%0 Journal Article
%T The growth dynamics of tumor subject to both immune surveillance and external therapy intervention
%A YuanZhi Shao
%A WeiRong Zhong
%A FengHua Wang
%A ZhenHui He
%A ZhongJun Xia
%J Chinese Science Bulletin
%@ 1861-9541
%D 2007
%I 
%R 10.1007/s11434-007-0234-9
%X Considering the growth of tumor cells modeled by an enzyme dynamic process under an immune surveillance, we studied in anti-tumor immunotherapy the single-variable growth dynamics of tumor cells subject to a multiplicative noise and an external therapy intervention simultaneously. The law of tumor growth of the above anti-tumor immunotherapy model was revealed through numerical simulations to the relevant stochastic dynamic differential equation. Two simulative parameters of therapy, i.e., therapy intensity and therapy duty-cycle, were introduced to characterize a treatment process similar to a tumor clinic therapy. There exists a critical therapy boundary which, in an exponent-decaying form, divides the parameter region of therapy into an invalid and a valid treatment zone, respectively. A greater critical therapy duty-cycle is necessary to achieve a valid treatment for a lower therapy intensity while the critical therapy intensity decreases accordingly with an enhancing immunity. A primary clinic observation of the patients with the typical non-hodgekin¡¯s lymphoma was carried out, and there appears a basic agreement between clinic observations and dynamic simulations.
%K logistic model
%K growth dynamics
%K noise
%K immunity
%K tumor
%U http://link.springer.com/article/10.1007/s11434-007-0234-9