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Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response  [PDF]
Radouane Yafia
Discrete Dynamics in Nature and Society , 2006, DOI: 10.1155/ddns/2006/95296
Abstract: The dynamics of the model for tumor-immune system competition with negative immune response and with one delay investigated. We show that the asymptotic behavior depends crucially on the time delay parameter. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state, by using the delay as a parameter of bifurcation. The obtained results provide the oscillations given by the numerical study in M. Gałach (2003), which are observed in reality by Kirschner and Panetta (1998).
Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response  [PDF]
Radouane Yafia
Discrete Dynamics in Nature and Society , 2006, DOI: 10.1155/ddns/2006/58463
Abstract: This paper is devoted to the study of the stability of limit cycles of a system of nonlinear delay differential equations with a discrete delay. The system arises from a model of population dynamics describing the competition between tumor and immune system with negative immune response. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We establish an explicit algorithm for determining the direction of the Hopf bifurcation and the stability or instability of the bifurcating branch of periodic solutions, using the methods presented by Diekmann et al.
Modeling the Dichotomy of the Immune Response to Cancer: Cytotoxic Effects and Tumor-Promoting Inflammation  [PDF]
Kathleen P. Wilkie,Philip Hahnfeldt
Quantitative Biology , 2013,
Abstract: Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor development and cancer dormancy. To study this biological phenomenon theoretically we construct a minimally parameterized framework that incorporates all aspects of the immune response. We combine the effects of all immune cell types, general principles of self-limited logistic growth, and the physical process of inflammation into one quantitative setting. Simulations suggest that while there are pro-tumor or antitumor immunogenic responses characterized by larger or smaller final tumor volumes, respectively, each response involves an initial period where tumor growth is stimulated beyond that of growth without an immune response. The mathematical description is non-identifiable which allows us to capture inherent biological variability in tumor growth that can significantly alter tumor-immune dynamics and thus treatment success rates. The ability of this model to predict immunomodulation of tumor growth may offer a template for the design of novel treatment approaches that exploit immune response to improve tumor suppression, including the potential attainment of an immune-induced dormant state.
Time-delayed model of immune response in plants  [PDF]
G. Neofytou,Y. N. Kyrychko,K. B. Blyuss
Quantitative Biology , 2015, DOI: 10.1016/j.jtbi.2015.10.020
Abstract: In the studies of plant infections, the plant immune response is known to play an essential role. In this paper we derive and analyse a new mathematical model of plant immune response with particular account for post-transcriptional gene silencing (PTGS). Besides biologically accurate representation of the PTGS dynamics, the model explicitly includes two time delays to represent the maturation time of the growing plant tissue and the non-instantaneous nature of the PTGS. Through analytical and numerical analysis of stability of the steady states of the model we identify parameter regions associated with recovery and resistant phenotypes, as well as possible chronic infections. Dynamics of the system in these regimes is illustrated by numerical simulations of the model.
Control of the Adaptive Immune Response by Tumor Vasculature  [PDF]
Laetitia Mauge,Magali Terme,Eric Tartour,Dominique Helley
Frontiers in Oncology , 2014, DOI: 10.3389/fonc.2014.00061
Abstract: The endothelium is nowadays described as an entire organ that regulates various processes: vascular tone, coagulation, inflammation, and immune cell trafficking, depending on the vascular site and its specific microenvironment as well as on endothelial cell-intrinsic mechanisms like epigenetic changes. In this review, we will focus on the control of the adaptive immune response by the tumor vasculature. In physiological conditions, the endothelium acts as a barrier regulating cell trafficking by specific expression of adhesion molecules enabling adhesion of immune cells on the vessel, and subsequent extravasation. This process is also dependent on chemokine and integrin expression, and on the type of junctions defining the permeability of the endothelium. Endothelial cells can also regulate immune cell activation. In fact, the endothelial layer can constitute immunological synapses due to its close interactions with immune cells, and the delivery of co-stimulatory or co-inhibitory signals. In tumor conditions, the vasculature is characterized by an abnormal vessel structure and permeability, and by a specific phenotype of endothelial cells. All these abnormalities lead to a modulation of intra-tumoral immune responses and contribute to the development of intra-tumoral immunosuppression, which is a major mechanism for promoting the development, progression, and treatment resistance of tumors. The in-depth analysis of these various abnormalities will help defining novel targets for the development of anti-tumoral treatments. Furthermore, eventual changes of the endothelial cell phenotype identified by plasma biomarkers could secondarily be selected to monitor treatment efficacy.
Immune Response to Combination Therapy for Non-Hodgkin Lymphomas  [PDF]
Robert F. Weiss, Merlin G. Miller, John F. Cronin
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0081672
Abstract: A parametric model of tumor response to combination therapy in the presence of an immune system is described. Synergistic mechanisms which induce tumor regression are simulated with a coupled set of equations. The simulations are first compared to tumor history data obtained with a SCID mouse model to determine key parameters; predictions are then made for an immune-competent animal. The minimum immune cell birth rate relative to malignant B-cell birth rate necessary to induce tumor regression is determined, and optimization of drug combinations in the presence of an immune response is explored. The delayed effect of an immune response relative to drug scheduling is examined, and a mechanism for disease transformation in heterogeneous tumors is proposed.
Chaos in a Tumor Growth Model with Delayed Responses of the Immune System
M. Saleem,Tanuja Agrawal
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/891095
Abstract: A simple prey-predator-type model for the growth of tumor with discrete time delay in the immune system is considered. It is assumed that the resting and hunting cells make the immune system. The present model modifies the model of El-Gohary (2008) in that it allows delay effects in the growth process of the hunting cells. Qualitative and numerical analyses for the stability of equilibriums of the model are presented. Length of the time delay that preserves stability is given. It is found that small delays guarantee stability at the equilibrium level (stable focus) but the delays greater than a critical value may produce periodic solutions through Hopf bifurcation and larger delays may even lead to chaotic attractors. Implications of these results are discussed.
Role of Gene Methylation in Antitumor Immune Response: Implication for Tumor Progression  [PDF]
Alfonso Serrano,Isabel Castro-Vega,Maximino Redondo
Cancers , 2011, DOI: 10.3390/cancers3021672
Abstract: Cancer immunosurveillance theory has emphasized the role of escape mechanisms in tumor growth. In this respect, a very important factor is the molecular characterization of the mechanisms by which tumor cells evade immune recognition and destruction. Among the many escape mechanisms identified, alterations in classical and non-classical HLA (Human Leucocyte Antigens) class I and class II expression by tumor cells are of particular interest. In addition to the importance of HLA molecules, tumor-associated antigens and accessory/co-stimulatory molecules are also involved in immune recognition. The loss of HLA class I antigen expression and of co-stimulatory molecules can occur at genetic, transcriptional and post-transcriptional levels. Epigenetic defects are involved in at least some mechanisms that preclude mounting a successful host-antitumor response involving the HLA system, tumor-associated antigens, and accessory/co-stimulatory molecules. This review summarizes our current understanding of the role of methylation in the regulation of molecules involved in the tumor immune response.
Mirtazapine Inhibits Tumor Growth via Immune Response and Serotonergic System  [PDF]
Chun-Kai Fang, Hong-Wen Chen, I-Tsang Chiang, Chia-Chieh Chen, Jyh-Fei Liao, Ton-Ping Su, Chieh-Yin Tung, Yosuke Uchitomi, Jeng-Jong Hwang
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0038886
Abstract: To study the tumor inhibition effect of mirtazapine, a drug for patients with depression, CT26/luc colon carcinoma-bearing animal model was used. BALB/c mice were randomly divided into six groups: two groups without tumors, i.e. wild-type (no drug) and drug (mirtazapine), and four groups with tumors, i.e. never (no drug), always (pre-drug, i.e. drug treatment before tumor inoculation and throughout the experiment), concurrent (simultaneously tumor inoculation and drug treatment throughout the experiment), and after (post-drug, i.e. drug treatment after tumor inoculation and throughout the experiment). The “psychiatric” conditions of mice were observed from the immobility time with tail suspension and spontaneous motor activity post tumor inoculation. Significant increase of serum interlukin-12 (sIL-12) and the inhibition of tumor growth were found in mirtazapine-treated mice (always, concurrent, and after) as compared with that of never. In addition, interferon-γ level and immunocompetent infiltrating CD4+/CD8+ T cells in the tumors of mirtazapine-treated, tumor-bearing mice were significantly higher as compared with that of never. Tumor necrosis factor-α (TNF-α) expressions, on the contrary, are decreased in the mirtazapine-treated, tumor-bearing mice as compared with that of never. Ex vivo autoradiography with [123I]ADAM, a radiopharmaceutical for serotonin transporter, also confirms the similar results. Notably, better survival rates and intervals were also found in mirtazapine-treated mice. These findings, however, were not observed in the immunodeficient mice. Our results suggest that tumor growth inhibition by mirtazapine in CT26/luc colon carcinoma-bearing mice may be due to the alteration of the tumor microenvironment, which involves the activation of the immune response and the recovery of serotonin level.
Global Dynamics of a Delayed HIV-1 Infection Model with CTL Immune Response  [PDF]
Yunfei Li,Rui Xu,Zhe Li,Shuxue Mao
Discrete Dynamics in Nature and Society , 2011, DOI: 10.1155/2011/673843
Abstract: A delayed HIV-1 infection model with CTL immune response is investigated. By using suitable Lyapunov functionals, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infection is less than or equal to unity; if the basic reproduction ratio for CTL immune response is less than or equal to unity and the basic reproduction ratio for viral infection is greater than unity, the CTL-inactivated infection equilibrium is globally asymptotically stable; if the basic reproduction ratio for CTL immune response is greater than unity, the CTL-activated infection equilibrium is globally asymptotically stable. 1. Introduction Recently, many mathematical models have been developed to describe the infection with HIV-1 (human immunodeficiency virus 1). By investigating these models, researchers have gained much important knowledge about the HIV-1 pathogenesis and have enhanced progress in the understanding of HIV-1 infection (see, e.g., [1–4]). It is pointed out by the work of [5] that immune response is universal and necessary to eliminate or control the disease during viral infections. In particular, as a part of innate response, cytotoxic T lymphocytes (CTLs) play a particularly important role in antiviral defense by attacking infected cells. Thus, many authors have studied the mathematical modelling of viral dynamics with CTL immune response (see, e.g., [5–9]). In [7], Nowak and Bangham considered an HIV-1 infection model with CTL immune response which is described by the following differential equations: where , , , and represent the densities of uninfected target cells, infected cells, virions, and CTL cells at time , respectively. Uninfected cells are produced at rate , die at rate , and become infected cells at rate . Infected cells are produced from uninfected cells at rate and die at rate . The parameter accounts for the strength of the lytic component. Free virions are produced from uninfected cells at rate and are removed at rate . The parameter is the death rate for CTLs, and describes the rate of CTL immune response activated by the infected cells. Moreover, infection rate plays an important role in the modelling of epidemic dynamics. Holling type-II functional response seems more reasonable than the bilinear incidence rate (see, [10]). In [11], by stability analysis, Song and Avidan obtained that the system with the bilinear incidence rate was an extreme case of the model with Holling type-II functional response term. In [3, 4, 7], the researchers used ordinary differential equations
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