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Human immunodeficiency virus (HIV) infection may cause death by damaging some of the patient's vital organs through weakening the body's immune system, including CD 4 + T cells. In the meantime, mathematical models can be useful in dealing with this deadly virus by providing effective strategies based on the examination of different infection states. The major aim pursued in this paper is to present a computational algorithm for solving nonlinear systems of ordinary and partial differential equations resulting from the HIV infection models of CD 4 + T cells. The offered method is developed according to the use of local radial basis functions (LRBFs) as shape functions in the discrete collocation scheme. The new technique approximates the solution by a small set of nodes instead of all points located in the domain where the HIV mathematical model is given. Thus the presented method uses less computing volume compared to the globally supported radial basis functions, and as a result, its algorithm can be quickly run on a computer with relatively low memory. The computational efficiency of the scheme is studied by several test examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider the distributed filtering problem for continuous-time stochastic systems over sensor networks subject to Markovian switching topologies. Due to limited communication energy and bandwidth, an event-based communication scheme is proposed with the aim to decrease the transmission frequency. An individual triggering condition is put forward to regulate the communication rates for each component of the system state in order to better reflect the engineering requirements. The aim of this paper is to design a distributed filter over sensor networks with Markovian switching topologies such that the dynamics of the estimation error is exponentially mean-square bounded. It is shown that, with the proposed event-based distributed filtering algorithm, the exponential mean-square boundedness of the estimation errors is guaranteed if the sensor network is distributively detectable and the combined communication topology is strongly connected. A numerical example is presented to illustrate the usefulness of the developed algorithm. [ABSTRACT FROM AUTHOR]

The immune system turns out to have both stimulatory and inhibitory factors influencing on tumor growth. In recent years, the pro-tumor role of immunity factors such as regulatory T cells and TGF-β cytokines has specially been considered in mathematical modeling of tumor-immune interactions. This paper presents a novel structural methodology for reviewing these models and classifies them into five subgroups on the basis of immune factors included. By using our experimental data due to immunotherapy experimentation in mice, these five modeling groups are evaluated and scored. The results show that a model with a small number of variables and coefficients performs efficiently in predicting the tumor-immune system interactions. Though immunology theorems suggest to employ a larger number of variables and coefficients, more complicated models are here shown to be inefficient due to redundant parallel pathways. So, these models are trapped in local minima and restricted in prediction capability. This paper investigates the mathematical models that were previously developed and proposes variables and pathways that are essential for modeling tumor-immune. Using these variables and pathways, a minimal structure for modeling tumor-immune interactions is proposed for future studies. [ABSTRACT FROM AUTHOR]

The "shock and kill" strategy is being widely explored to purge Human Immunodeficiency Virus (HIV) latent reservoirs. Romidepsin, a kind of latency-reversing agents (LRAs), has been shown to induce HIV RNA transcription. However, several clinical trials testing this drug have resulted in limited effect in reducing the HIV latent reservoirs. To understand the mechanisms underlying such limited effect, we develop a multi-scale model that incorporates pharmacokinetics and considers the toxicity of romidepsin to T cells in this paper. By fitting the model to the viral load data from plasma of six patients received romidepsin, we find that the model with T cell toxicity of romidepsin can well explain the clinical data. The dynamics of latently infected cells during romidepsin administration are explored using the best-fit parameter values. The results show that latently infected cells decrease very slowly and remain very stable overall in four of the six participants under the assumption of T cell toxicity of romidepsin. This implies that the ineffectiveness of romidepsin on latent reservoirs can be explained by its toxicity to T cells. In the remaining two participants, however, latently infected cells are quite stable without T cell toxicity of LRAs. It is found that the estimated activation rate of latently infected cells by romidepsin and the estimated elimination rate of romidepsin on immune cells for these two patients are very different from those for the other four patients. Thus we speculate that the heterogeneous response to romidepsin across participants may also be a determining factor of the effectiveness of romidepsin. These results may have significant implications in the search for the control of HIV infection. • An HIV model is proposed to understand the cause of ineffectiveness of romidepsin in the "shock and kill" strategy. • The model has a good fit to patients' data when T cell toxicity of romidepsin is considered. • The toxicity of romidepsin to T cell may contribute to the ineffectiveness of "shock and kill" strategy concerning romidepsin. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model describing the interaction of malignant glioma cells, macrophages and glioma specific CD8+T cells is discussed. The biologically feasible equilibria and corresponding local stability are deduced. The bifurcations and related dynamical behaviors of this model are further studied thoroughly. The existence of transcritical bifurcation and saddle–node bifurcation is derived based on Sotomayor's theorem and Hopf bifurcation is well discussed. The codimension 2 bifurcation such as Bogdanov–Takens bifurcation is investigated using the normal form theory and center manifold theorem in more detail. Finally, numerical simulations are obtained to validate our analytical findings by varying the parameters. • The dynamics of a mathematical model describing the interaction of malignantglioma cells, macrophages and glioma specific CD8+T cells are discussed. • The co-existence of equilibria of the model are obtained by numerical simulation. • The existence of codimension 1 and codimension 2 bifurcations is investigated. • Extensive numerical simulations are obtained to validate our analytical findings. [ABSTRACT FROM AUTHOR]

A novel risk-sensitive (RS) control law is proposed for linear systems with stochastic system parameters. RS control laws are efficient means of handling risk in various failures in control caused by stochastic disturbances. However, stochastic parameters invoke problems, resulting controllers may become nonlinear in the state variable and incompatible with linear systems, cannot be obtained in an exact sense, and are defined only on a bounded state region. To solve these problems, this paper presents a risk-sensitive linear (RSL) control method. The important idea is that a standard RS-type cost function is converted to an expectation of a weighted cost function such that the resulting optimal controller is linear in the state. The weight is designed such that the weighted cost function preserves the characteristics of the original RS control. The designed weight allows one to derive the proposed RSL controller whose exact solution is obtained as a linear feedback law for all states. Furthermore, the RSL control law over an infinite horizon guarantees stochastic stability of the feedback system with the control law. The effectiveness of the proposed RSL control law is demonstrated by a numerical simulation. [ABSTRACT FROM AUTHOR]

Mathematical modeling of biological systems is an interesting research topic that attracted the attention of many researchers. One of the main goals in this area is the design of mathematical models that more accurately illustrate the characteristics of the real-world phenomena. Among the existing research projects, modeling of immune systems has given a growing attention due to its natural capabilities in identifying and destroying abnormal cells. The main objective of this paper is to investigate the pathological behavior of HIV-infection using a new model in fractional calculus. The proposed model is examined through three different operators of fractional derivatives. An efficient numerical method is also presented to solve these fractional models effectively. In fact, we believe that the new models presented on the basis of these three operators show various asymptomatic behaviors that do not appear during the modeling with the integer-order derivatives. Therefore, the fractional calculus provides more precise models of biological systems that help us to make more realistic judgments about their complex dynamics. Finally, simulations results are provided to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper is a continuation of our previous work (Huang and Yong, 2013) for simplifying the Fas signaling-induced apoptotic pathway identified by Hua et al. (2005) for human tumor T cells. The previous paper studied the downstream intracelluar-signaling subsystem, while the present one is concerned with the upstream death-inducing signaling complex (DISC) subsystem. Under the assumption that the bind of Fas-associated death domains and FLICE-inhibitory proteins to the DISC is much faster than that of the initiator procaspases, we greatly simplify the upstream subsystem from 35 reactions with 26 species to 6 reactions with 9 species by adopting the classical and recently justified partial equilibrium approximation method. Numerical simulations show that the simplified model is in an excellent agreement with the original model. Most importantly, the simplified model clearly reveals the key reactants and dominated pathways in the Fas signaling process, and thus provides new insights into the apoptosis. [ABSTRACT FROM AUTHOR]

In this paper we study a three-dimensional tumor–immune system interaction model consisted of tumor cells, activated T cells, and immune checkpoint inhibitor anti-PD-1. Based on the uncontrollable character of tumor cells in the absence of immune response and treatment, the growth of tumor cells is assumed to be exponential. We discuss the distribution of equilibria qualitatively and study the stability of all possible equilibria with and without anti-PD-1 drug. When no drug is applied, the model has a tumor-free equilibrium and at most one tumorous equilibrium. Biologically, there exists a threshold d T 1 for the death rate d T of T cells: when d T ≥ d T 1 tumor cells will keep growing; when d T < d T 1 tumor cells may be eradicated for some positive initial values and keep growing for some other positive initial values. For the case with anti-PD-1 treatment, the model has at most five tumor-free equilibria and two interior equilibria. Our analysis indicates that there exists a threshold γ A 1 for the intravenous continuous injection γ A : when γ A ≤ γ A 1 the fate of tumor cells is the same as the case with no drug applied; when γ A > γ A 1 the model may exhibit bistable phenomena and periodic orbits. Furthermore, we establish the existence of local Hopf bifurcation around the interior equilibrium and determine the stability of the bifurcating periodic orbits. Our simulations show that the model exhibits a stable periodic orbit which implies the long term coexistence and balance of the tumor and immune system. • Study a tumor–immune system interaction model with an immune checkpoint inhibitor. • Discuss the number and stability of all possible equilibria. • Establish the existence of Hopf bifurcation and the stability of the periodic orbit. • Carry out numerical simulations to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

HIV can infect different cell populations such as CD4+ T cells and macrophages. In this paper, we study the global property of the solution of an HIV model with two target cell populations. The model includes general nonlinear rates of viral infection and cell death. For each class of target cells, the time delay between viral entry into cells and viral production is included in the model. We obtain the basic reproductive number of the model, which is shown to provide a threshold condition determining the long-term behavior of the solution of the model. Specifically, we show that the infection-free equilibrium is globally asymptotically stable when the basic reproductive number is less than or equal to 1, and that the infected equilibrium is globally asymptotically stable when the basic reproductive number is greater than 1. We also extend the model with two target cell populations to a general model with n populations. Similar global properties are obtained for the general model. Numerical simulations are performed to illustrate the stability results and to evaluate the relative contribution to viral production from the two cell populations. [ABSTRACT FROM AUTHOR]

• This paper studies the chronic, multiphases, and relapse-remitting autoimmune disease outcomes. • Our results show that stable states, recurrent oscillations, and three co-existing limit cycles determine the rich disease outcomes. • The mathematical theory is related to the well-known Hilbert's 16th problem. • Numerical simulation demonstrates that the solution (effector T cell population) travels between two stable periodic solutions in a random manner. • Our approach presented in this paper is not only theoretically significant, but also very useful in predicting dynamical behaviors in real systems. In this paper, we investigate the influence of the effector-regulatory (Teff-Treg) T cell interaction on the T-cell-mediated autoimmune disease dynamics. The simple 3-dimensional Teff-Treg model is derived from the two-step model reduction of an established 5-dimensional model. The reduced 4- and 3-dimensional models preserve the dynamical behaviors in the original 5-dimensional model, which represents the chronic and relapse-remitting autoimmune symptoms. Moreover, we find three co-existing limit cycles in the reduced 3-dimensional model, in which two stable periodic solutions enclose an unstable one. The existence of multiple limit cycles provides a new mechanism to explain varying oscillating amplitudes of lesion grade in multiple sclerosis. The complex multiphase symptom could be caused by a noise-driven Teff population traveling between two coexisting stable periodic solutions. The simulated phase portrait and time history of coexisting limit cycles are given correspondingly. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm inspired on the T-Cell model of the immune system (i.e., an artificial immune system), which is used to solve economic dispatch problems. The proposed approach is called IA_EDP, which stands for Immune Algorithm for Economic Dispatch Problem , and it uses two versions of a redistribution power operator which tries to keep feasible the solutions that it finds. The proposed approach is validated using eight problems taken from the specialized literature. Our results are compared with respect to those obtained by several other approaches. We also perform some statistical analysis in order to determine the sensitivity of our proposed approach to its parameters. [ABSTRACT FROM AUTHOR]

• A reaction-diffusion fractional-order model for M1 oncolytic virotherapy with CTL immune response is presented. • Threshold parameters and equilibria are determined. • Stability analysis are rigorously established. • Numerical simulations are given to illustrate the analytical results. Despite many years of research, cancer continues to be a major worldwide concern. Several researchers proposed their mathematical models to understand and describe the dynamics of tumor cells under some cancer treatments. In this paper, we present a fractional partial differential equation system to describe the dynamics in space and time of the concentration of normal cells, tumor cells, nutrient, M1 virus, and cytotoxic T lymphocytes (CTL) cells, as well as the interaction between them. We study and analyze the equilibrium points of the presented system. The global stability of these equilibrium points is proved by constructing adequate Lyapunov functional for each equilibrium point. Furthermore, we give some numerical simulations to illustrate our results. [ABSTRACT FROM AUTHOR]

• Obtain threshold values and formulas of the Hopf bifurcation. • Show the interesting chaotic attractors and the periodic oscillation. • Use bifurcation theory to explain the chaotic attractor formation. • Obtain the biomedical significance corresponding to model dynamics. In this paper, a tumor and Lymphatic immune system interaction model with two time delays is discussed in which the delays describe the proliferation of tumor cells and the transmission from immature T lymphocytes to mature T lymphocytes respectively. Conditions for the asymptotic stability of the equilibrium and the existence of Hopf bifurcations are obtained by analyzing the roots of a characteristic equation. The computing formulas for the stability and the direction of the Hopf bifurcating periodic solutions are given. Numerical simulation show that different values of time delays can generate different behaviors, including the stable-state, the periodic oscillation and the chaotic attractors, as well as the coexistence of two periodic oscillations. These theoretical and numerical results not only can be useful for explaining the occurrence of chaotic attractors, but also can help for understanding the biomedical significance corresponding to the interaction dynamics of tumor cells and T lymphocytes. [ABSTRACT FROM AUTHOR]

• A mathematical model of the interactions between Th1 and Th2 cells with Treg cell inhibition and stochastic effects is developed. • Sufficient conditions for different asymptotic phases of Th1 and Th2 responses under the Treg cell regulation are obtained. • Numerical simulations are performed to identify the basins of attraction of different steady states and illustrate different dynamical scenarios. • The effect of stochastic effect under the Treg cell regulation is discussed. • The switching probability and the mean residence time are applied to study the effect of noise. T cells differentiate into Th1 or Th2 cells upon maturation to influence different patterns of the immune response. Th1 and Th2 cells regulate each other and their responses are inhibited by Treg cells. With noisy external stimulation, Th1/Th2 cell differentiation can be dynamically balanced. The underlying mechanisms of Th cell differentiation under Treg cell inhibition and the extrinsic noise effects are not yet completely understood. In this paper, a mathematical model of the interactions between Th1 and Th2 cells with Treg cell inhibition and stochastic effects is developed to study the preference of outcomes and the noise-induced hopping among different states. First, we provide the conditions for different asymptotic phases of Th1 and Th2 responses under Treg cell regulation. Numerical simulations are applied to calculate the switching probability and the mean residence time to study how the noise affects the attractiveness of different states. Our results support that due to the stronger inhibitory effect of Treg cells on Th1 cell development, the high-Th2-low-Th1 state is more attractive under small noise effects. Additionally, we show that the attractiveness of the states is affected mainly by the extrinsic noise in Th2 cell signaling. [ABSTRACT FROM AUTHOR]

In this paper, we formulate the intricate process of Human Immunodeficiency Virus (HIV) infection in a mathematical model. In the formulation of the model, the density of CD 4 + T-cells is categorized into healthy and infected classes while the density of free HIV viruses in the human host's blood is considered a separate class. It is reported that when HIV enters a human's body, it infects a large amount of CD 4 + T-cells and unbalance the supply of new cells from the thymus. Therefore, we incorporate variable source term relying on the viral load for the supply of new cells instead of using a fixed value for the supply of these cells. We implement a continuous Galerkin Petrov time discretization scheme, particularly cGP(2)-scheme to visualize the dynamical behavior of the mentioned model and a detailed description of the effects of different physical parameters of interest are depicts graphically and discuss that how the level of healthy, infected CD 4 + T-cells and free HIV particles varies concerning the emerging parameters in the model. In the proposed cGP(2)-method, two unknowns terms can be found by solving a 2 × 2 block system. This method is accurate of order 3 in the whole time interval and shows even superconvergence of order 4 in the discrete-time points. Furthermore, determine the solution of the model utilizing the fourth-order Runge-Kutta (RK4)-method and find out the absolute errors between the solutions obtained from both approaches. Finally, the validity and reliability of the proposed scheme are verified by comparing the numerical and graphical results with the RK-4 method. We examine the accuracy of the cGP(2)-sheme and observe that it produces more accurate results at relatively larger step sizes as in comparison to RK-4 scheme. Correspondence between the findings of cGP(2)-method and RK4-method reveal that the new technique is a promising tool for obtaining approximate solutions to the nonlinear systems of real-world problems. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes an adaptive immunity HIV infection model. The model describes the interaction between healthy CD 4 + T cells, silent (latent) infected cells, active infected cells, free HIV particles, Cytotoxic T lymphocytes (CTLs) and antibodies. The healthy CD 4 + T cells can be infected when they are contacted by one of the following: (i) free HIV particles, and this is known as virus-to-cell (VTC) transmission (ii) silent infected cells, and we call this mode of infection as silent HIV-infected cell-to-cell (CTC) transmission, and (iii) active infected cells, and we call this mechanism active HIV-infected CTC transmission. The incidence rates of the healthy CD 4 + T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the incidence between the silent infected cells and healthy CD 4 + T cells. We first show that the model is well-posed. Then, we show that the model has five equilibria and their existence are governed by five threshold parameters. Under a set of conditions on the general functions and the threshold parameters, we have proven the global asymptotic stability of all equilibria by using Lyapunov's method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of CTC transmission on the dynamical behavior of the system. We have shown that inclusion of CTC transmission decreases the concentration of the healthy CD4 + T cells and increases the concentrations of the infected cells and free HIV particles. [ABSTRACT FROM AUTHOR]

The article discusses the research paper "Results from a phase I study of AMG 160, a half-life extended (HLE), PSMA-targeted, bispecific T-cell engager (BiTE) immune therapy for metastatic castration-resistant prostate cancer (mCRPC)," by Ben Tran, L. Horvath, T. Dorff, et al., which was presented at the 2020 European Society for Medical Oncology Virtual Congress held on September 19-21. Also detailed are the safety and the antitumor activity of AMG 160.