Laboratory of Analysis Modeling and Simulation (LAMS), Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan II University, Mohammedia, BP 7955, Sidi Othman, Casablanca, Morocco.
Laboratory of Modeling Applied to Economy and Management (LMAEGE), Faculty of Law, Economics and Social Sciences Ain Sebaa Casablanca, Hassan II University, Casablanca, Morocco.
Comput Math Methods Med. 2019 Sep 30;2019:1732815. doi: 10.1155/2019/1732815. eCollection 2019.
Despite advanced discoveries in cancerology, conventional treatments by surgery, chemotherapy, or radiotherapy remain ineffective in some situations. Oncolytic virotherapy, i.e., the involvement of replicative viruses targeting specific tumor cells, opens new perspectives for better management of this disease. Certain viruses naturally have a preferential tropism for the tumor cells; others are genetically modifiable to present such properties, as the lytic cycle virus, which is a process that represents a vital role in oncolytic virotherapy. In the present paper, we present a mathematical model for the dynamics of oncolytic virotherapy that incorporates multiple time delays representing the multiple time periods of a lytic cycle. We compute the basic reproductive ratio , and we show that there exist a disease-free equilibrium point (DFE) and an endemic equilibrium point (DEE). By formulating suitable Lyapunov function, we prove that the disease-free equilibrium (DFE) is globally asymptotically stable if < 1 and unstable otherwise. We also demonstrate that under additional conditions, the endemic equilibrium is stable. Also, a Hopf bifurcation analysis of our dynamic system is used to understand how solutions and their stability change as system parameters change in the case of a positive delay. To illustrate the effectiveness of our theoretical results, we give numerical simulations for several scenarios.
尽管在癌症学方面取得了先进的发现，但在某些情况下，传统的手术、化疗或放疗治疗仍然无效。溶瘤病毒疗法，即针对特定肿瘤细胞的复制病毒的介入，为更好地治疗这种疾病开辟了新的前景。某些病毒天然对肿瘤细胞具有优先趋向性；其他病毒可以通过基因修饰来呈现这种特性，如溶细胞病毒，这是溶瘤病毒疗法中至关重要的作用过程。在本文中，我们提出了一个包含多个时间延迟的溶瘤病毒动力学数学模型，这些延迟代表了溶细胞周期的多个时间段。我们计算了基本再生数 ，并表明存在无病平衡点（DFE）和地方病平衡点（DEE）。通过构建合适的李雅普诺夫函数，我们证明了当 < 1 时，无病平衡点（DFE）是全局渐近稳定的，否则是不稳定的。我们还表明，在附加条件下，地方病平衡点是稳定的。此外，我们还对我们的动态系统进行了 Hopf 分支分析，以了解在正延迟的情况下，当系统参数变化时，解及其稳定性如何变化。为了说明我们理论结果的有效性，我们针对几种情况给出了数值模拟。
