Villasana Minaya, Radunskaya Ami
Departamento de Cómputo Científico y Estadística, Universidad Simón Bolivar, Venezuela.
J Math Biol. 2003 Sep;47(3):270-94. doi: 10.1007/s00285-003-0211-0. Epub 2003 May 15.
We present a competition model of tumor growth that includes the immune system response and a cycle-phase-specific drug. The model considers three populations: Immune system, population of tumor cells during interphase and population of tumor during mitosis. Delay differential equations are used to model the system to take into account the phases of the cell cycle. We analyze the stability of the system and prove a theorem based on the argument principle to determine the stability of a fixed point and show that the stability may depend on the delay. We show theoretically and through numerical simulations that periodic solutions may arise through Hopf Bifurcations.
我们提出了一个肿瘤生长的竞争模型，该模型包括免疫系统反应和一种细胞周期阶段特异性药物。该模型考虑了三个群体：免疫系统、间期肿瘤细胞群体和有丝分裂期肿瘤群体。使用延迟微分方程对系统进行建模，以考虑细胞周期的各个阶段。我们分析了系统的稳定性，并基于辐角原理证明了一个定理，以确定不动点的稳定性，并表明稳定性可能取决于延迟。我们通过理论分析和数值模拟表明，周期解可能通过霍普夫分岔出现。
