Mathematical model of replication-mutation dynamics in coronaviruses.

RNA viruses are known for their fascinating evolutionary dynamics, characterised by high mutation rates, fast replication, and ability to form quasispecies - clouds of genetically related mutants. Fast replication in RNA viruses is achieved by a very fast but error-prone RNA-dependent RNA polymerase (RdRP). High mutation rates are a double-edged sword: they provide RNA viruses with a mechanism of fast adaptation to a changing environment or host immune system, but at the same time they pose risk to virus survivability in terms of either virus population being dominated by mutants (error catastrophe), or extinction of all viral sequences due to accumulation of mutations (lethal mutagenesis).

Sex, ducks, and rock "n" roll: Mathematical model of sexual response.

In this paper, we derive and analyze a mathematical model of a sexual response. As a starting point, we discuss two studies that proposed a connection between a sexual response cycle and a cusp catastrophe and explain why that connection is incorrect but suggests an analogy with excitable systems. This then serves as a basis for derivation of a phenomenological mathematical model of a sexual response, in which the variables represent levels of physiological and psychological arousal.

Vaccination games and imitation dynamics with memory.

In this paper, we model dynamics of pediatric vaccination as an imitation game, in which the rate of switching of vaccination strategies is proportional to perceived payoff gain that consists of the difference between perceived risk of infection and perceived risk of vaccine side effects. To account for the fact that vaccine side effects may affect people's perceptions of vaccine safety for some period of time, we use a delay distribution to represent how memory of past side effects influences current perception of risk. We find disease-free, pure vaccinator, and endemic equilibria and obtain conditions for their stability in terms of system parameters and characteristics of a delay distribution.

Dynamics of coupled Kuramoto oscillators with distributed delays.

This paper studies the effects of two different types of distributed-delay coupling in the system of two mutually coupled Kuramoto oscillators: one where the delay distribution is considered inside the coupling function and the other where the distribution enters outside the coupling function. In both cases, the existence and stability of phase-locked solutions is analyzed for uniform and gamma distribution kernels. The results show that while having the distribution inside the coupling function only changes parameter regions where phase-locked solutions exist, when the distribution is taken outside the coupling function, it affects both the existence, as well as stability properties of in- and anti-phase states.

Time-delayed and stochastic effects in a predator-prey model with ratio dependence and Holling type III functional response.

In this article, we derive and analyze a novel predator-prey model with account for maturation delay in predators, ratio dependence, and Holling type III functional response. The analysis of the system's steady states reveals conditions on predation rate, predator growth rate, and maturation time that can result in a prey-only equilibrium or facilitate simultaneous survival of prey and predators in the form of a stable coexistence steady state, or sustain periodic oscillations around this state. Demographic stochasticity in the model is explored by means of deriving a delayed chemical master equation.