Physiologically structured populations with diffusion and dynamic boundary conditions

JZ Farkas, P Hinow - arXiv preprint arXiv:1004.4141, 2010 - arxiv.org
We consider a linear size-structured population model with diffusion in the size-space.
Individuals are recruited into the population at arbitrary sizes. The model is equipped with …

Steady states in a structured epidemic model with Wentzell boundary condition

À Calsina, JZ Farkas - Journal of Evolution Equations, 2012 - Springer
We introduce a non-linear structured population model with diffusion in the state space.
Individuals are structured with respect to a continuous variable which represents a pathogen …

Structured populations with distributed recruitment: from PDE to delay formulation

À Calsina, O Diekmann… - Mathematical Methods in …, 2016 - Wiley Online Library
In this work, first, we consider a physiologically structured population model with a
distributed recruitment process. That is, our model allows newly recruited individuals to enter …

Nonlinear physiologically structured population models with two internal variables

H Kang, X Huo, S Ruan - Journal of Nonlinear Science, 2020 - Springer
First-order hyperbolic partial differential equations with two internal variables have been
used to model biological and epidemiological problems with two physiological structures …

Asymptotic behaviour of a structured population model on a space of measures

JZ Farkas, P Gwiazda, A Marciniak-Czochra - arXiv preprint arXiv …, 2019 - arxiv.org
In this paper we consider a physiologically structured population model with distributed
states at birth, formulated on the space of non-negative Radon measures. Using a …

Modelling effects of rapid evolution on persistence and stability in structured predator-prey systems

JZ Farkas, AY Morozov - Mathematical Modelling of Natural …, 2014 - cambridge.org
In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the
prey population is structured according to a certain life history trait. The trait distribution …

Asymptotic analysis of a size-structured population model with infinite states-at-birth

D Yan, X Fu - Applicable Analysis, 2019 - Taylor & Francis
In this paper, we study a size-structured population model with infinite states-at-birth and
distributed delay in birth process. We are interested in the asymptotic behavior of the …

Steady states in hierarchical structured populations with distributed states at birth

JZ Farkas, P Hinow - arXiv preprint arXiv:1004.3968, 2010 - arxiv.org
We investigate steady states of a quasilinear first order hyperbolic partial integro-differential
equation. The model describes the evolution of a hierarchical structured population with …

Positive steady states of evolution equations with finite dimensional nonlinearities

A Calsina, JZ Farkas - SIAM Journal on Mathematical Analysis, 2014 - SIAM
We study the question of existence of positive steady states of nonlinear evolution
equations. We recast the steady state equation in the form of eigenvalue problems for a …

On a two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process

M Bai, S Xu - Journal of Biological Dynamics, 2014 - Taylor & Francis
In this paper we study the two-phase size-structured population model with infinite states-at-
birth and distributed delay in birth process. The model distinguishes individuals by two …