Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

TL;DR

This paper analyzes a simplified mathematical model of tumor cell dynamics, revealing how mutation rates influence tumor growth and healthy cell dominance, with implications for mutagenic therapies.

Contribution

It introduces a quasispecies differential equation model for tumor dynamics, identifying bifurcations and transient behaviors relevant for therapy strategies.

Findings

Identification of a transcritical bifurcation at critical mutation rates

Healthy cell dominance can be achieved with slight increases in mutation rates

Transient times to reach low tumor populations are short near the bifurcation point

Abstract

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least qualitatively, also allowing us to make predictions. Here we analyze a simplified quasispecies mathematical model given by differential equations describing the time behaviour of tumor cells populations with different levels of genomic instability. We find the equilibrium points, also characterizing their stability and bifurcations focusing on replication and mutation rates. We identify a transcritical bifurcation at increasing mutation rates of the tumor cells population. Such a bifurcation involves an scenario with dominance of healthy cells and impairment of tumor populations. Finally, we characterize the transient times for this scenario, showing that a slight increase beyond the critical mutation rate may be enough to have a fast response towards the desired state (i.e., low tumor populations) during directed mutagenic therapies.