Threshold for extinction and survival in stochastic tumor immune system

Li, Dongxi; Cheng, Fangjuan

doi:10.1016/j.cnsns.2017.03.007

Cited by 33 publications

(11 citation statements)

References 32 publications

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“…It has been shown that the growth rate of tumours is inevitably affected by environmental noise [18][19][20][21] and that periodical applications of immunotherapy and chemotherapy are effective for treating tumours [9,29,30], with the latter confirmed by experimental and clinical studies [22,23]. In this study, we have proposed a stochastic tumour-immune dynamical model with pulsed comprehensive treatment to investigate how stochastic fluctuations and combinations of immunotherapy with chemotherapy affect the evolution of tumours.…”

Section: Discussionmentioning

confidence: 95%

“…But most natural phenomena are influenced by stochastic processes rather than only M A N U S C R I P T by strictly deterministic laws [17], and the tumour cells are no exception [18]. For instance, changes in the environment can lead to changes in the enzymatic activity of proteins, which will affect the growth of tumour cells [19]. Thus, it is more reasonable to describe the growth of tumour cells by using stochastic differential equations.…”

mentioning

confidence: 99%

“…Thus, it is more reasonable to describe the growth of tumour cells by using stochastic differential equations. Li and Cheng considered a stochastic tumour growth model and obtained conditions for extinction and persistence of tumour cells [19], and Caravagna investigated the effects of stochastic oscillations on tumour suppression [20]. Wang and co-authors studied how environmental fluctuations affected the dynamics of tumour cells [21].…”

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confidence: 99%

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Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy

Tan

Cheke

2019

Communications in Nonlinear Science and Numerical Simulation

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Highlights• We developed a stochastic tumour-immune dynamical model concerning pulsed treatment.• Conditions for the three phases of cancer immunoediting are provided.• The results reveal that comprehensive therapy or noise can dominate evolution of tumours.• Biological implications for cancer treatment are presented. AbstractPeriodical applications of immunotherapy and chemotherapy play significant roles in cancer treatment and studies have shown that the evolution of tumour cells is subject to random events. In order to capture the effects of such noise we developed a stochastic tumour-immune dynamical model with pulsed treatment to describe combinations of immunotherapy with chemotherapy. By using theorems of the impulsive stochastic dynamical equation, the tumour free solution and the global positive solution of the proposed system were investigated. We then show that the expectations of the solutions are bounded. Furthermore, threshold conditions for extinction, non-persistence in the mean, weak persistence and stochastic persistence of tumour cells are provided. The results reveal that comprehensive therapy or noise can dominate the evolution of tumours. Finally, biological implications are addressed and a conclusion is presented.

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Section: Discussionmentioning

confidence: 95%

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confidence: 99%

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confidence: 99%

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Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy

Tan

Cheke

2019

Communications in Nonlinear Science and Numerical Simulation

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“…Li and Cheng [20] established the tumor-immune model describing the interaction and competition between the tumor cells and immune system based on the Michaelis-Menten enzyme kinetics, and gave the threshold conditions for extinction, weak persistence and stochastic persistence of tumor cells by the rigorous theoretical proofs, to name a few.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviors of the Tumor-Immune System in a Stochastic Environment

Li¹,

Song²,

Xia³

et al. 2019

SIAM J. Appl. Math.

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This paper investigates dynamic behaviors of the tumor-immune system perturbed by environmental noise. The model describes the response of the cytotoxic T lymphocyte (CTL) to the growth of an immunogenic tumour. The main methods are stochastic Lyapunov analysis, comparison theorem for stochastic differential equations (SDEs) and strong ergodicity theorem. Firstly, we prove the existence and uniqueness of the global positive solution for the tumor-immune system. Then we go a further step to study the boundaries of moments for tumor cells and effector cells and the asymptotic behavior in the boundary equilibrium points. Furthermore, we discuss the existence and uniqueness of stationary distribution and stochastic permanence of the tumor-immune system. Finally, we give several examples and numerical simulations to verify our results.

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“…Building on aforementioned earlier work, the effect of time delay in tumorimmune interactions are also extensively studied [1,4,8,28]. On the other hand, stochasticity in tumor-immune interaction is less often studied, and mostly focused on single-equation models of tumor population growth ignoring explicit interaction with immune system [20,2,21]. Models that take into account both time delay and stochasticity are even rarer.…”

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confidence: 99%

Dynamics of a model of tumor-immune interaction with time delay and noise

Han

Kuang

2020

Discrete &Amp; Continuous Dynamical Systems - S

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We propose a model of tumor-immune interaction with time delay in immune reaction and noise in tumor cell reproduction. Immune response is modeled as a non-monotonic function of tumor burden, for which the tumor is immunogenic at nascent stage but starts inhibiting immune system as it grows large. Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and uncertainty in the tumor innate proliferation rate are studied by including delay and noise in the appropriate model terms. Stability, persistence and extinction of the tumor are analyzed. We find that delay and noise can both induce the transition from low tumor burden equilibrium to high tumor equilibrium. Moreover, our result suggests that the elimination of cancer depends on the basal level of the immune system rather than on its response speed to tumor growth.

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Threshold for extinction and survival in stochastic tumor immune system

Cited by 33 publications

References 32 publications

Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy

Thresholds for extinction and proliferation in a stochastic tumour-immune model with pulsed comprehensive therapy

Dynamical Behaviors of the Tumor-Immune System in a Stochastic Environment

Dynamics of a model of tumor-immune interaction with time delay and noise

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