Shock waves in virus fitness evolution

We consider a nonlinear partial differential equation of conservation type to describe the dynamics of transmission with sampling of viral populations observed in aliquots of fixed particle number taken from an evolving clone at periodic intervals of time [I.S. Novella, E.A. Duarte, S.F. Elena, A. Moya, E. Domingo, Exponential increases of RNA virus fitness during large population transmissions, Proc. Natl. Acad. Sci. USA 92 (1995) 5841–5844]. The fast processes of mutation and natural selection that occur within each transmission are incorporated into the conservation equation as parameters. With this, the changes in time behavior of fitness function noticed in experimental data are related to a crossover exhibited by the solutions to this equation in the transient regime for pulse-like initial conditions. As a consequence, the average replication rate of the population is predicted to reach a plateau as a power t-1/2t-1/2.