On the dynamics of Kirschner tumor-immune model
Zaghrout, A., El-Sheikh, M., El-Namoury, A., El-Ashry, A. (2017). On the dynamics of Kirschner tumor-immune model. EKB Journal Management System, 38(1), 53-62. doi: 10.21608/djs.2017.139426
A. Zaghrout; M.M.A. El-Sheikh; A.R. El-Namoury; A. El-Ashry. "On the dynamics of Kirschner tumor-immune model". EKB Journal Management System, 38, 1, 2017, 53-62. doi: 10.21608/djs.2017.139426
Zaghrout, A., El-Sheikh, M., El-Namoury, A., El-Ashry, A. (2017). 'On the dynamics of Kirschner tumor-immune model', EKB Journal Management System, 38(1), pp. 53-62. doi: 10.21608/djs.2017.139426
Zaghrout, A., El-Sheikh, M., El-Namoury, A., El-Ashry, A. On the dynamics of Kirschner tumor-immune model. EKB Journal Management System, 2017; 38(1): 53-62. doi: 10.21608/djs.2017.139426

On the dynamics of Kirschner tumor-immune model

Delta Journal of Science
Article 7, Volume 38, Issue 1, June 2017, Page 53-62  XML PDF (1.49 MB)
Document Type: Research and Reference
DOI: 10.21608/djs.2017.139426
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Authors
A. Zaghrout1; M.M.A. El-Sheikh2; A.R. El-Namoury3; A. El-Ashry3
1Faculty of Science for girls, Department of Mathematics, Al-Azhar University, Egypt.
2Faculty of Science, Department of Mathematics, Menoufia University, Egypt..
3Faculty of Science, Department of Mathematics, Tanta University, Egypt..
Abstract
A tumor-immune model of Kirschner type is considered. The boundedness of solutions are discussed. Criteria
for existence and the stability of equiliria are established. Using similar technique to that we used before in the literature,
we study the existence of Hopf-Andronov-Poincaré bifurcation. Using Liapunov function sufficient conditions are
guaranteed the existence of a unique periodic asymptotically stable solution for the system are established. Numerical
simulations are given to illustrate the results.
Keywords
Kirschner model; Equilibrium points; Global stability; Hopf bifurcation
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