Shaoli Wang

• Xi'an Jiaotong University

Tumor immune escape refers to the inability of the immune system to clear tumor cells, which is one of the major obstacles in designing effective treatment schemes for cancer diseases. Although clinical studies have led to promising treatment outcomes, it is imperative to design theoretical models to investigate the long-term treatment effects. In...

In this paper, we study a delayed HIV infection model with nonmonotonic immune response and perform stability and bifurcation analysis. Our results show that the delayed HIV infection system with nonmonotonic immune response has bistability and stable periodic solution appear. We find that both the uninfected and immune‐free equilibria are globally...

Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose an SEIRE epidemic model to describe the spread of the epidemic with reinfection. We obtain the important thresholds [Formula: see text] (the basic reproduction nu...

Recent studies have demonstrated that immune impairment is an essential factor in viral infection for disease development and treatment. In this paper, we formulate an age-structured viral infection model with a nonmonotonic immune response and perform dynamical analysis to explore the effects of both immune impairment and virus control. The basic...

Recently, bistable viral infection systems have attracted increased attention. In this paper, we study bistability and robustness for virus infection models with nonmonotonic immune responses in viral infection systems. The results show that the existing transcritical bifurcation undergoes backward or forward bifurcation in viral infection models w...

Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose a SEIRE epidemic model to describe the spread of the epidemic with reinfection. We obtain the important thresholds $R_0$ (the basic reproduction number) and Rc (a...

Recently, Wang and Xu [ Appl. Math. Lett. 78 (2018) 105-111] studied thresholds and bi-stability in virus-immune dynamics. In this paper, we show there also exist backward bifurcation and saddle node bifurcation in this model. Our investigation demonstrates the existence of post-bifurcation phenomenon in the system when the immune strength was sele...

In this paper, a prey–predator-top predator food chain model with nonmonotonic functional response in the predators is studied. With an emphasis on the nutrition conversion rate of predator to top predator, one can get two important thresholds: the top predator extinction threshold and the coexistence threshold. The top predator will die out if the...

In this paper, certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated. For the viral model with a single strain, we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number [Formula: see text] and structuring proper Lyapunov...

In this paper, we study the psychological effect in a SIS epidemic model. The basic reproduction number is obtained. However, the disease free equilibrium is always asymptotically stable, which doesn't depends on the basic reproduction number. The system has a saddle-node bifurcation appear and displays bistable behavior, which is a new phenomenon...

In this paper, we consider a SIRS model with general nonmonotone and saturated incidence rate and perform stability and bifurcation analysis. We show that the system has saddle-node bifurcation and displays bistable behavior. We obtain the critical thresholds that characterize the dynamical behaviors of the model. We find with surprise that the sys...

In this paper, we study two-dimensional, three-dimensional monotonic and nonmonotonic immune responses in viral infection systems. Our results show that the viral infection systems with monotonic immune response has no bistability appear. However, the systems with nonmonotonic immune response has bistability appear under some conditions. For immune...

In this paper, we construct a mathematical model to investigate the interaction between the tumor cells, the immune cells and the helper T cells (HTCs). We perform mathematical analysis to reveal the stability of the equilibria of the model. In our model, the HTCs are stimulated by the identification of the presence of tumor antigens. Our investiga...

Recent investigation indicated that latent reservoir and immune impairment are responsible for the post-treatment control of HIV infection. In this paper, we simplify the disease model with latent reservoir and immune impairment and perform a series of mathematical analysis. We obtain the basic infection reproductive number R 0 to characterize the...

In this paper, we study two-dimensional, three-dimensional monotonic and nonmonotonic immune responses in viral infection systems. Our results show that the viral infection systems with monotonic immune response has no bistability appear. However, the systems with nonmonotonic immune response has bistability appear under some conditions. For immune...

In this paper, we consider the local discontinuous Galerkin (LDG) finite element method for one-dimensional time-fractional Fisher's equation, which is obtained from the standard one-dimensional Fisher's equation by replacing the first-order time derivative with a fractional derivative (of order alpha, with 0 < alpha < 1). The proposed LDG is based...

The Hopf bifurcation for a predator-prey system with θ -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- θ passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal f...

In this paper we present and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional Schrödinger equation, where the fractional derivative is described in the Caputo sense. The scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space....

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We show that our scheme is unconditional stable and L error estimate...

A delayed oncolytic virus dynamics with continuous control is investigated. The local stability of the infected equilibrium is discussed by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. Using th...

In this paper, the dynamical behavior of a delayed viral infection model with immune impairment is studied. It is shown that if the basic reproductive number of the virus is less than one, then the uninfected equilibrium is globally asymptotically stable for both ODE and DDE model. And the effect of time delay on stabilities of the equilibria of th...

In this Letter, a variable-coefficient discrete (G′G)-expansion method is proposed to seek new and more general exact solutions of nonlinear differential–difference equations. Being concise and straightforward, this method is applied to the (2+1)(2+1)-dimension Toda equation. As a result, many new and more general exact solutions are obtained inclu...

This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equili...

A class of more general delayed viral infection model with lytic immune response is proposed based on some important biological meanings. The effect of time delay on stabilities of the equilibria is given. The sufficient criteria for local and global asymptotic stabilities of the viral free equilibrium and the local asymptotic stabilities of the no...

In this paper, a class of more general viral infection model with delayed non-lytic immune response is proposed based on some important biological meanings. The sufficient criteria for local and global asymptotic stabilities of the viral free equilibrium are given. And the stability and Hopf bifurcation of the infected equilibrium have been studied...