A Mathematical Model for Chemotherapy, Immunotherapy and Virotherapy Treatments of Cancer

We extend the model for cancer treatment by adding the modality of virotherapy in addition to chemotherapy and immunotherapy. This dynamical system models three different ways to fight the spread of solid cancer, such as melanoma, glioblastoma, head and neck cancers, and pancreatic cancer, among others, in healthy tissue. It allows for computer experiments of various combinations of the three modalities, which cannot be performed in the laboratory or experimentally. The novelty lies in the addition of virotherapy. The analysis shows that model solutions exist, are bounded and nonnegative on each finite time interval, and are thus biologically and mathematically feasible. A time-stepping algorithm is constructed and implemented, and computer simulations are presented. The simulations show the development of the disease under various treatment options, including a baseline case without treatment, cases for each of the three treatments individually, and some combinations of the three treatments. These simulations show that combinations of the treatments are more effective; however, the model does not take into account any possible incompatibilities in the joint application of the three modalities that may exist in practice. Once validated by field data and appropriately updated, the model may be used to design treatment schedules of combinations of the three modalities for improved outcomes, which is the main contribution of this work.