Hopf Bifurcation in Differential Equations with Delay for Tumor--Immune System Competition Model Export

@article{citeulike:1771329, abstract = {This paper deals with the qualitative analysis of the solutions to a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a system of differential equations with one delay. It is shown that the dynamics depends crucially on the time delay parameter. By using the time delay as a parameter of bifurcation, the analysis is focused on the Hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state. The obtained results depict the oscillations, given by simulations (see [M. Galach, Int. J. Appl. Math. Comput. Sci., 13 (2003), pp. 395\–406]), which are observed in reality (see [D. Kirschner and J. C. Panetta, J. Math. Biol., 37 (1998), pp. 235\–252]). It is suggested to examine by laboratory experiments how to employ these results for control of tumor growth.}, author = {Yafia, Radouane}, citeulike-article-id = {1771329}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000067000006001693000001&idtype=cvips&gifs=yes}, citeulike-linkout-1 = {http://link.aip.org/link/?SMM/67/1693}, journal = {SIAM Journal on Applied Mathematics}, keywords = {delay, hopf, tumor}, number = {6}, pages = {1693--1703}, posted-at = {2007-10-15 22:03:52}, priority = {2}, publisher = {SIAM}, title = {Hopf Bifurcation in Differential Equations with Delay for Tumor--Immune System Competition Model}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000067000006001693000001&idtype=cvips&gifs=yes}, volume = {67}, year = {2007} }

TY - JOUR ID - citeulike:1771329 L3 - citeulike-article-id:1771329 N2 - This paper deals with the qualitative analysis of the solutions to a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a system of differential equations with one delay. It is shown that the dynamics depends crucially on the time delay parameter. By using the time delay as a parameter of bifurcation, the analysis is focused on the Hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state. The obtained results depict the oscillations, given by simulations (see [M. Galach, Int. J. Appl. Math. Comput. Sci., 13 (2003), pp. 395–406]), which are observed in reality (see [D. Kirschner and J. C. Panetta, J. Math. Biol., 37 (1998), pp. 235–252]). It is suggested to examine by laboratory experiments how to employ these results for control of tumor growth. IS - 6 JF - SIAM Journal on Applied Mathematics EP - 1703 TI - Hopf Bifurcation in Differential Equations with Delay for Tumor--Immune System Competition Model PB - SIAM VL - 67 SP - 1693 KW - delay KW - hopf KW - tumor AU - Yafia, Radouane PY - 2007/// UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000067000006001693000001&idtype=cvips&gifs=yes ER -