相关论文: Generalized Hopf Bifurcation in a Cancer Model wit…
Development of resistance limits efficiency of present anticancer therapies and preventing it remains big challenge in cancer research. It is accepted, at intuitive level, that the resistance emerges as a consequence of cancer cells…
Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay…
In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with…
In this paper, we analyze some local stability and local bifurcation properties of the Proportionally fair, TCP fair, and the Delay-based dual algorithms in the presence of two distinct time delays. In particular, our focus is on the…
Astounding properties of biological sensors can often be mapped onto a dynamical system in the vicinity a bifurcation. For mammalian hearing, a Hopf bifurcation description has been shown to work across a whole range of scales, from…
Recently, research on the complex periodic behavior of multi-scale systems has become increasingly popular. Krupa et al. \cite{krupa2} provided a way to obtain relaxation oscillations in slow-fast systems through singular Hopf bifurcations…
We consider the SIRWJS epidemiological model that includes the waning and boosting of immunity via secondary infections. We carry out combined analytical and numerical investigations of the dynamics. The formulae describing the existence…
In the current manuscript, a first two-patch model with Allee effect and nonlinear dispersal is presented. We study both the ODE case and the PDE case here. In the ODE model, the stability of the equilibrium points and the existence of…
An SIS model is investigated in which the infective individuals are assumed to have an infection-age structure. The model is formulated as an abstract non-densely defined Cauchy problem. We study some dynamical properties of the model by…
Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or…
In this paper, we study the existence and the property of the Hopf bifurcation in the two-strategy replicator dynamics with distributed delays. In evolutionary games, we assume that a strategy would take an uncertain time delay to have a…
The competition between cancer cells and immune system cells in inhomogeneous conditions is described at cell scale within the framework of the thermostatted kinetic theory. Cell learning is reproduced by increased cell activity during…
Motivation: Epigenetic heterogeneity within a tumour can play an important role in tumour evolution and the emergence of resistance to treatment. It is increasingly recognised that the study of DNA methylation (DNAm) patterns along the…
We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with…
This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed (see [P. Colli et…
This study introduces an innovative framework for merging ecological and epidemiological modeling via the formulation of a sophisticated predator-prey model that addresses the intricacies of disease dynamics, the Allee effect, and defensive…
Predator-prey models in theoretical ecology have a long and complex history, spanning decades of research. Most of the models rely upon simple reproduction and mortality rates associated with different types of functional responses. A key…
The establishment and spreading of biological populations depends crucially on population growth at low densities. The Allee effect is a problem in those populations where the per-capita growth rate at low densities is reduced. We examine…
Inevitably, almost all cancer patients develop resistance to targeted therapy. Intratumor heterogeneity (ITH) is a major cause of drug resistance. Mathematical models that explain experiments quantitatively is useful in understanding the…
In this paper, we investigate an SVIRS epidemic model that incorporates both temporary immunity and an age-structured recovery process. By reformulating the system as a non-densely defined abstract Cauchy problem, we establish the existence…