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Updated: Jun 17, 2025
Ex Vivo Infection of Live Tissue with Oncolytic Viruses
Published on: June 25, 2011
Finding Hopf bifurcation islands and identifying thresholds for success or failure in oncolytic viral therapy
Sana Jahedi1, Lin Wang2, James A Yorke1
1Department of Mathematics, University of Maryland, College Park, MD, United States; Institute for Physical Sciences and Technology, University of Maryland, College Park, MD, United States.
Abstract:
We model interactions between cancer cells and viruses during oncolytic viral therapy. One of our primary goals is to identify parameter regions that yield treatment failure or success. We show that the tumor size under therapy at a particular time is less than the size without therapy. Our analysis demonstrates two thresholds for the horizontal transmission rate: a "failure threshold" below which treatment fails, and a "success threshold" above which infection prevalence reaches 100% and the tumor shrinks to its smallest size. Moreover, we explain how changes in the virulence of the virus alter the success threshold and the minimum tumor size. Our study suggests that the optimal virulence of an oncolytic virus depends on the timescale of virus dynamics. We identify a threshold for the virulence of the virus and show how this threshold depends on the timescale of virus dynamics. Our results suggest that when the timescale of virus dynamics is fast, administering a more virulent virus leads to a greater reduction in the tumor size. Conversely, when the viral timescale is slow, higher virulence can induce oscillations with high amplitude in the tumor size. Furthermore, we introduce the concept of a "Hopf bifurcation Island" in the parameter space, an idea that has applications far beyond the results of this paper and is applicable to many mathematical models. We elucidate what a Hopf bifurcation Island is, and we prove that small Islands can imply very slowly growing oscillatory solutions.
Insights
Oncolytic viral therapy success depends on virus transmission and virulence. Mathematical modeling reveals critical thresholds for treatment failure or success, guiding optimal oncolytic virus selection for cancer therapy.
Area of Science:
- Mathematical Oncology
- Virology
- Systems Biology
Background:
- Oncolytic viral therapy utilizes viruses to selectively infect and destroy cancer cells.
- Understanding the complex interactions between viruses, tumor cells, and the immune system is crucial for optimizing treatment efficacy.
- Mathematical modeling provides a framework to explore these dynamics and predict treatment outcomes.
Purpose of the Study:
- To identify parameter regions predicting treatment failure or success in oncolytic viral therapy.
- To investigate the impact of viral horizontal transmission rate and virulence on tumor size dynamics.
- To introduce and analyze the concept of a 'Hopf bifurcation Island' in the model's parameter space.
Main Methods:
- Development of a mathematical model simulating cancer cell-virus interactions during oncolytic therapy.
- Analysis of model parameters, including horizontal transmission rate and viral virulence.
- Identification of critical thresholds and bifurcations within the parameter space.
Main Results:
- Two thresholds for horizontal transmission rate identified: one for treatment failure and one for treatment success (100% infection prevalence).
- Optimal oncolytic virus virulence is dependent on the timescale of virus dynamics; higher virulence benefits fast viral dynamics but can cause oscillations in slow dynamics.
- A 'Hopf bifurcation Island' concept was introduced, demonstrating potential for slowly growing oscillatory solutions.
Conclusions:
- Treatment outcomes in oncolytic viral therapy are highly sensitive to viral transmission rates and virulence.
- The optimal choice of oncolytic virus virulence is context-dependent, particularly concerning the viral dynamics timescale.
- The 'Hopf bifurcation Island' concept offers a novel perspective for analyzing complex dynamics in mathematical models beyond oncolytic virotherapy.
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