier:14251237.
Liu, X. and Yang, L., 2012. Stability analysis of an SEIQV epidemic model with saturated incidence rate. Nonlinear analysis: real world applications, 13(6), pp.2671-2679. https://doi.org/10.1016/j.nonrwa.2012.03.010.
Marsden J.E., Sirovich L., Golubitsky M., Advisors G. boss P. Holmes, Barkley D., Dellnitz M. and Newton P., 2022. Differential equations and dynamical systems. Third edition. Spring, New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo, ISBN. 0-387-95116-4 (alk. paper).
Mohammed, A.A. and Hummady, L.Z., 2023. Influence of heat transform and rotation of sutterby fluid in an asymmetric channel. Iraqi Journal of Science, pp.5766-5777. http://dx.doi.org/10.24996/ijs.2023.64.11.24.
Nadim, S.S. and Chattopadhyay, J., 2020. Occurrence of backward bifurcation and prediction of disease transmission with imperfect lockdown: A case study on COVID-19. Chaos, Solitons & Fractals, 140, p.110163. https://doi.org/10.1016/j.chaos.2020.110163.
Naji R. K. and Hasan K. A., 2013. Stability analysis and bifurcation of discrete prey –predator model with holing type III , International J. of Math. Sci. & Eng. Apples', vol. 7, pp. 1-12. https://doi.org/10.1080/17513758.2019.1638976.
Naji, R.K., 2012. Global stability and persistence of three species food web involving omnivory. Iraqi Journal of Science, 53(4), pp.866-876. https://doi.org/aa01060eb6c1538d.pdf.
Pašic, M.E.R.V.A.N., Zubrinic, D.A.R.K.O. and Zupanovic, V.E.S.N.A., 2011. Fractal properties of solutions of differential equations. Classification and Application of Fractals, ed. William, LH,(Nova Science Publishers), pp.1-62.
Shadabfar, M., Mahsuli, M., Khoojine, A.S. and Hosseini, V.R., 2021. Time-variant reliability-based prediction of COVID-19 spread using extended SEIVR model and Monte Carlo sampling. Results in Physics, 26, p.104364. https://doi.org/10.1016/j.rinp.2021.104364.
Shakya, S. and Lamichhane, S., 2016. Secured crypto stegano data hiding using least significant bit substitution and encryption. Journal of Advanced College of Engineering and Management, 2, pp.105-112. https://https://doi.org/10.3126/jacem.v2i0.16103.
Smale, S. and Hirsch, M.W., 1974. Differential equations, dynamical systems, and linear algebra (Vol. 60). New York: Academic. A Subsidiary of Harcourr Brace Jovanovich, Publishers.
Van den Driessche, P. and Watmough, J., 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences, 180(1-2), pp.29-48.
Yaro, A.S., 2004. Surface treatment effects on the corrosion of reinforced steel in concrete exposed to dry condition. Journal of Engineering, 10(1), pp. 25-35. https://https://doi.org/10.31026/j.eng.2004.01.03.
Zahraa K. A. and Saad N. Al_Azzawi, 2022. Modifying and studying COVID-19 models via caputo sense. University of Baghdad in Partial Fulfilment of the Requirements for the Degree of Master in Applied Mathematics, Thesis of Univercity of Baghdad, Iraq.
Zhang, J., Jia, J. and Song, X., 2014. Analysis of an SEIR epidemic model with saturated incidence and saturated treatment function. The Scientific World Journal, 2014(1), p.910421. https://doi.org/10.1155/2014/910421.