The abstract renewal equation.
The analysis of epidemic network model with infectious force in latent and infected period.
The architecture of viral capsids based on tiling theory.
The Basic Reproduction Number of an Infectious Disease in a Stable Population: The Impact of Population Growth Rate on the Eradication Threshold
Although age-related heterogeneity of infection has been addressed in various epidemic models assuming a demographically stationary population, only a few studies have explicitly dealt with age-specific patterns of transmission in growing or decreasing population. To discuss the threshold principle realistically, the present study investigates an age-duration-structured SIR epidemic model assuming a stable host population, as the first scheme to account for the non-stationality of the host population....
The Becker-Döring model with diffusion. I. Basic properties of solutions
The combinatorics of evolutionary trees---a survey.
The common ancestor process for a Wright-Fisher diffusion.
The complete ellipsoidal shell-model in EEG imaging.
The complete parameters analysis of the asymptotic behaviour of a logistic epidemic model with two stochastic perturbations.
The conjugacy between Cascades generated by a weakly nonlinear system and the Euler method of a flow
Sufficient conditions for the existence of a topological conjugacy between a cascade obtained from a weakly nonlinear flow by fixing the time step and a cascade obtained by the Euler method are analysed. The aim of this paper is to provide relations between constants in the Fečkan theorem. Given such relations an implementation of a weakly nonlinear neuron is possible.
The continuum reaction-diffusion limit of a stochastic cellular growth model
A competition-diffusion system, where populations of healthy and malignant cells compete and move on a neutral matrix, is analyzed. A coupled system of degenerate nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The healthy cells move much slower than the malignant ones, such that no diffusion for their density survives in the limit. The malignant cells may locally accumulate, while for the healthy ones an exclusion rule is considered....
The diameter distribution of the stem villi arteries does not discriminate between normal and intra uterine growth restricted placentas.
The discrete Beverton-Holt model with periodic harvesting in a periodically fluctuating environment.
The dynamic behaviors of a new impulsive predator prey model with impulsive control at different fixed moments
In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the "infection-free" periodic solution and the "predator-free" solution are analyzed...
The dynamic complexity of a Holling type-IV predator-prey system with stage structure and double delays.
The dynamics of living and thinking systems, biological networks, and the laws of physics.
The dynamics of mutation-selection algorithms with large population sizes
The dynamics of the pulse birth in an SIR epidemic model with standard incidence.
The Effect of Bacteria on Epidermal Wound Healing
Epidermal wound healing is a complex process that repairs injured tissue. The complexity of this process increases when bacteria are present in a wound; the bacteria interaction determines whether infection sets in. Because of underlying physiological problems infected wounds do not follow the normal healing pattern. In this paper we present a mathematical model of the healing of both infected and uninfected wounds. At the core of our model is an...
The effect of impulsive diffusion on dynamics of a stage-structured predator-prey system.