RNA viruses replicate with a very high error rate and give rise to heterogeneous, highly plastic populations able to adapt very rapidly to changing environments. Viral diseases are thus difficult to control because of the appearance of drug-resistant mutants, and it becomes essential to seek mechanisms able to force the extinction of the quasispecies before adaptation emerges. An alternative to the use of conventional drugs consists in increasing the replication error rate through the use of mutagens. Here, we report about persistent infections of lymphocytic choriomeningitis virus treated with fluorouracil, where a progressive debilitation of infectivity leading to eventual extinction occurs. The transition to extinction is accompanied by the production of large amounts of RNA, indicating that the replicative ability of the quasispecies is not strongly impaired by the mutagen. By means of experimental and theoretical approaches, we propose that a fraction of the RNA molecules synthesized can behave as a defective subpopulation able to drive the viable class extinct. Our results lead to the identification of two extinction pathways, one at high amounts of mutagen, where the quasispecies completely loses its ability to infect and replicate, and a second one, at lower amounts of mutagen, where replication continues while the infective class gets extinct because of the action of defectors. The results bear on a potential application of increased mutagenesis as an antiviral strategy in that low doses of a mutagenic agent may suffice to drive persistent virus to extinction.

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively different regimes are observed, corresponding to intermittent and regular behavior. In the boundary between them, the mean value of the relevant variable is time independent, and the exponent of the stationary distribution equals $-2$. The addition of diffusion to the system modifies in a nontrivial way the profile of the stationary distribution. Numerical and analytical results are presented.

Significance: Susceptible–infected–removed (SIR) models and their extensions are widely used to describe the dynamics of infection spreading. Certain generic features of epidemics are well-illustrated by these models, which can be remarkably good at reproducing empirical data through suitably chosen parameters. However, this does not assure a good job anticipating the forthcoming stages of the process. To illustrate this point, we accurately describe the propagation of COVID-19 in Spain using one such model and show that predictions for its subsequent evolution are disparate, even contradictory. The future of ongoing epidemics is so sensitive to parameter values that predictions are only meaningful within a narrow time window and in probabilistic terms, much as what we are used to in weather forecasts.

A stochastic model that incorporates the essential mechanisms supposed to govern city formation is numerically analyzed. The model generates intermittent spatiotemporal structures and predicts a power-law population distribution whose exponent is in excellent agreement with the universal exponent observed in real human demography. Preliminary results of cluster analysis of the model also coincide with actual data. We thus suggest that urban development at large scales could be driven by intermittency processes.