An extended mathematical model of tumor growth and its interaction with the immune system, to be used for developing an optimized immunotherapy treatment protocol

Qomlaqi, Milad; Bahrami, Fariba; Ajami, Mansoureh; Hajati, Jamshid

doi:10.1016/j.mbs.2017.07.006

Cited by 44 publications

(15 citation statements)

References 31 publications

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“…The techniques and results used in treating the third-order transcendental equations in Ruan et al [105] can be employed to analyze the stability and bifurcations in such three-dimensional models with delays. Higher-dimensional models with delays can be found in Abdulrashid et al [1], Barbarossa et al [12], Feyissa and Banerjee [51], Qomlaqi et al [99], Yu and Wei [126], Yu et al [127,128], and the references cited therein.…”

Section: The Positive (Coexistence) Equilibriummentioning

confidence: 99%

Nonlinear dynamics in tumor-immune system interaction models with delays

Ruan¹

2021

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, we review some recent results on the nonlinear dynamics of delayed differential equation models describing the interaction between tumor cells and effector cells of the immune system, in which the delays represent times necessary for molecule production, proliferation, differentiation of cells, transport, etc. First we consider a tumor-immune system interaction model with a single delay and present results on the existence and local stability of equilibria as well as the existence of Hopf bifurcation in the model when the delay varies. Second we investigate a tumor-immune system interaction model with two delays and show that the model undergoes various possible bifurcations including Hopf, Bautin, Fold-Hopf (zero-Hopf), and Hopf-Hopf bifurcations. Finally we discuss a tumor-immune system interaction model with three delays and demonstrate that the model exhibits more complex behaviors including chaos. Numerical simulations are provided to illustrate the nonlinear dynamics of the delayed tumor-immune system interaction models. More interesting issues and questions on modeling and analyzing tumor-immune dynamics are given in the discussion section.

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Section: The Positive (Coexistence) Equilibriummentioning

confidence: 99%

Nonlinear dynamics in tumor-immune system interaction models with delays

Ruan¹

2021

Discrete &Amp; Continuous Dynamical Systems - B

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“…They performed a sensitivity analysis and observed highly complex bistability, but not of the type discovered here, and in a four-variable model. In a well-documented paper, Qomlaqi et al (36) modeled adaptive immunity in immunotherapy and showed how efficacy depended on dosage dynamics, but without analyzing the complex stability of the system. Kumar developed a three-component model that simulated the dynamic response of the immune system to a pathogen (54).…”

Section: This Model's Noveltymentioning

confidence: 99%

“…Rullmann et al developed the Entelos Rheumatoid Arthritis Physiolab platform to predict the therapeutic effects of drugs (33). Separately, the National Institute of Allergy and Infectious Diseases established the Systems Biology for Infectious Diseases Research (SysBio) program that facilitates research lines in systems influenza, systems virology, systems biology of enteropathogens, and Mycobacterium tuberculosis systems biology (34), and there is much application in the realm of tumorigenesis [e.g., (35)(36)(37)].…”

Section: Introductionmentioning

confidence: 99%

Complex Stability and an Irrevertible Transition Reverted by Peptide and Fibroblasts in a Dynamic Model of Innate Immunity

et al. 2020

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We here apply a control analysis and various types of stability analysis to an in silico model of innate immunity that addresses the management of inflammation by a therapeutic peptide. Motivation is the observation, both in silico and in experiments, that this therapy is not robust. Our modeling results demonstrate how (1) the biological phenomena of acute and chronic modes of inflammation may reflect an inherently complex bistability with an irrevertible flip between the two modes, (2) the chronic mode of the model has stable, sometimes unique, steady states, while its acute-mode steady states are stable but not unique, (3) as witnessed by TNF levels, acute inflammation is controlled by multiple processes, whereas its chronic-mode inflammation is only controlled by TNF synthesis and washout, (4) only when the antigen load is close to the acute mode's flipping point, many processes impact very strongly on cells and cytokines, (5) there is no antigen exposure level below which reduction of the antigen load alone initiates a flip back to the acute mode, and (6) adding healthy fibroblasts makes the transition from acute to chronic inflammation revertible, although (7) there is a window of antigen load where such a therapy cannot be effective. This suggests that triple therapies may be essential to overcome chronic inflammation. These may comprise (1) anti-immunoglobulin light chain peptides, (2) a temporarily reduced antigen load, and (3a) fibroblast repopulation or (3b) stem cell strategies.

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“…and any one of the seven conditions (2)(3)(4)(5)(6)(7)(8) above is satisfied; ie, at least one of m 1 , m 2 , m 3 is positive.…”

Section: Coexisting Equilibrium Pointmentioning

confidence: 99%

Optimal chemotherapy and immunotherapy schedules for a cancer‐obesity model with Caputo time fractional derivative

Yıldız

Arshad

Băleanu

2018

Math Methods in App Sciences

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Communicated by: M. Kirane MSC Classification: 49K99; 34A08; 37N25; 92B05; 65L07This work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy and immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population and minimize the drug dose over a finite time interval. The constraint is a model including tumor cells, immune cells, fat cells, and chemotherapeutic and immunotherapeutic drug concentrations with the Caputo time fractional derivative. We investigate the existence and stability of the equilibrium points, namely, tumor-free equilibrium and coexisting equilibrium, analytically. We discretize the cancer-obesity model using the L1 method. Simulation results of the proposed model are presented to compare three different treatment strategies: chemotherapy, immunotherapy, and their combination. In addition, we investigate the effect of the differentiation order and the value of the decay rate of the amount of chemotherapeutic drug to the value of the cost functional. We find out the optimal treatment schedule in case of chemotherapy and immunotherapy. KEYWORDS chemotherapy, fractional differential equations, immunotherapy, optimal control, stability 9390

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An extended mathematical model of tumor growth and its interaction with the immune system, to be used for developing an optimized immunotherapy treatment protocol

Cited by 44 publications

References 31 publications

Nonlinear dynamics in tumor-immune system interaction models with delays

Nonlinear dynamics in tumor-immune system interaction models with delays

Complex Stability and an Irrevertible Transition Reverted by Peptide and Fibroblasts in a Dynamic Model of Innate Immunity

Optimal chemotherapy and immunotherapy schedules for a cancer‐obesity model with Caputo time fractional derivative

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