On the dynamics of Kirschner tumor-immune model

Document Type : Research and Reference

Authors

1 Faculty of Science for girls, Department of Mathematics, Al-Azhar University, Egypt.

2 Faculty of Science, Department of Mathematics, Menoufia University, Egypt..

3 Faculty 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.

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