Dynamic behavior of prostate cancer cells under antitumor immunity and pulse vaccination in a random environment

Yang, Huan; Tan, Yi

doi:10.1007/s11071-021-06614-w

Cited by 7 publications

(3 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Compare with reference [36], the differences are listed as follows: (1) It is critical for ADT to control androgen concentration, then we consider not only the dendritic cell vaccine, but also the pulse effect of periodic injection of androgen. Since the antigenicity of tumours always exists in the whole process of invasion, the antigenicity of prostate cancer cells is also considered.…”

Section: Discussionmentioning

confidence: 99%

“…Later, Yang utilized a stochastic impulsive tumour model combining ADT and immunotherapy to analyze the elimination of AD and AI cells. It is proved that high intensity noise interference is unfavorable to the evolution of prostate cancer cells [36].…”

mentioning

confidence: 99%

“…Piece-wise functions are usually employed to describe IAD therapy. Injections or use of drugs are usually applied at fixed intervals, and Yang verified that frequent vaccination can improve the survival time of patients with ADT [36], so they can be characterized by impulsive differential equations. Hence, we make use of impulsive differential equations to capture the characteristics of IAD therapy.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Stationary distribution and persistence of a stochastic mathematical model for prostate cancer with pulsed therapy

Chen

Tan

et al. 2023

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Stationary distribution and persistence of a stochastic mathematical model for prostate cancer with pulsed therapy

Chen

Tan

et al. 2023

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

Investigation of phase-field models of tumor growth based on a reduced-order meshless Galerkin method

Abbaszadeh,

Dehghan,

Xiao

2023

Engineering with Computers

View full text Add to dashboard Cite

Dual CAR-T cell therapy for glioblastoma: strategies to cure tumour diseases based on a mathematical model

Bodnar,

Piotrowska,

Bodzioch

et al. 2024

Nonlinear Dyn

View full text Add to dashboard Cite

The CAR-T cell immunotherapy entails the genetic reprogramming of T-lymphocytes, which then engage with cancer cells, triggering an anti-tumour immune response. While this treatment has gained approval for hematological cancers, addressing solid tumours presents new obstacles. Challenges include the heterogeneity of antigen expression within solid tumours, encompassing antigen-positive non-tumoural cells, the presence of immune inhibitory molecules, and the difficulty of CAR-T cell trafficking within the tumour microenvironment. In this article, we analytically study a generalisation of a mathematical model proposed by León-Triana et al. (Cancers 13(4):703, 2021a. https://doi.org/10.3390/cancers13040703, Commun Nonlinear Sci Numer Simul 94:105570). This model focuses on the dynamics of glioblastoma, the most aggressive brain tumour, and its response to CAR-T cell treatment. We study the basic properties of the model, the dynamics of the solutions of the model when the treatment is not sustained during the time, and finally we study analytically the model when the therapy is constant, periodic and/or impulsive. We derive sufficient conditions for global stability of tumour-free equilibrium, as well as necessary and sufficient conditions for local stability of the equilibrium obtaining conditions for an effective treatment. Finally, we perform different numerical simulations to find the strategies to keep the tumour under control. The obtained results are based on a combination of different analytical techniques in differential equations, dynamical systems and numerical simulations.

show abstract

Dynamic behavior of prostate cancer cells under antitumor immunity and pulse vaccination in a random environment

Cited by 7 publications

References 36 publications

Stationary distribution and persistence of a stochastic mathematical model for prostate cancer with pulsed therapy

Stationary distribution and persistence of a stochastic mathematical model for prostate cancer with pulsed therapy

Investigation of phase-field models of tumor growth based on a reduced-order meshless Galerkin method

Dual CAR-T cell therapy for glioblastoma: strategies to cure tumour diseases based on a mathematical model

Contact Info

Product

Resources

About