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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]