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Updated: Jun 23, 2025

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Oscillations in a Spatial Oncolytic Virus Model

Arwa Abdulla Baabdulla1, Thomas Hillen2

  • 1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada. baabdull@ualberta.ca.

Bulletin of Mathematical Biology
|June 19, 2024
PubMed

Insights

Virotherapy, a promising cancer treatment, uses oncolytic viruses that create spatial patterns. This study identifies conditions for the hollow ring pattern, crucial for tumor eradication, and analyzes virus invasion dynamics.

Area of Science:

  • Mathematical Oncology
  • Virology
  • Biophysics

Background:

  • Virotherapy utilizes oncolytic viruses for targeted cancer treatment.
  • Mathematical models reveal predator-prey dynamics and spatio-temporal patterns in virus-cancer interactions.
  • Hopf bifurcations underlie oscillatory patterns in these models.

Purpose of the Study:

  • To systematically analyze spatial oscillations in virotherapy models.
  • To identify conditions for specific spatio-temporal patterns, particularly the hollow ring pattern for tumor eradication.
  • To determine the minimal speeds of cancer and virus invasion waves.

Main Methods:

  • Bifurcation analysis of a spatially explicit reaction-diffusion model.
  • Numerical simulations in 2-D to observe virus-cancer spatial dynamics.
  • Derivation of traveling wave speeds.

Main Results:

  • Exact conditions for the occurrence of the hollow ring pattern were determined.
  • Minimal invasion speeds for cancer cells and oncolytic viruses were derived.
  • Complex spatial interactions and a novel 'periodic peak splitting' phenomenon were observed in simulations.

Conclusions:

  • The hollow ring pattern is achievable and clinically relevant for tumor eradication via virotherapy.
  • The study provides insights into the dynamics of oncolytic virus spread and interaction with tumors.
  • Further research is needed to explain the observed 'periodic peak splitting' phenomenon.
Keywords:
Hopf bifurcationOncolytic virusReaction diffusion systemSpatial viral distributionTravelling waveTumor control probability

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