Fighting Cancer with Mathematics and Viruses

Abstract

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments.

Multiscale modelling of cancer response to oncolytic viral therapy

“…In this study we consider a mathematical modelling and computational approach to help us improve our understanding of the physical barriers that limit virus spread. The use of mathematical models to understand the temporal and spatio-temporal dynamics of viruses (including oncolytic viruses) has seen great developments over the last three decades [7,8,9,10,11,12,13]. While the majority of these models focused on the temporal dynamics of oncolytic viruses (mainly due to the availability of temporal data) [14,15,16,17,18,19,20,21,22,23], more recent advances in tumour imaging generated data on the spatial spread of tumours and viruses, which then led to the development of different mathematical models investigating the spatial spread of these viruses [21,23,24,25,26,27].…”

Backward Hopf bifurcation in a mathematical model for oncolytic virotherapy with the infection delay and innate immune effects

“…However, this model did not include the free virus population, and it may not give a complete the dynamic picture of viral therapy with innate immune response. There also are some other mathematical models that describe the dynamics of oncolytic viral therapy [20,24].…”

“…The viral oncolytic process has five stages, attachment, penetration, replication, assembly, and release [18], and each stage is preprogrammed and tightly regulated in time and space [25]. There are several articles which give a detailed description about the five stages of viral infection, for example, the reader is referred to review article [21], [24] and [39] for more details. The following paragraph is cited from [24]: "For a productive infection, one or more virus particles must enter the host cell.…”

Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment

“…Oncolytic virus therapy is a strategy that utilizes viral infection to kill cancer cells, but not normal cells, with the potential of enhancing T-cell recruitment to the tumor and increasing their access to cancer cells. Several computational models have examined the conditions of success for this type of therapeutic in silico [122]. Walker et al developed an agent-based model of pancreatic tumors to study the synergy between chimeric antigen receptor (CAR) T-cell therapy and oncolytic virus therapy [123].…”