Virus Replication as a Phenotypic Version of Polynucleotide Evolution

TL;DR

This paper adapts a branching process model to viral evolution, providing analytical tools and criteria for understanding virus extinction, mutagenesis, and evolutionary stages, with implications for antiviral strategies.

Contribution

It introduces a multivariate branching process model for viral evolution that incorporates beneficial effects and offers analytical criteria for extinction and mutagenesis.

Findings

New criterion for 'no sure extinction'

Generalization of lethal mutagenesis theory for viruses

Quantitative description of evolutionary stages

Abstract

In this paper we revisit and adapt to viral evolution an approach based on the theory of branching process advanced by Demetrius, Schuster and Sigmund ("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46 (1985) 239-262), in their study of polynucleotide evolution. By taking into account beneficial effects we obtain a non-trivial multivariate generalization of their single-type branching process model. Perturbative techniques allows us to obtain analytical asymptotic expressions for the main global parameters of the model which lead to the following rigorous results: (i) a new criterion for "no sure extinction", (ii) a generalization and proof, for this particular class of models, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930-2939), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in in four distinct "stages": extinction threshold, lethal mutagenesis, stationary "equilibrium" and transient. Finally, based on these quantitative results we are able to draw some qualitative conclusions.