ODE models for oncolytic virus dynamics

Replicating oncolytic viruses are able to infect and lyse cancer cells and spread through the tumor, while leaving normal cells largely unharmed. This makes them potentially useful in cancer therapy, and a variety of viruses have shown promising results in clinical trials. Nevertheless, consistent success remains elusive and the correlates of success have been the subject of investigation, both from an experimental and a mathematical point of view. Mathematical modeling of oncolytic virus therapy is often limited by the fact that the predicted dynamics depend strongly on particular mathematical terms in the model, the nature of which remains uncertain. We aim to address this issue in the context of ODE modeling, by formulating a general computational framework that is independent of particular mathematical expressions. By analyzing this framework, we find some new insights into the conditions for successful virus therapy. We find that depending on our assumptions about the virus spread, there can be two distinct types of dynamics. In models of the first type (the “fast spread” models), we predict that the viruses can eliminate the tumor if the viral replication rate is sufficiently high. The second type of models is characterized by a suboptimal spread (the “slow spread” models). For such models, the simulated treatment may fail, even for very high viral replication rates. Our methodology can be used to study the dynamics of many biological systems, and thus has implications beyond the study of virus therapy of cancers.