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The AIDS is a chronic disease and the researchers still exert their high efforts to reach the cure of HIV infection. The most common treatment is the antiretroviral therapy (cART) and the virus can be more effected if the patients stop using cART. The other problem is that the CD8+ T cells might be exhausted by persistent immune activation by cART. This paper introduces fractional-order into a mathematical model of HIV infection combining with stem cell therapy and control the infection by the immune system cells (CD8+ T cells). The paper introduced the numerical solutions for the mathematical model. The results show that the stem cell therapy with the activation of immune system cells might causes the cure for a HIV patient. This results are consistent with medical studies. Also, we proposed the effect of the fractional order (α) on the figures of the components. [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]

Tuberculosis infection is still a major threat to humans and it may progress slowly or rapidly to clearance, latent infection, or active disease. In this paper, considering T cells can perform acceleration effect on their own recruitment, an in-host model of Mycobacterium tuberculosis is studied. Focus type and elliptic type of nilpotent singularities of codimension 3 are analyzed in this four dimensional model. Complex dynamical behaviors such as homoclinic loop, saddle-node bifurcation of limit cycle and co-existence of two limit cycles are revealed by bifurcation analysis. Especially, the slow-fast periodic solution with large-amplitude or small-amplitude is observed in numerical simulations, which provides a perfect explanation for the reactivation of latent infection. [ABSTRACT FROM AUTHOR]

Leukemia is a malignant cancer of the blood. It is the most common type of cancer in children. In this paper, a mathematical model of leukemia in terms of ordinary differential equations has been developed. We propose a model to study the spread of leukemia by considering the effect of adoptive T cell therapy. The disease dynamics are given by a system of ordinary nonlinear differential equations that describe the interaction among susceptible blood cells, infected blood cells, cancer cells, and immune cells. The model is analyzed by using the stability theory of nonlinear differential equations and numerical simulations. A major goal of this work is to determine the spread of leukemia after applying the adoptive T cell therapy. We have observed that the system is stable locally and globally if stimulation rate or antigenicity rate of immune cells is greater than a threshold value dependent on the density of immune cells in the blood. We have also observed that the external reinfusion of immune cells by adoptive T cell therapy reduces the concentration of cancer cells and infected cells in the blood, which implies that immune cells kill cancer cells after being stimulated in the body. [ABSTRACT FROM AUTHOR]

HIV can infect cells via cell-to-cell and virus-to-cell transmissions. These two types of transmission may occur in a combined way and enable viral spread. In this paper, we investigate analytically and numerically the influence of these two transmission modes, as well as the viral loss due to infection of T-cells. We introduce, analyze, and compare three mathematical models and show that viral loss due to infection of cells has little effect on the dynamics of HIV. Moreover, we show that additional conditions for the steady state stability are needed when virus-to-cell-transmission is included and a critical value for this parameter is provided. Numerical simulations illustrate the theoretical results and further investigate the differences between these systems. [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]

In this paper, we introduce ordinary and delay differential equations to describe the interactions between a malignant tumour and the immune systemin vivoin the presence of human immunodeficiency virus (HIV) infection of CD4+T-cells. In the delay model, we take into account the time lags required by the healthy effector cell components to recognize the pathogens and tumour cells. The models consist of four populations: tumour cells, healthy effector cells (CD4+T-cells), effector cells infected by HIVs and free viral particles. The presence of delay term in the model leads to a notable increase in the complexity of the observed behaviour. We investigate the qualitative behaviour of the models and find the conditions that guarantee the asymptotic stability of the steady states. Numerical simulations are provided to illustrate and extend the theoretical results. The obtained results are consistent with the real phenomena and give a better understanding of cancer immunity and viral oncogenesis. [ABSTRACT FROM PUBLISHER]

In this paper, an ordinary differential equation model of HIV infection of CD4+ T-cells with saturated reverse function is studied. We prove that if the basic reproduction number R0 < 1, the virus-free equilibrium is locally asymptotically stable. And there will exhibit backward bifurcation when R0 < 1. If R0 > 1, some feasibly sufficient conditions are obtained for the global asymptotic stability of a positive equilibrium of the model by using the theory of competitive systems, compound matrices and stability of periodic orbits. Furthermore, we also obtain the conditions for which the model exists an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

Simple Summary: As computer performance continues to grow at more affordable costs, mathematical modelling and in silico experimentation begin to play a larger role in understanding cancer evolution. The aim of our work is to formulate a control strategy for the Adaptive Cellular Therapy (ACT) that can fully eradicates the Chronic Myelogenous Leukemia (CML) cells population in a mathematical model describing interactions between naive T cells, effector T cells and CML cancer cells in the circulatory blood system. Mathematical analysis and numerical simulations allow us to conclude that it is possible to design a personalized administration protocol for the ACT in the form of a pulse train with asymmetrical waves and a fixed amplitude to achieve complete CML cancer cells eradication. The amplitude of the impulse on which the treatment is applied is given by an arithmetical combination of the parameters of the system with at least a duty cycle of 45 min/day. This paper is devoted to exploring personalized applications of cellular immunotherapy as a control strategy for the treatment of chronic myelogenous leukemia described by a dynamical system of three first-order ordinary differential equations. The latter was achieved by applying both the Localization of Compact Invariant Sets and Lyapunov's stability theory. Combination of these two approaches allows us to establish sufficient conditions on the immunotherapy treatment parameter to ensure the complete eradication of the leukemia cancer cells. These conditions are given in terms of the system parameters and by performing several in silico experimentations, we formulated a protocol for the therapy application that completely eradicates the leukemia cancer cells population for different initial tumour concentrations. The formulated protocol does not dangerously increase the effector T cells population. Further, complete eradication is considered when solutions go below a finite critical value below which cancer cells cannot longer persist; i.e., one cancer cell. Numerical simulations are consistent with our analytical results. [ABSTRACT FROM AUTHOR]

This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of CD4+ T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

Abstract: Epstein–Barr virus (EBV) is an important human pathogen that establishes a life-long persistent infection and for which no precise animal model exists. In this paper, we describe in detail an agent-based model and computer simulation of EBV infection. Agents representing EBV and sets of B and T lymphocytes move and interact on a three-dimensional grid approximating Waldeyer''s ring, together with abstract compartments for lymph and blood. The simulation allows us to explore the development and resolution of virtual infections in a manner not possible in actual human experiments. Specifically, we identify parameters capable of inducing clearance, persistent infection, or death. [Copyright &y& Elsevier]

In vivo imaging of cytotoxic T lymphocyte (CTL) killing activity revealed that infected cells have a higher observed probability of dying after multiple contacts with CTLs. We developed a three-dimensional agent-based model to discriminate different hypotheses about how infected cells get killed based on quantitative 2-photon in vivo observations. We compared a constant CTL killing probability with mechanisms of signal integration in CTL or infected cells. The most likely scenario implied increased susceptibility of infected cells with increasing number of CTL contacts where the total number of contacts was a critical factor. However, when allowing in silico T cells to initiate new interactions with apoptotic target cells (zombie contacts), a contact history independent killing mechanism was also in agreement with experimental datasets. The comparison of observed datasets to simulation results, revealed limitations in interpreting 2-photon data, and provided readouts to distinguish CTL killing models. Author summary: Despite having a clear understanding of cytotoxic T lymphocyte (CTL) mediated cytotoxicity mechanisms, its quantitative dynamics remain unexplored at a cellular level. We developed an agent-based model to compare different hypotheses for mechanisms of CTL mediated cytotoxicity that could lead to an increased killing of infected cells at higher interactions with CTLs as seen in vivo. We showed that this behaviour can be explained by modulation of properties by infected cells or CTLs with increasing number of contacts. For the modulation, we compared two modes of signal integration and showed that the number of contacts is the main determinant of cell death. We also studied the impact of contacts between CTLs and apoptotic infected cells on observed killing properties. [ABSTRACT FROM AUTHOR]

The relationship between tumor immune responses and tumor neoantigens is one of the most fundamental and unsolved questions in tumor immunology, and is the key to understanding the inefficiency of immunotherapy observed in many cancer patients. However, the properties of neoantigens that can elicit immune responses remain unclear. This biological problem can be represented and solved under a multiple instance learning framework, which seeks to model multiple instances (neoantigens) within each bag (patient specimen) with the continuous response (T cell infiltration) observed for each bag. To this end, we develop a Bayesian multiple instance regression method, named BMIR, using a Gaussian distribution to address continuous responses and latent binary variables to model primary instances in bags. By means of such Bayesian modeling, BMIR can learn a function for predicting the bag-level responses and for identifying the primary instances within bags, as well as give access to Bayesian statistical inference, which are elusive in existing works. We demonstrate the superiority of BMIR over previously proposed optimization-based methods for multiple instance regression through simulation and real data analyses. Our method is implemented in R package entitled "BayesianMIR" and is available at https://github.com/inmybrain/BayesianMIR. [ABSTRACT FROM AUTHOR]

In this study, an extended spatiotemporal model of a human immunodeficiency virus (HIV) CD4+ T cell with a drug therapy effect is proposed for the numerical investigation. The stability analysis of equilibrium points is carried out for temporal and spatiotemporal cases where stability regions in the space of parameters for each case are acquired. Three numerical techniques are used for the numerical simulations of the proposed HIV reaction–diffusion system. These techniques are the backward Euler, Crank–Nicolson, and a proposed structure preserving an implicit technique. The proposed numerical method sustains all the important characteristics of the proposed HIV model such as positivity of the solution and stability of equilibria, whereas the other two methods have failed to do so. We also prove that the proposed technique is positive, consistent, and Von Neumann stable. The effect of different values for the parameters is investigated through numerical simulations by using the proposed method. The stability of the proposed model of the HIV CD4+ T cell with the drug therapy effect is also analyzed. [ABSTRACT FROM AUTHOR]

In silico T-cell epitope prediction plays an important role in immunization experimental design and vaccine preparation. Currently, most epitope prediction research focuses on peptide processing and presentation, e.g., proteasomal cleavage, transporter associated with antigen processing (TAP), and major histocompatibility complex (MHC) combination. To date, however, the mechanism for the immunogenicity of epitopes remains unclear. It is generally agreed upon that T-cell immunogenicity may be influenced by the foreignness, accessibility, molecular weight, molecular structure, molecular conformation, chemical properties, and physical properties of target peptides to different degrees. In this work, we tried to combine these factors. Firstly, we collected significant experimental HLA-I T-cell immunogenic peptide data, as well as the potential immunogenic amino acid properties. Several characteristics were extracted, including the amino acid physicochemical property of the epitope sequence, peptide entropy, eluted ligand likelihood percentile rank (EL rank(%)) score, and frequency score for an immunogenic peptide. Subsequently, a random forest classifier for T-cell immunogenic HLA-I presenting antigen epitopes and neoantigens was constructed. The classification results for the antigen epitopes outperformed the previous research (the optimal AUC = 0.81 , external validation data set AUC = 0.77). As mutational epitopes generated by the coding region contain only the alterations of one or two amino acids, we assume that these characteristics might also be applied to the classification of the endogenic mutational neoepitopes also called "neoantigens." Based on mutation information and sequence-related amino acid characteristics, a prediction model of a neoantigen was established as well (the optimal AUC = 0.78). Further, an easy-to-use web-based tool "INeo-Epp" was developed for the prediction of human immunogenic antigen epitopes and neoantigen epitopes. [ABSTRACT FROM AUTHOR]

Leukocyte adhesion is important for the proper functioning of the immune system. While leukocyte homing is mediated by adhesion receptors, the activation of these receptors is modulated by intracellular signaling molecules. In Leukocyte Adhesion Deficiency Type 3, the loss of the kindlin-3 prevents the activation of Leukocyte Function-associated Antigen-1 (LFA-1), which leads to a defect in adhesion, causing recurrent infections and bleeding disorders. Here, we use Integrated Signaling Adhesive Dynamics, a computer model of leukocyte rolling and adhesion combined with a simulated intracellular signaling cascade, to predict the response of T cells to depletion of kindlin-3. Our model predicts that cell adhesion is hypersensitive to the amount of kindlin-3 in the cell, while the rolling velocity is independent of kindlin-3 concentration. In addition, our simulation predicted that the time to stop, an important metric of adhesion, would increase with decreasing kindlin-3 expression. These predictions were confirmed experimentally in experiments using Jurkat cells with reduced expression of kindlin-3. These results suggest that Adhesive Dynamics is a versatile tool for quantifying adhesion in the immune response and predicting the effects of engineering cellular components. [ABSTRACT FROM AUTHOR]

In the immune system, T cells can quickly discriminate between foreign and self ligands with high accuracy. There is evidence that T-cells achieve this remarkable performance utilizing a network architecture based on a generalization of kinetic proofreading (KPR). KPR-based mechanisms actively consume energy to increase the specificity beyond what is possible in equilibrium. An important theoretical question that arises is to understand the trade-offs and fundamental limits on accuracy, speed, and dissipation (energy consumption) in KPR and its generalization. Here, we revisit this question through numerical simulations where we simultaneously measure the speed, accuracy, and energy consumption of the KPR and adaptive sorting networks for different parameter choices. Our simulations highlight the existence of a “feasible operating regime” in the speed-energy-accuracy plane where T-cells can quickly differentiate between foreign and self ligands at reasonable energy expenditure. We give general arguments for why we expect this feasible operating regime to be a generic property of all KPR-based biochemical networks and discuss implications for our understanding of the T cell receptor circuit. [ABSTRACT FROM AUTHOR]

We consider general virus dynamics model with virus-to-target and infected-to-target infections. The model is incorporated by intracellular discrete or distributed time delays. We assume that the virus-target and infected-target incidences, the production, and clearance rates of all compartments are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The non-negativity and boundedness of the solutions are studied. The existence and stability of the equilibria are determined by a threshold parameter. We use suitable Lyapunov functionals and apply LaSalle's invariance principle to prove the global asymptotic stability of the all equilibria of the model. We confirm the theoretical results by numerical simulations. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The advent of two-photon microscopy now reveals unprecedented, detailed spatio-temporal data on cellular motility and interactions in vivo. Understanding cellular motility patterns is key to gaining insight into the development and possible manipulation of the immune response. Computational simulation has become an established technique for understanding immune processes and evaluating hypotheses in the context of experimental data, and there is clear scope to integrate microscopy-informed motility dynamics. However, determining which motility model best reflects in vivo motility is non-trivial: 3D motility is an intricate process requiring several metrics to characterize. This complicates model selection and parameterization, which must be performed against several metrics simultaneously. Here we evaluate Brownian motion, Lévy walk and several correlated random walks (CRWs) against the motility dynamics of neutrophils and lymph node T cells under inflammatory conditions by simultaneously considering cellular translational and turn speeds, and meandering indices. Heterogeneous cells exhibiting a continuum of inherent translational speeds and directionalities comprise both datasets, a feature significantly improving capture of in vivo motility when simulated as a CRW. Furthermore, translational and turn speeds are inversely correlated, and the corresponding CRW simulation again improves capture of our in vivo data, albeit to a lesser extent. In contrast, Brownian motion poorly reflects our data. Lévy walk is competitive in capturing some aspects of neutrophil motility, but T cell directional persistence only, therein highlighting the importance of evaluating models against several motility metrics simultaneously. This we achieve through novel application of multi-objective optimization, wherein each model is independently implemented and then parameterized to identify optimal trade-offs in performance against each metric. The resultant Pareto fronts of optimal solutions are directly contrasted to identify models best capturing in vivo dynamics, a technique that can aid model selection more generally. Our technique robustly determines our cell populations’ motility strategies, and paves the way for simulations that incorporate accurate immune cell motility dynamics. [ABSTRACT FROM AUTHOR]

We consider a mathematical model that describes a viral infection with lytic and non-lytic immune responses. One of the main features of the model is that it includes a rate of linear activation of cytotoxic T lymphocytes (CTLs) immune response, a constant production rate of CTLs export from thymus, and a nonlinear attack rate for each immune effector mechanism. Stability of the infection-free equilibrium, and existence, uniqueness and stability of an immune-controlled equilibrium, are investigated. The stability results are given in terms of the basic reproductive number. We use the method of Lyapunov functions to study the global stability of the infection-free equilibrium and the immune-controlled equilibrium. We give a sufficient condition on the non-lytic-immune attack rate for the global asymptotic stability of the immune-controlled equilibrium. By theoretical analysis and numerical simulations, we show that the lytic and non-lytic activities are required to combat a viral infection. [ABSTRACT FROM AUTHOR]

TGF- β is an immunoregulatory protein that contributes to inadequate antitumor immune responses in cancer patients. Recent experimental data suggests that TGF- β inhibition alone, provides few clinical benefits, yet it can significantly amplify the anti-tumor immune response when combined with a tumor vaccine. We develop a mathematical model in order to gain insight into the cooperative interaction between anti-TGF- β and vaccine treatments. The mathematical model follows the dynamics of the tumor size, TGF- β concentration, activated cytotoxic effector cells, and regulatory T cells. Using numerical simulations and stability analysis, we study the following scenarios: a control case of no treatment, anti-TGF- β treatment, vaccine treatment, and combined anti-TGF- β vaccine treatments. We show that our model is capable of capturing the observed experimental results, and hence can be potentially used in designing future experiments involving this approach to immunotherapy. [ABSTRACT FROM AUTHOR]

Over the past decade, multi-level complex behavior and reactive nature of biological systems, has been a focus point for the biomedical community. We have developed a computational approach, termed Reactive Animation (RA) for simulating such complex biological systems. RA is an approach for describing the dynamic characteristics of biological systems based on facts collected from experiments. These data are integrated bottom-up by computational tools and methods for reactive systems development and are simulated concomitantly to a front-end user friendly visualization and reporting systems. Using RA, the experimenter may intervene mid-simulation, suggest new hypotheses for cellular and molecular interactions, apply them to the simulation and observe their resulting outcomes ''on-line''. Several RA models have been developed including models of T cell activation, thymocyte development and pancreatic organogenesis, which are describe in the in this review. [ABSTRACT FROM AUTHOR]

We develop an agent-based framework to model the emergence of collective emotions, which is applied to online communities. Agent's individual emotions are described by their valence and arousal. Using the concept of Brownian agents, these variables change according to a stochastic dynamics, which also considers the feedback from online communication. Agents generate emotional information, which is stored and distributed in a field modeling the online medium. This field affects the emotional states of agents in a non-linear manner. We derive conditions for the emergence of collective emotions, observable in a bimodal valence distribution. Dependent on a saturated or a superlinear feedback between the information field and the agent's arousal, we further identify scenarios where collective emotions only appear once or in a repeated manner. The analytical results are illustrated by agent-based computer simulations. Our framework provides testable hypotheses about the emergence of collective emotions, which can be verified by data from online communities. [ABSTRACT FROM AUTHOR]

Despite the various processing steps involved in V(D)J recombination, which could potentially introduce many biases in the length distribution of complementarity determining region 3 (CDR3) segments, the observed CDR3 length distributions for complete repertoires are very close to a normal-like distribution. This raises the question of whether this distribution is simply a result of the random steps included in the process of gene rearrangement, or has been optimized during evolution. We have addressed this issue by constructing a simulation of gene rearrangement, which takes into account the DNA modification steps included in the process, namely hairpin opening, nucleotide additions, and nucleotide deletions. We found that the near-Gaussian- shape of CDR3 length distribution can only be obtained under a relatively narrow set of parameter values, and thus our model suggests that specific biases govern the rearrangement process. In both B-cell receptor (BCR) heavy chain and T-cell receptor β chain, we obtained a Gaussian distribution using identical parameters, despite the difference in the number and the lengths of the D segments. Hence our results suggest that these parameters most likely reflect the optimal conditions under which the rearrangement process occurs. We have subsequently used the insights gained in this study to estimate the probability of occurrence of two exactly identical BCRs over the course of a human lifetime. Whereas identical rearrangements of the heavy chain are highly unlikely to occur within one human lifetime, for the light chain we found that this probability is not negligible, and hence the light chain CDR3 alone cannot serve as an indicator of B-cell clonality.Immunology and Cell Biology (2007) 85, 323–332; doi:10.1038/sj.icb.7100055; published online 3 April 2007 [ABSTRACT FROM AUTHOR]