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In this paper, a mathematical ordinary differential tumor-immune model is proposed based on an immune checkpoint inhibitor, which is an innovative method for tumor immunotherapies. Two important factors in tumor-immune response are the programmed cell death protein 1 (PD-1) and its ligand PD-L1. The model consists of three populations: tumor cells, activated T cells and anti-PD-1. By analyzing the dynamics of the model, it is found that there is always a unique tumor-free equilibrium and at most two tumor interior equilibria. The nonexistence of nontrivial positive periodic orbits is established by using the new Dulac function, and then a global dynamics of the model is obtained. The conclusions of our analysis show that increasing the possibility of T cells killing tumor cells (p), early detection of tumor cells, or the use of PD-1 inhibitors to activate T cells are effective in eliminating tumor cells. [ABSTRACT FROM AUTHOR]

In this paper, we study a mathematical model of Hepatitis C Virus (HCV) infection. We present a compartmental mathematical model involving healthy hepatocytes, infected hepatocytes, non-activated dendritic cells, activated dendritic cells and cytotoxic T lymphocytes. The derivative used is of non-local fractional order and with non-singular kernel. The existence and uniqueness of the system is proven and its stability is analyzed. Then, by applying the Laplace Adomian decomposition method for the fractional derivative, we present the semi-analytical solution of the model. Finally, some numerical simulations are performed for concrete values of the parameters and several graphs are plotted to reveal the qualitative properties of the solutions. [ABSTRACT FROM AUTHOR]

Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that infect the susceptible CD 4 + T cells. It is known that HIV and HTLV-I have in common a way of transmission through direct contact with certain body fluids related to infected individuals. Therefore, it is not surprising that a mono-infected person with one of these viruses can be co-infected with the other virus. In the literature, a great number of mathematical models has been presented to describe the within-host dynamics of HIV or HTLV-I mono-infection. However, the within-host dynamics of HIV/HTLV-I co-infection has not been modeled. In this paper, we develop a new within-host HIV/HTLV-I co-infection model. The model includes the impact of Cytotoxic T lymphocytes (CTLs) immune response, which is important to control the progression of viral co-infection. The model describes the interaction between susceptible CD 4 + T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. We first show the nonnegativity and boundedness of the model's solutions and then we calculate all possible equilibria. We derive the threshold parameters which govern the existence and stability of all equilibria of the model. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have presented numerical simulations to illustrate the effectiveness of our main results. In addition, we discuss the effect of HTLV-I infection on the HIV-infected patients and vice versa. [ABSTRACT FROM AUTHOR]

HIV infection is one of the most serious causes of death throughout the world. CD4+ T cells which play an important role in immune protection, are the primary targets for HIV infection. The hallmark of HIV infection is the progressive loss in population of CD4+ T cells. However, the pathway causing this slow T cell decline is poorly understood [16]. This paper studies a discontinuous mathematical model for HIV-1 infection, to investigate the effect of pyroptosis on the disease. For this purpose, we use the theory of discontinuous dynamical systems. In this way, we can better analyze the dynamical behavior of the HIV-1 system. Especially, considering the dynamics of the system on its discontinuity boundary enables us to obtain more comprehensive results rather than the previous researches. A stability region for the system, corresponding to its equilibria on the discontinuity boundary, will be determined. In such a parametric region, the trajectories of the system will be trapped on the discontinuity manifold forever. It is also shown that in the obtained stability region, the disease can lead to a steady state in which the population of uninfected T cells and viruses will preserve at a constant level of cytokines. This means that the pyroptosis will be restricted and the disease cannot progress for a long time. Some numerical simulations based on clinical and experimental data are given which are in good agreement with our theoretical results. [ABSTRACT FROM AUTHOR]

Changes in cellular Ca 2 + concentration control a variety of physiological activities including hormone and neurotransmitter release, muscular contraction, synaptic plasticity, ionic channel permeability, apoptosis, enzyme activity, gene transcription and reproduction process. Spatial–temporal Ca 2 + dynamics due to Ca 2 + release, buffering and re-uptaking plays a central role in studying the Ca 2 + regulation in T lymphocytes. In most cases, Ca 2 + has its major signaling function when it is elevated in the cytosolic compartment. In this paper, a two-dimensional mathematical model to study spatiotemporal variations of intracellular Ca 2 + concentration in T lymphocyte cell is proposed and investigated. The cell is assumed to be a circular shaped geometrical domain for the representation of properties of Ca 2 + dynamics within the cell including important parameters. Ca 2 + binding proteins for the dynamics of Ca 2 + are itself buffer and other physiological parameters located in Ca 2 + stores. The model incorporates the important biophysical processes like diffusion, reaction, voltage-gated Ca 2 + channel, leak from endoplasmic reticulum (ER), efflux from cytosol to ER via sarco–ER Ca 2 + adenosine triphosphate (SERCA) pumps, buffers and Na + / Ca 2 + exchanger. The proposed mathematical model is solved using a finite difference method and the finite element method. Appropriate initial and boundary conditions are incorporated in the model based on biophysical conditions of the problem. Computer simulations in MATLAB R2019b are employed to investigate mathematical models of reaction–diffusion equation. The effect of source, buffer, Na + /Ca 2 + exchanger, etc. on spatial and temporal patterns of Ca 2 + in T lymphocyte has been studied with the help of numerical results. From the obtained results, it is observed that, the coordinated combination of the incorporated parameters plays a significant role in Ca 2 + regulation in T lymphocytes. ER leak and voltage-gated Ca 2 + channel provides the necessary Ca 2 + to the cell when required for its proper functioning, while on the other side buffers, SERCA pump and Na + /Ca 2 + exchanger makes balance in the Ca 2 + concentration, so as to prevent the cell from death as higher concentration for longer time is harmful for the cell and can cause cell death. [ABSTRACT FROM AUTHOR]

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 investigation implies that the presence of tumor antigens may inhibit the existence of high steady state of tumor cells, which leads to the elimination of the bistable behavior of the tumor-immune system, i.e. the equilibrium corresponding to the high steady state of tumor cells is destabilized. Choosing immune intensity c as bifurcation parameter, there exists saddle-node bifurcation. Besides, there exists a critical value c ∗ , at which a Hopf bifurcation occurs. The stability and direction of Hopf bifurcation are discussed. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the stability of a CD 4 + T cell viral infection model with diffusion. First, we discuss the well-posedness of the model and the existence of endemic equilibrium. Second, by analyzing the roots of the characteristic equation, we establish the local stability of the virus-free equilibrium. Furthermore, by constructing suitable Lyapunov functions, we show that the virus-free equilibrium is globally asymptotically stable if the threshold value ℛ 0 ≤ 1 ; the endemic equilibrium is globally asymptotically stable if ℛ 0 > 1 and d u ∗ − δ w ∗ ≥ 0. Finally, we give an application and numerical simulations to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, the human immunodeficiency virus (HIV) infection model of CDT-cells is considered. In order to numerically solve the model problem, an operational method is proposed. For that purpose, we construct the operational matrix of integration for bases of Taylor polynomials. Then, by using this matrix operation and approximation by polynomials, the HIV infection problem is transformed into a system of algebraic equations, whose roots are used to determine the approximate solutions. An important feature of the method is that it does not require collocation points. In addition, an error estimation technique is presented. We apply the present method to two numerical examples and compare our results with other methods. [ABSTRACT FROM AUTHOR]

Based on a multi-scale view, in this paper, we study an age-structured within-host model with Crowley-Martin functional response for the control of viral infections. By means of semigroup and Lyapunov function, the global asymptotical property of infected steady state of the model is obtained. The results show that when the basic reproductive number falls below unity, the infection dies out. However, when the basic reproductive number exceeds unity, there exists a unique positive equilibrium which is globally asymptotically stable. This model can be deduced to different viral models with or without time delay. [ABSTRACT FROM AUTHOR]

In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. We derive that the global dynamics are completely determined by the values of the basic reproduction number: if the basic reproduction number is less than one, the uninfected equilibrium is globally asymptotically stable, and the virus is cleared; if the basic reproduction number is larger than one, then the infection persists, and the infected equilibrium is globally asymptotically stable. [ABSTRACT FROM AUTHOR]