相关论文: Generalized Hopf Bifurcation in a Cancer Model wit…

Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We…

A Hopf bifurcation theorem is established for the abstract evolution equation $\frac{\mathrm{d}x}{\mathrm{d}t}=F(x,\lambda)$ in infinite dimensions under the degeneracy condition $Re \mu ^{\prime}(\lambda_0)= 0$ and suitable assumptions.…

Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the…

We analyze an epidemiological model with treatment and recruitment considering the risk perception. In this model, we consider an exponential function as a recruitment rate. We have found that this model undergoes the transcritical…

Herewith we discuss a network model of the ferroptosis avascular and vascular tumor growth based on our previous proposed framework. Chiefly, ferroptosis should be viewed as a first order phase transition characterized by a supercritical…

This paper analyses the dynamics of infectious disease with a concurrent spread of disease awareness. The model includes local awareness due to contacts with aware individuals, as well as global awareness due to reported cases of infection…

Cancer cells are widely known to be protected from apoptosis, which is a major hurdle to successful anti-cancer therapy. Over-expression of several anti-apoptotic proteins, or mutations in pro-apoptotic factors, has been recognized to…

In this paper, we consider a general single population model with delay and patch structure, which could model the population loss during the dispersal. It is shown that the model admits a unique positive equilibrium when the dispersal rate…

We investigate the effect of time delay on the dynamical model of love. The local stability analysis proves that the time delay on the return function can cause a Hopf bifurcation and a cyclic love dynamics. The condition for the occurrence…

The system of partial differential equations describing tumor-immune dynamics with angiogenesis taken into account is presented. For spatially homogeneous case, the steady state analysis of the model is carried out. The effects of single…

In this paper we analyse a dynamical system based on the so-called KCG (K\"all\'en, Crafoord, Ghil) conceptual climate model. This model describes an evolution of the globally averaged temperature and the average extent of the ice sheets.…

In this paper, the replicator dynamics of the two-locus two-allele system under weak mutation and weak selection is investigated in a generation-wise non-overlapping unstructured population of individuals mating at random. Our main finding…

In this contribution, the non-local, integro-partial differential system of equations proposed by Hillen et al. (Bull. Math. Biol. 75, 2013, no.1, 161-184) to account for the the tumor growth paradox (or the observation that some incomplete…

In the study of cancer evolution and therapeutic strategies, scientific evidence shows that a key dynamics lies in the tumor-environment interaction. In particular, oxygen concentration plays a central role in the determination of the…

In the paper we investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells is based on the generic Michaelis-Menten kinetics depicting…

Adaptive therapy improves cancer treatment by controlling the competition between sensitive and resistant cells through treatment holidays. This study highlights the critical role of treatment-holiday thresholds in adaptive therapy for…

We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth term and continue the analysis of the previous article [6]. We now take the viral diffusion in a two-dimensional environment. The model consists of two ODEs for…

We propose and study {a generalized Beverton-Holt competition model} subject to Allee effects to obtain insights on how the interplay of Allee effects and contest competition affects the persistence and the extinction of two competing…

This paper is devoted to the study of a predator-prey model with predator-age structure that involves Michaelis-Menten type ratio-dependent functional response. We study some dynamical properties of the model by using the theory of…

This article is concerned with a stochastic multi-patch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch…