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Eigen's quasi-species model describes viruses as ensembles of different mutants of a high fitness "master" genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasi-species. When…

Viral quasispecies can be regarded as a swarm of genetically related mutants or a quasispecies (QS). A common formalism to approach QS is the replicator-mutator equation (RME). However, a problem with the RME is how to quantify the…

Several pathogens use evolvability as a survival strategy against acquired immunity of the host. Despite their high variability in time, some of them exhibit quite low variability within the population at any given time, a somehow…

Viruses present an amazing genetic variability. An ensemble of infecting viruses, also called a viral quasispecies, is a cloud of mutants centered around a specific genotype. The simplest model of evolution, whose equilibrium state is…

RNA viruses comprise vast populations of closely related, but highly genetically diverse, entities known as quasispecies. Understanding the mechanisms by which this extreme diversity is generated and maintained is fundamental when…

Based on a recent model of evolving viruses competing with an adapting immune system [1], we study the conditions under which a viral quasispecies can maximize its growth rate. The range of mutation rates that allows viruses to thrive is…

RNA viruses are a widely used tool to study evolution experimentally. Many standard protocols of virus propagation and competition are done at nominally low multiplicity of infection (m.o.i.), but lead during one passage to two or more…

In this research, we present a generalized quasispecies model in which population growth is governed by an arbitrary nonlinear function incorporating time delays. We begin by demonstrating that, under the constant population constraint, the…

The probability that an advantageous mutant rises to fixation in a viral quasispecies is investigated in the framework of multi-type branching processes. Whether fixation is possible depends on the overall growth rate of the quasispecies…

Multipartite viruses replicate through a puzzling evolutionary strategy. Their genome is segmented into two or more parts, and encapsidated in separate particles that appear to propagate independently. Completing the replication cycle,…

Stochastic phenotype switching has been suggested to play a beneficial role in microbial populations by leading to the division of labour among cells, or ensuring that at least some of the population survives an unexpected change in…

The coexistence of different viral strains (quasispecies) within the same host are nowadays observed for a growing number of viruses, most notably HIV, Marburg and Ebola, but the conditions for the formation and survival of new strains have…

In this paper, we extend a model of host-parasite co-evolution to incorporate the semi-conservative nature of DNA replication for both the host and the parasite. We find that the optimal mutation rate for the semi-conservative and…

Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in…

We study an abstract model for the co-evolution between mutating viruses and the adaptive immune system. In sequence space, these two populations are localized around transiently dominant strains. Delocalization or error thresholds exhibit…

Co-evolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this co-adaptive model, besides the classical error catastrophe for high virus mutation rates, a…

A quasispecies is a set of interrelated genotypes that have reached a situation of equilibrium while evolving according to the usual Darwinian principles of selection and mutation. Quasispecies studies invariably assume that it is possible…

Biofilm infections on medical implants are difficult to eradicate because insufficient nutrient availability promotes antibiotic-tolerant persister cells that survive treatment and reseed growth. Existing mathematical models usually omit…

We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted…

Chronic viral infections can persist in an infected person for decades. From the perspective of the virus, a single infection can span thousands of generations, leading to a highly diverse population of viruses with its own complex…