Virotherapy is a novel treatment for cancer, which may be delivered as a single agent or in combination with other therapies. Research studies indicated that the combination of viral therapy and radiation therapy has synergistic antitumor effects in in vitro and in vivo. In this paper, we proposed two models in the form of partial differential equations to investigate the spatiotemporal dynamics of tumor cells under virotherapy and radiovirotherapy. We first presented a virotherapy model and solved it numerically for different values of the parameters related to the oncolytic virus, which is administered continuously. The results showed that virotherapy alone cannot eradicate cancer, and thus, we extended the model to include the effect of radiotherapy in combination with virotherapy. Numerical investigations were carried out for three modes of radiation delivery which are constant, decaying, and periodic. The numerical results showed that radiovirotherapy leads to complete eradication of the tumor provided that the delivery of radiation is constant. Moreover, there is an optimal timing for administering radiation, as well as an ideal dose that improves the results of the treatment. The virotherapy in our model is given continuously over a certain period of time, and bolus treatment (where virotherapy is given in cycles) could be considered and compared with our results.

中文翻译：

---

模拟溶瘤病毒的时空动力学和放射疗法作为癌症的治疗方法。

病毒疗法是一种新颖的癌症治疗方法，可以单药或与其他疗法联合使用。调查研究表明，病毒疗法和放射疗法的组合具有在协同抗肿瘤效果的体外和体内。在本文中，我们以偏微分方程的形式提出了两个模型，以研究病毒治疗和放射病毒治疗下肿瘤细胞的时空动态。我们首先提出了一种病毒治疗模型，并针对与溶瘤病毒相关的参数的不同值进行了数值求解，该模型是连续给药的。结果表明，仅病毒疗法不能根除癌症，因此，我们扩展了模型，将放射疗法与病毒疗法相结合的作用包括在内。对辐射传递的三种模式进行了数值研究，它们是恒定的，衰减的和周期性的。数值结果表明，只要辐射的传递是恒定的，放射线病毒疗法就可以完全根除肿瘤。此外，放射治疗的最佳时机以及改善治疗效果的理想剂量。我们模型中的病毒疗法在一定时期内连续进行，可以考虑推注治疗（周期内进行病毒疗法）并将其与我们的结果进行比较。