Mathematical Modelling of the Interaction Between Cancer Cells and an Oncolytic Virus: Insights into the Effects of Treatment Protocols

Bull Math Biol. 2018 Jun;80(6):1615-1629. doi: 10.1007/s11538-018-0424-4. Epub 2018 Apr 11.


Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system, preventing them from arriving at the tumour site. To improve virus survival and infectivity Kim et al. (Biomaterials 32(9):2314-2326, 2011) modified virus particles with the polymer polyethylene glycol (PEG) and the monoclonal antibody herceptin. Whilst PEG modification appeared to improve plasma retention and initial infectivity, it also increased the virus particle arrival time. We derive a mathematical model that describes the interaction between tumour cells and an oncolytic virus. We tune our model to represent the experimental data by Kim et al. (2011) and obtain optimised parameters. Our model provides a platform from which predictions may be made about the response of cancer growth to other treatment protocols beyond those in the experiments. Through model simulations, we find that the treatment protocol affects the outcome dramatically. We quantify the effects of dosage strategy as a function of tumour cell replication and tumour carrying capacity on the outcome of oncolytic virotherapy as a treatment. The relative significance of the modification of the virus and the crucial role it plays in optimising treatment efficacy are explored.

Keywords: Mathematical modelling; Oncolytic virus; Optimisation; Ordinary differential equations.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adenoviruses, Human / genetics
  • Adenoviruses, Human / physiology
  • Animals
  • Antineoplastic Agents, Immunological / therapeutic use
  • Breast Neoplasms / pathology
  • Breast Neoplasms / therapy
  • Cell Line, Tumor
  • Clinical Protocols
  • Computer Simulation
  • Female
  • Humans
  • Mathematical Concepts
  • Mice
  • Models, Biological*
  • Neoplasms / pathology
  • Neoplasms / therapy*
  • Oncolytic Virotherapy* / statistics & numerical data
  • Oncolytic Viruses / genetics
  • Oncolytic Viruses / physiology*
  • Polyethylene Glycols
  • Trastuzumab / genetics
  • Trastuzumab / therapeutic use
  • Xenograft Model Antitumor Assays


  • Antineoplastic Agents, Immunological
  • Polyethylene Glycols
  • Trastuzumab