Journal of Applied Probability

A branching process for virus survival

J. Theodore Cox and Rinaldo B. Schinazi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Quasispecies theory predicts that there is a critical mutation probability above which a viral population will go extinct. Above this threshold the virus loses the ability to replicate the best-adapted genotype, leading to a population composed of low replicating mutants that is eventually doomed. We propose a new branching model that shows that this is not necessarily so. That is, a population composed of ever changing mutants may survive.

Article information

J. Appl. Probab., Volume 49, Number 3 (2012), 888-894.

First available in Project Euclid: 6 September 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 92D25: Population dynamics (general)

Quasispecies branching process random environment evolution


Cox, J. Theodore; Schinazi, Rinaldo B. A branching process for virus survival. J. Appl. Probab. 49 (2012), no. 3, 888--894. doi:10.1239/jap/1346955342.

Export citation


  • Eigen, M. (1971). Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58, 465–523.
  • Eigen, M. (2002). Error catastrophe and antiviral strategy. Proc. Nat. Acad. Sci. USA 99, 13374–13376.
  • Eigen, M. and Schuster, P. (1977). The hypercycle. A principle of self-organization. Part A: emergence of the hypercycle. Naturwissenschaften 64, 541–565.
  • Elena, S. F. and Moya, A. (1999). Rate of deleterious mutation and the distribution of its effects on fitness in vesicular stomatitis virus. J. Evol. Biol. 12, 1078–1088.
  • Harris, T. E. (1989). The Theory of Branching Processes. Dover Publications, New York.
  • Karlin, S. and Taylor, H. M. (1975). A First Course in Stochastic Processes, 2nd edn. Academic Press, New York.
  • Manrubia, S. C., Domingo, E. and Lázaro, E. (2010). Pathways to extinction: beyond the error threshold. Phil. Trans. R. Soc. London B 365, 1943–1952.
  • Nowak, M. A. and May, R. M. (2000). Virus Dynamics. Oxford University Press.
  • Sanjuan, R., Moya, A. and Elena, S. F. (2004). The distribution of fitness effects caused by single-nucleotide substitutions in an RNA virus. Proc. Nat. Acad. Sci. USA 101, 8396–8401.
  • Schinazi, R. B. and Schweinsberg, J. (2008). Spatial and non spatial stochastic models for immune response. Markov Process. Relat. Fields 14, 255–276.
  • Smith, W. L. and Wilkinson, W. E. (1969). On branching processes in random environments. Ann. Math. Statist. 40, 814–827.
  • Vignuzzi, M. \et (2006). Quasispecies diversity determines pathogenesis through cooperative interactions in a viral population. Nature 439, 344–348 \endharvreferences