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


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.

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  1. Nude mice have non-functioning immune systems.


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The authors received support through an Australian Postgraduate Award (ALJ) and Australian Research Council Discovery Project DP180101512 (PSK and ACFC).

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Correspondence to Adelle C. F. Coster.



Table 3 Parameter values and fit statistics for the optimisation of the individual mouse-specific data in Fig. 2

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Jenner, A.L., Yun, CO., Kim, P.S. et al. Mathematical Modelling of the Interaction Between Cancer Cells and an Oncolytic Virus: Insights into the Effects of Treatment Protocols. Bull Math Biol 80, 1615–1629 (2018).

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  • Oncolytic virus
  • Optimisation
  • Mathematical modelling
  • Ordinary differential equations