84 citations · 355 across the 29 of their papers we have counts for
29 papers
Asynchronous exponential growth for structured population models in measure space
Christian Düll, József Z. Farkas, Piotr Gwiazda +1
This paper studies the asymptotic behaviour of a structured population model on the space of nonnegative Radon measures. Such formulations naturally arise when solutions develop co…
Stability results for a hierarchical size-structured population model with distributed delay
Dandan Hu, József Z. Farkas, Gang Huang
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individ…
On competition through growth reduction
Carles Barril, Àngel Calsina, Odo Diekmann +1
We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the presence of larger individuals. As…
Assessing the Impact of (Self)-Quarantine Through a Basic Model of Infectious Disease Dynamics
Jozsef Z. Farkas, Roxane Chatzopoulos
We introduce a system of differential equations to assess the impact of (self-)quarantine of symptomatic infectious individuals on disease dynamics. To this end we depart from usin…
Dengue transmission dynamics in age-structured human populations in the presence of Wolbachia
Jozsef Z. Farkas, Stephen A. Gourley, Rongsong Liu
According to the World Health Organization the global incidence rate of dengue infections have risen drastically in recent years. It is estimated that globally the number of new in…
On the formulation of size-structured consumer resource models (with special attention for the principle of linearised stability)
Carles Barril, Àngel Calsina, Odo Diekmann +1
To describe the dynamics of a size-structured population and its unstructured resource, we formulate bookkeeping equations in two different ways. The first, called the PDE formulat…
A General Model of Structured Cell Kinetics
Michael Grinfeld, Nigel Mottram, Jozsef Farkas
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cel…
Boundary perturbations and steady states of structured populations
Àngel Calsina, József Z. Farkas
In this work we establish conditions which guarantee the existence of (strictly) positive steady states of a nonlinear structured population model. In our framework the steady stat…
Asymptotic behaviour of a structured population model on a space of measures
József Z. Farkas, Piotr Gwiazda, Anna Marciniak-Czochra
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 characteri…
Net reproduction functions for nonlinear structured population models
József Z. Farkas
The goal of this note is to present a general approach to define the net reproduction function for a large class of nonlinear physiologically structured population models. In parti…
Mathematical Analysis of a Clonal Evolution Model of Tumour Cell Proliferation
József Z. Farkas, Glenn F. Webb
We investigate a partial differential equation model of a cancer cell population, which is structured with respect to age and telomere length of cells. We assume a continuous telom…
Structured populations with distributed recruitment: from PDE to delay formulation
Àngel Calsina, Odo Diekmann, József Z. Farkas
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…
On a strain-structured epidemic model
Àngel Calsina, József Z. Farkas
We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the viru…
Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication
Jozsef Z. Farkas, Andrew Yu Morozov, E. G. Arashkevich +1
We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, th…
Wolbachia infection in a sex-structured mosquito population carrying West Nile virus
József Z. Farkas, Stephen A. Gourley, Rongsong Liu +1
Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin b…
Modelling effects of rapid evolution on persistence and stability in structured predator-prey systems
József Z. Farkas, A. Yu. Morozov
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 distri…
Positive steady states of evolution equations with finite dimensional nonlinearities
Àngel Calsina, József Z. Farkas
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 parametr…
Finite difference approximations for a size-structured population model with distributed states in the recruitment
A. S. Ackleh, J. Z. Farkas, X. Li +1
In this paper we consider a size-structured population model where individuals may be recruited into the population at different sizes. First and second order finite difference sch…
On the net reproduction rate of continuous structured populations with distributed states at birth
Azmy S. Ackleh, Jozsef Z. Farkas
We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least!) in th…
Steady states in a structured epidemic model with Wentzell boundary condition
Angel Calsina, Jozsef Z. Farkas
We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen…
Pathogen evolution in switching environments: a hybrid dynamical system approach
Jozsef Z. Farkas, Peter Hinow, Jan Engelstädter
We propose a hybrid dynamical system approach to model the evolution of a pathogen that experiences different selective pressures according to a stochastic process. In every enviro…
Physiologically structured populations with diffusion and dynamic boundary conditions
J. Z. Farkas, P. Hinow
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 hierarchical structured populations with distributed states at birth
J. Z. Farkas, P. Hinow
We investigate steady states of a quasilinear first order hyperbolic partial integro-differential equation. The model describes the evolution of a hierarchical structured populatio…
Size-structured populations: immigration, (bi)stability and the net growth rate
Jozsef Z. Farkas
We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a const…