T-periodic dynamics in a 3D delayed quasispecies model

Area of Science:

• Mathematical Biology
• Theoretical Ecology
• Evolutionary Dynamics

Background:

• The quasispecies model describes the evolution of large populations of self-replicating entities.
• Understanding periodic dynamics and error-threshold phenomena is crucial for evolutionary biology and disease modeling.

Purpose of the Study:

• To investigate periodic dynamics and error-threshold behavior in a delayed quasispecies model.
• To establish conditions for the existence and absence of T-periodic solutions.
• To link quasispecies dynamics to cancer-related phenomena.

Main Methods:

• Formulation of the model using delay differential equations with time-periodic replication rates.
• Application of topological degree arguments to analyze periodic solutions.
• Analysis of systems with varying mutation probabilities and fitness functions.

Main Results:

• Periodic replication rates and mutation probabilities between 0 and 1 can lead to non-trivial positive periodic orbits, indicating oscillatory genotype distributions in fluctuating environments.
• Unidirectional mutations coupled with dominant master sequence fitness prevent positive periodic orbits.
• Time delays induce non-monotonic decay of the master sequence, revealing the error-threshold phenomenon.

Conclusions:

• Fluctuating environments can sustain oscillatory genotype distributions in quasispecies models.
• The error-threshold phenomenon, influenced by time delays, is relevant to cancer-related quasispecies dynamics.
• The study provides new conditions for the existence and absence of periodic solutions in delayed quasispecies models.