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Modeling oncolytic virus therapy with distributed delay and non-local diffusion

Zizi Wang

TL;DR

A basic framework for an oncolytic virus dynamics model with a general growth rate and the existence and uniqueness of solutions to the model, as well as the existence of a global attractor are introduced.

Abstract

In the field of modeling the dynamics of oncolytic viruses, researchers often face the challenge of using specialized mathematical terms to explain uncertain biological phenomena. This paper introduces a basic framework for an oncolytic virus dynamics model with a general growth rate $\mathcal{F}$ and a general nonlinear incidence term $\mathcal{G}$. The construction and derivation of the model explain in detail the generation process and practical significance of the distributed time delays and non-local infection terms. The paper provides the existence and uniqueness of solutions to the model, as well as the existence of a global attractor. Furthermore, through two auxiliary linear partial differential equations, the threshold parameters $σ_1$ are determined for sustained tumor growth and $λ_1$ for successful viral invasion of tumor cells to analyze the global dynamic behavior of the model. Finally, we illustrate and analyze our abstract theoretical results through a specific example.

Modeling oncolytic virus therapy with distributed delay and non-local diffusion

TL;DR

A basic framework for an oncolytic virus dynamics model with a general growth rate and the existence and uniqueness of solutions to the model, as well as the existence of a global attractor are introduced.

Abstract

In the field of modeling the dynamics of oncolytic viruses, researchers often face the challenge of using specialized mathematical terms to explain uncertain biological phenomena. This paper introduces a basic framework for an oncolytic virus dynamics model with a general growth rate and a general nonlinear incidence term . The construction and derivation of the model explain in detail the generation process and practical significance of the distributed time delays and non-local infection terms. The paper provides the existence and uniqueness of solutions to the model, as well as the existence of a global attractor. Furthermore, through two auxiliary linear partial differential equations, the threshold parameters are determined for sustained tumor growth and for successful viral invasion of tumor cells to analyze the global dynamic behavior of the model. Finally, we illustrate and analyze our abstract theoretical results through a specific example.
Paper Structure (6 sections, 11 theorems, 74 equations, 1 figure, 2 tables)

This paper contains 6 sections, 11 theorems, 74 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Model development
  3. Well posed and global compact attractor
  4. Global extinction and persistence
  5. A simple example of the correlation between logistics growth and mass action infection.
  6. Conclusion

Key Result

Theorem 3.1

For any function $\phi\in\mathbb{C}_{\tau}$, the system 2020c-eq8-2020c-maineq3 admits a unique non-continuable solution $u$ defined on $\bar{\Omega} \times[-\tau, t_{\infty})$, where $t_{\infty}=$$t_{\infty}(\phi)$ with $0<t_\infty \leq \infty$. Furthermore, for $(t, x) \in[-\tau, t_\infty) \times

Figures (1)

  • Figure 1: This figure shows the quadratic curves for all fixed $A<0$ and $C<0$. We use dashed lines to represent the case of $B<0$, dotted lines to represent the case of $B>0$, and solid lines to represent the quadratic curves with $B=0$.

Theorems & Definitions (21)

  • Remark 1.1
  • Remark 1.2
  • Theorem 3.1
  • proof
  • Lemma 3.1
  • Theorem 3.2
  • proof
  • Theorem 4.1
  • proof
  • Lemma 4.1
  • ...and 11 more