Department of Mathematics and Statistics, McGill University, Montreal, Canada.
Department of Physiology, McGill University, Montreal, Canada.
Math Med Biol. 2020 Feb 28;37(1):117-151. doi: 10.1093/imammb/dqz008.
We develop and analyse a mathematical model of tumour-immune interaction that explicitly incorporates heterogeneity in tumour cell cycle duration by using a distributed delay differential equation. We derive a necessary and sufficient condition for local stability of the cancer-free equilibrium in which the amount of tumour-immune interaction completely characterizes disease progression. Consistent with the immunoediting hypothesis, we show that decreasing tumour-immune interaction leads to tumour expansion. Finally, by simulating the mathematical model, we show that the strength of tumour-immune interaction determines the long-term success or failure of viral therapy.
我们开发并分析了一个肿瘤免疫相互作用的数学模型，该模型通过使用分布式时滞微分方程明确纳入了肿瘤细胞周期持续时间的异质性。我们推导出了无癌平衡点局部稳定性的充要条件，其中肿瘤免疫相互作用的程度完全刻画了疾病的进展。与免疫编辑假说一致，我们表明减少肿瘤免疫相互作用会导致肿瘤的扩张。最后，通过模拟数学模型，我们表明肿瘤免疫相互作用的强度决定了病毒治疗的长期成败。
