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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 recent years, due to advancements in medical conditions and the development of scientific research, the fundamental research of TCM antitumor treatments has progressed from the cellular level to the molecular and genetic levels. Previous studies have demonstrated the significant role of traditional Chinese medicine (TCM) in antitumor therapy through various mechanisms and pathways. Its mechanism of action is closely associated with cancer biology across different stages. This includes inhibiting tumor cell proliferation, blocking invasion and metastasis to surrounding tissues, inducing tumor cell apoptosis, inhibiting tumor angiogenesis, regulating immune function, maintaining genome stability, preventing mutation, and regulating cell energy metabolism. The use of TCM for eliciting antitumor effects not only has a good therapeutic effect and low side effects, it also provides a solid theoretical basis for clinical treatment and medication. This paper reviews the mechanism of the antitumor effects of TCM based on tumor characteristics. Through our review, we found that TCM not only directly inhibits tumors, but also enhances the body's immunity, thereby indirectly inducing an antitumor effect. This function aligns with the TCM theory of "strengthening the body's resistance to eliminate pathogenic factors". Furthermore, TCM will play a significant role in tumor treatment in clinical settings. [ABSTRACT FROM AUTHOR]

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 this paper, we develop a mathematical model to study the interactions among tumor cells, immune escape tumor cells, and T lymphocyte. The chimeric antigen receptor (CAR) T-cell therapy is also described by the mathematical model. Bifurcation analysis shows that there exists backward bifurcation and saddle-node bifurcation when the immune intensity is used as the bifurcation parameter. The proposed model also exhibits bistability when its parameters are located between the saddle-node threshold and backward bifurcation threshold. Sensitivity analysis is performed to illustrate the effects of different mechanisms on the backward bifurcation threshold and basic immune reproduction number. Simulation studies confirm the bifurcation analysis results and predict various types of treatment outcomes using different CAR T-cell therapy strengths. Analysis and simulation results show that the immune intensity can be used to control the tumor size, but it has no effect on the control of the immune escape tumor size. The introduction of the CAR T-cell therapy will reduce the immune escape tumor size and the treatment effect depends on the CAR T-cell therapy strength. [ABSTRACT FROM AUTHOR]

Cancer has evolved into a substantial public health concern as the second-leading cause of mortality globally. Radiotherapy and chemotherapy have been the two most widely used cancer therapies in recent years; however, both have drawbacks. Therefore, the focus has shifted to the creation of herbal medicines, the extraction of active ingredients, replacement therapy, and the adverse effects of these medications. Ginsenoside Rh2, which is extracted from ginseng, has been identified in many cancer cells. The immune system of the body is strengthened by ginsenoside Rh2, which can also cause the proliferation, death, and differentiation of tumor cells through various pathways. For instance, it inhibits the expression of the NF- κ B signaling pathway and induces cell apoptosis, affects the expression levels of mitochondrial apoptosis proteins Bcl-2 and Bax, and cooperates with the PD-1 blockade to reactivate T cells to promote an antitumor immune response. Furthermore, ginsenosides Rh2 has the effect of reversing the toxic effect of chemotherapy drugs on normal cells, reducing myocardial damage, and relieving bone marrow function suppression. For clinical applications, it is mainly used as an adjuvant drug for preoperative neoadjuvant chemotherapy, postoperative adjuvant chemotherapy, and rescue treatment of advanced cancer. This paper summarizes the pharmacological action and mechanism of ginsenosides Rh2 in all kinds of cancer and looks forward to its future development and application. [ABSTRACT FROM AUTHOR]

The SARS-CoV-2 leads to a worldwide COVID-19 pandemic, which has caused tremendous damage to the world. In this paper, we develop a dynamic model in vivo, fitting and estimating parameters for T lymphocytes and pro-inflammatory cytokines IL-6 in patients with mild and severe COVID-19 at Yale New Haven Hospital through the GWMCMC algorithm. Meanwhile, we also analyze the structural identifiability and practical identifiability of the model. Further, we add time-varying parameters to the model, using the least squares method to perform data fitting and parameter estimation on survivors and non-survivors of the Italian infectious disease hospital. Then analyze the similarities and differences in immune response mechanisms between the two countries. Finally, we demonstrate the existence and stability of the equilibrium state of the model and analyze the Hopf bifurcation at the positive equilibrium state by using the central manifold theory and normal form theory. This result may explain the recurrence of infection in some COVID-19 patients. [ABSTRACT FROM AUTHOR]

The tumor microenvironment (TME) plays an important role in the development of tumors. Immunoregulatory cells and cytokines facilitate cancer cells to avoid immune surveillance. Overexpression of immune checkpoint molecules such as CTLA-4 and PD-1/PD-L1 inhibits immune function and enables cancer cells to avoid clearance by the immune system. Thus, minimizing tumor immunosuppression could be an important strategy for cancer therapy. Currently, many immune checkpoint-targeted drugs, such as PD-1/PD-L1 inhibitors, have been approved for marketing and have shown unique advantages in the clinical treatment of cancers. The concept of "strengthening resistance to eliminate pathogenic factors" in traditional Chinese medicine (TCM) is consistent with the immunotherapy of cancer. According to previous studies, the role of TCM in tumor immunotherapy is mainly associated with the positive regulation of natural killer cells, CD8/CD4 T cells, dendritic cells, M2 macrophages, interleukin-2, tumor necrosis factor- α , and IFN- γ , as well as with the negative regulation of Tregs, myeloid-derived suppressor cells, cancer-associated fibroblasts, PD-1/PD-L1, transforming growth factor- β , and tumor necrosis factor- β. This paper summarizes the current research on the effect of TCM targeting the TME, and further introduces the research progress on studying the effects of TCM on immune checkpoints. Modern pharmacological studies have demonstrated that TCM can directly or indirectly affect the TME by inhibiting the overexpression of immune checkpoint molecules and enhancing the efficacy of tumor immunotherapy. TCM with immunomodulatory stimulation could be the key factor to achieve benefits from immunotherapy for patients with non-inflammatory, or "cold", tumors. [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]

The Th17/Treg axis plays a crucial role in immune-mediated inflammatory diseases (IMID) and might represent an interesting drug target of treatment strategy for these diseases. Accumulating evidence suggests a role for traditional Chinese medicine (TCM) in the modulation of Th17/Treg axis, but a comprehensive overview which summarizes this field hitherto is lacked. This paper performs a systematic literature review of the regulatory effects of TCM on the imbalance of Th17/Treg axis and its potential mechanisms. In addition, the frequency analysis and network pharmacology for the collected TCM herbs from clinical trial data were performed. The studies reported the changes in the ratio of Th17 and/or Treg cells as well as their transcription factor and related cytokines were included. Frequency analysis of composition of the 39 assessed TCM prescriptions showed that Astragalus membranaceus var.mongholicus (5.20%), Glycyrrhiza uralensis (3.67%), Paeonia obovate (3.06%), Salvia digitaloides (3.06%), and Angelica sinensis (2.75%) were the top five herbal components, which were closely associated to the treatment of IMID. Network pharmacology showed that six target proteins (transforming growth factor (TGF)-beta receptor type-1, TGF-beta receptor type-2, retineic-acid-receptor-related orphan nuclear receptor gamma (ROR-gamma), TGFB2, IL-17 and IL-2, respectively) might be involved in the regulatory effects of TCM on Th17/Treg axis. Moreover, there were nine active ingredients (including Oxymatrine, Baicalin, Triptolide, Paeoniflorin, Sinomenine, Celastrol, Emodin, Diosgenin and Chlorogenic acid) originating from TCM reported to have an immunological regulation effect on the Th17/Treg axis. The highlight of this systematic review is to reveal the pharmacological basis of TCM treating IMID and is helpful for supporting future pharmacologic-driven studies. Further research elucidates the immune-modulating mechanisms on Th17/Treg axis by TCM might provide a broader insight for the treatment of IMID. [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 investigates the dynamics of immune response and autoimmunity with particular emphasis on the role of regulatory T cells (Tregs), T cells with different activation thresholds, and cytokines in mediating T cell activity. Analysis of the steady states yields parameter regions corresponding to regimes of normal clearance of viral infection, chronic infection, or autoimmune behavior, and the boundaries of stability and bifurcations of relevant steady states are found in terms of system parameters. Numerical simulations are performed to illustrate different dynamical scenarios, and to identify basins of attraction of different steady states and periodic solutions, highlighting the important role played by the initial conditions in determining the outcome of immune interactions. [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 artificial immune system, many algorithms based on negative selection methods have been proposed to achieve satisfying classification performances. However, there are still many problems required to be solved, such as parameters sensibility and computational complexity. In this paper, a novel classification algorithm based on T-cells maturation algorithm was proposed for anomaly detection. Data set from UC Irvine Machine Learning Repository was used for 10-fold cross-validation, and simulation results confirmed its similar performances with AIRS. Compared with other classification algorithms based on negative selection methods, the proposed algorithm has no parameters and lower complexity, and can achieve satisfying classification 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]

In this paper, we investigate a mathematical model of pancreatic cancer, which extends the existing pancreatic cancer models with regulatory T cells (Tregs) and Treg inhibitory therapy. The model consists of tumor-immune interaction and immune suppression from Tregs. In the absence of treatments, we first characterize the system dynamics by locating equilibrium points and determining stability properties. Next, cytokine induced killer (CIK) immunotherapy is incorporated. Numerical simulations of prognostic results illustrate that the median overall survival associated with treatment can be prolonged approximately from 7 to 13 months, which is consistent with the clinical data. Furthermore, we consider cyclophosphamide (CTX) therapy as well as the combined therapy with CIK and CTX. Intensive simulation results suggest that both CTX therapy and the combined CIK/CTX therapy can reduce the number of Tregs and increase the overall survival (OS), but Tregs and tumor cells will gradually rise to equilibrium state as long as therapies are ceased. [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]