Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, People's Republic of China.
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA.
J Biol Dyn. 2019 Dec;13(1):733-748. doi: 10.1080/17513758.2019.1667443. Epub 2019 Sep 18.
In this paper, we consider a system of delay differential equations that models the oncolytic virotherapy on solid tumours with the delay of viral infection in the presence of the innate immune response. We conduct qualitative and numerical analysis, and provide possible medical implications for our results. The system has four equilibrium solutions. Fixed point analysis indicates that increasing the burst size and infection rate of the viruses has positive contribution to the therapy. However, increasing the immune killing infection rate, the immune stimulation rate, or the immune killing virus rate may lead the treatment failed. The viral infection time delay induces backward Hopf bifurcations, which means that the therapy may fail before time delay increases passing through a Hopf bifurcation. The parameter analysis also shows how saddle-node and Hopf bifurcations occur as viral burst size and other parameters vary, which yields further insights into the dynamics of the virotherapy.
在本文中，我们考虑了一个时滞微分方程组模型，该模型描述了在固有免疫反应存在的情况下，具有病毒感染时滞的溶瘤病毒治疗实体瘤。我们进行了定性和数值分析，并为我们的结果提供了可能的医学意义。该系统有四个平衡点。定点分析表明，增加病毒的爆发大小和感染率对治疗有积极的贡献。然而，增加免疫杀伤感染率、免疫刺激率或免疫杀伤病毒率可能导致治疗失败。病毒感染时间延迟会引起向后的 Hopf 分支，这意味着在时间延迟通过 Hopf 分支增加之前，治疗可能会失败。参数分析还表明，随着病毒爆发大小和其他参数的变化，鞍结和 Hopf 分支是如何发生的，这进一步深入了解了病毒治疗的动力学。
