scholarly journals Dynamical Behaviour of a Tumor-Immune System with Chemotherapy and Optimal Control

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Swarnali Sharma ◽  
G. P. Samanta

We have considered a tumor growth model with the effect of tumor-immune interaction and chemotherapeutic drug. We have considered two immune components—helper (resting) T-cells which stimulate CTLs and convert them into active (hunting) CTL cells and active (hunting) CTL cells which attack, destroy, or ingest the tumor cells. In our model there are four compartments, namely, tumor cells, active CTL cells, helper T-cells, and chemotherapeutic drug. We have discussed the behaviour of the solutions of our system. The dynamical behaviour of our system by analyzing the existence and stability of the system at various equilibrium points is discussed elaborately. We have set up an optimal control problem relative to the model so as to minimize the number of tumor cells and the chemotherapeutic drug administration. Here we used a quadratic control to quantify this goal and have considered the administration of chemotherapy drug as control to reduce the spread of the disease. The important mathematical findings for the dynamical behaviour of the tumor-immune model with control are also numerically verified using MATLAB. Finally, epidemiological implications of our analytical findings are addressed critically.

2021 ◽  
Author(s):  
kaushik dehingia

Abstract In this study, a cancer eradication model involving effector cells in the presence of gene therapy, immunotherapy, and chemotherapy has been proposed. Boundedness and positiveness of the solutions in the respective feasible domains of the proposed model are verified. Conditions for which the equilibrium points of the system are stable have been derived. Amounts of immunotherapy to be injected to a patient for eradication of cancerous tumor cells have been found. To minimize the chemotherapy drug-induced toxicity to the patient, an optimal control problem for the system has been constructed and solved. Numerical and graphical results have been presented. Through the investigation, it was seen that tumor cells can be eliminated in a specific time interval with the control of chemotherapeutic drug concentration.


Blood ◽  
2007 ◽  
Vol 110 (11) ◽  
pp. 3568-3568 ◽  
Author(s):  
Yenlin Huang ◽  
Anne Moreau ◽  
Jehan Dupuis ◽  
Berthold Streubel ◽  
Barbara Petit ◽  
...  

Abstract Nodal peripheral T-cell lymphomas represent a heterogeneous category, composed of three entities: anaplastic large cell lymphomas, peripheral T-cell lymphomas unspecified (PTCLu) and angioimmunoblastic T-cell lymphomas (AITL). The later entity has been recently recognized to derive from follicular helper T cells (TFH). Among PTCLu - which represents an ill-defined entity - a peculiar form with follicular growth pattern (PTCL-F) has been recently reported, and one article stated their association with t(5 ;9)(q33 ;q22) involving ITK and SYK (Leukemia2006; 20: 313–318). However, the origin of tumor cells and clinical aspects of this group of PTCL-F are still unknown. The aim of this study was to analyse a series of PTCL-F to describe their clinical and histopathological aspects, to identify their cell of origin, and their relationship with AITL. Fourty-two patients from 32 to 85 years of age with 51 biopsies were selected from three Departments of Pathology (Creteil, n=24, Nantes n=13, Vienna n=14). All patients showed histopathologic features of PTCL-F in at least one biopsy. Biopsies were classified into three categories according to predominant morphological features at low power magnification: follicular lymphoma-like (n=7), progressive transformation of germinal center-like (n=22), and AITL-like features with follicular colonization (n=19). Several cases have combinations of patterns. The neoplastic population is characterized by medium-sized cells with clear cytoplasm surrounded by IgD+ B-cells. Tumor cells are of helper T-cell immunophenotype [CD2+ (33/33 = 100%), CD3+ (45/48 = 93%), CD4+ (35/42 = 83%), CD5+ (39/39 = 100%), CD7+ (7/37 = 19%)], with frequent expression of CD10 (29/43 = 67%) and of TFH markers [PDCD-1 (32/36 = 88%), CXCL13+ (33/38 = 87%), BCL6+ (15/25 = 60%), CD57+ (9/16 = 56%)]. Scattered CD20+ B-immunoblasts (27/28 = 96%) and EBV+ cells (18/30 = 60%) are also frequently observed. Seven out of 31 patients (22%) in the 3 morphological patterns have t(5 ;9)(q33 ;q22) detected by fluorescent in situ hybridization. At prentation and/or at relapse, most patients had multiple lymphadenopathies (19/23 = 83%) and disseminated disease (stages III–IV, 22/28 = 79%). Skin lesions and B symptoms were present in 7/19 (37%) and 6/22 (27%) patients, respectively. In addition, 2 patients with sequential biopsies disclosed typical clinical & histopathological features of AITL in one episode. Our results show that this rare form of PTCL has an immunophenotype indicative of TFH origin, is associated with t(5 ;9) in a proportion of cases, shows some similarities in morphology and immunophenotype with AITL, suggesting a relationship, and generates diagnostic pitfalls, especially with atypical reactive lymphoid lesions and some B-cell lymphomas. The use of immunohistochemistry with TFH markers and molecular studies can help to make a correct diagnosis.


2019 ◽  
Vol 12 (07) ◽  
pp. 1950075
Author(s):  
Huixia Li ◽  
Shaoli Wang ◽  
Fei Xu

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 [Formula: see text] as bifurcation parameter, there exists saddle-node bifurcation. Besides, there exists a critical value [Formula: see text], at which a Hopf bifurcation occurs. The stability and direction of Hopf bifurcation are discussed.


1976 ◽  
Vol 144 (4) ◽  
pp. 1116-1120 ◽  
Author(s):  
H Shiku ◽  
T Takahashi ◽  
M A Bean ◽  
L J Old ◽  
H F Oettgen

Our present and previous findings may be summarized as follows: The phenotype of C57BL/6 (B6) cytotoxic cells for allogeneic target cells is Thy-1+, Ly-1- Ly-2/3+, MSLA+, and Ig-. the phenotype of B6 cytotoxic cells for syngeneic tumor cells is Thy-1+, Ly-1+, Ly-2/3+, MSLA+, and Ig-. The phenotype of B6 cytotoxic cells for syngeneic tumor cells is Thy-1+, Ly-1+, Ly-2/3+, MSLA+, AND Ig-. Thus, differences in Ly phenotype appear to be exhibited not only by cytotoxic T cells as opposed to helper T cells, but also within subcategories of cytotoxic T cells.


2021 ◽  
Vol 6 (10) ◽  
pp. 11530-11549
Author(s):  
Kaushik Dehingia ◽  
◽  
Hemanta Kumar Sarmah ◽  
Kamyar Hosseini ◽  
Khadijeh Sadri ◽  
...  

<abstract><p>This study addresses a cancer eradication model involving effector cells in the presence of gene therapy, immunotherapy, and chemotherapy. The main objective of this study is to understand the optimal effect of immuno-chemotherpay in the presence of gene therapy. The boundedness and positiveness of the solutions in the respective feasible domains of the proposed model are verified. Conditions for which the equilibrium points of the system exist and are stable have been derived. An optimal control problem for the system has been constructed and solved to minimize the immuno-chemotherapy drug-induced toxicity to the patient. Amounts of immunotherapy to be injected into a patient for eradication of cancerous tumor cells have been found. Numerical and graphical results have been presented. From the results, it is seen that tumor cells can be eliminated in a specific time interval with the control of immuno-chemotherapeutic drug concentration.</p></abstract>


2021 ◽  
Vol 16 ◽  
pp. 735-754
Author(s):  
Eshetu Dadi Gurmu ◽  
Boka Kumsa Bola ◽  
Purnachandra Rao Koya

In this study, a nonlinear deterministic mathematical model of Human Papillomavirus was formulated. The model is studied qualitatively using the stability theory of differential equations. The model is analyzed qualitatively for validating the existence and stability of disease ¬free and endemic equilibrium points using a basic reproduction number that governs the disease transmission. It's observed that the model exhibits a backward bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies viz. prevention strategy, treatment strategy, and screening strategy. Numerical results of the optimal control model reveal that a combination of prevention, screening, and treatment is the most effective strategy to wipe out the disease in the community.


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Cristiana J. Silva

<p style='text-indent:20px;'>In this paper, we propose a time-delayed HIV/AIDS-PrEP model which takes into account the delay on pre-exposure prophylaxis (PrEP) distribution and adherence by uninfected persons that are in high risk of HIV infection, and analyze the impact of this delay on the number of individuals with HIV infection. We prove the existence and stability of two equilibrium points, for any positive time delay. After, an optimal control problem with state and control delays is proposed and analyzed, where the aim is to find the optimal strategy for PrEP implementation that minimizes the number of individuals with HIV infection, with minimal costs. Different scenarios are studied, for which the solutions derived from the Minimum Principle for Multiple Delayed Optimal Control Problems change depending on the values of the time delays and the weights constants associated with the number of HIV infected individuals and PrEP. We observe that changes on the weights constants can lead to a passage from <i>bang-singular-bang</i> to <i>bang-bang</i> extremal controls.</p>


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