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Updated: Aug 10, 2026
Paramyxoviruses for Tumor-targeted Immunomodulation: Design and Evaluation Ex Vivo
Published on: January 7, 2019
Mathematical modeling of tumor therapy with oncolytic viruses: regimes with complete tumor elimination within the
Artem S Novozhilov1, Faina S Berezovskaya, Eugene V Koonin
1National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA. novozhil@ncbi.nlm.nih.gov
Background:
Oncolytic viruses that specifically target tumor cells are promising anti-cancer therapeutic agents. The interaction between an oncolytic virus and tumor cells is amenable to mathematical modeling using adaptations of techniques employed previously for modeling other types of virus-cell interaction.
Results:
A complete parametric analysis of dynamic regimes of a conceptual model of anti-tumor virus therapy is presented. The role and limitations of mass-action kinetics are discussed. A functional response, which is a function of the ratio of uninfected to infected tumor cells, is proposed to describe the spread of the virus infection in the tumor. One of the main mathematical features of ratio-dependent models is that the origin is a complicated equilibrium point whose characteristics determine the main properties of the model. It is shown that, in a certain area of parameter values, the trajectories of the model form a family of homoclinics to the origin (so-called elliptic sector). Biologically, this means that both infected and uninfected tumor cells can be eliminated with time, and complete recovery is possible as a result of the virus therapy within the framework of deterministic models.
Conclusion:
Our model, in contrast to the previously published models of oncolytic virus-tumor interaction, exhibits all possible outcomes of oncolytic virus infection, i.e., no effect on the tumor, stabilization or reduction of the tumor load, and complete elimination of the tumor. The parameter values that result in tumor elimination, which is, obviously, the desired outcome, are compatible with some of the available experimental data.
Reviewers:
This article was reviewed by Mikhail Blagosklonny, David Krakauer, Erik Van Nimwegen, and Ned Wingreen.
Open Peer Review:
Reviewed by Mikhail Blagosklonny, David Krakauer, Erik Van Nimwegen, and Ned Wingreen. For the full reviews, please go to the Reviewers' comments section.
Insights
Mathematical modeling of oncolytic virus therapy shows that specific parameter values can lead to complete tumor elimination. This study explores virus-tumor dynamics, offering insights into effective anti-cancer strategies.
Area of Science:
- Mathematical Biology
- Virology
- Oncology
Background:
- Oncolytic viruses are promising anti-cancer agents targeting tumor cells.
- Virus-tumor cell interactions can be mathematically modeled.
- Previous models have limitations in predicting all therapeutic outcomes.
Purpose of the Study:
- To present a parametric analysis of a conceptual model for anti-tumor virus therapy.
- To investigate the dynamics of oncolytic virus infection within tumors.
- To identify conditions for complete tumor elimination.
Main Methods:
- Developed a conceptual mathematical model for oncolytic virus-tumor interaction.
- Performed a complete parametric analysis of the model's dynamic regimes.
- Utilized ratio-dependent functional responses to describe virus spread.
Main Results:
- The model demonstrates that both infected and uninfected tumor cells can be eliminated.
- Specific parameter values lead to trajectories forming homoclinics to the origin, indicating recovery.
- The model accounts for all possible outcomes: no effect, stabilization, reduction, or complete elimination of the tumor.
Conclusions:
- The proposed model exhibits all potential outcomes of oncolytic virus therapy, unlike previous models.
- Tumor elimination is achievable under specific parameter conditions.
- These parameter values are consistent with available experimental data.
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