Konstantin E. Starkov
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View article: On the Dynamics of Immune-Tumor Conjugates in a Four-Dimensional Tumor Model
On the Dynamics of Immune-Tumor Conjugates in a Four-Dimensional Tumor Model Open
We examine the ultimate dynamics of the four-dimensional model describing interactions between host cells, immune cells, tumor cells, and immune-tumor conjugate cells proposed by Abernethy and Gooding in 2018. In our paper, the ultimate up…
View article: Ultimate Dynamics of the Two-Phenotype Cancer Model: Attracting Sets and Global Cancer Eradication Conditions
Ultimate Dynamics of the Two-Phenotype Cancer Model: Attracting Sets and Global Cancer Eradication Conditions Open
In this paper we consider the ultimate dynamics of one 4D cancer model which was created for studying the immune response to the two-phenotype tumors. Our approach is based on the localization method of compact invariant sets. The existenc…
View article: Eradication Conditions of Infected Cell Populations in the 7-Order HIV Model with Viral Mutations and Related Results
Eradication Conditions of Infected Cell Populations in the 7-Order HIV Model with Viral Mutations and Related Results Open
In this paper, we study possibilities of eradication of populations at an early stage of a patient’s infection in the framework of the seven-order Stengel model with 11 model parameters and four treatment parameters describing the interact…
View article: Ultimate dynamics and optimal control of a multi-compartment model of tumor resistance to chemotherapy
Ultimate dynamics and optimal control of a multi-compartment model of tumor resistance to chemotherapy Open
In this paper, a non-trivial generalization of a mathematical model put forward in [35] to account for the development of resistance by tumors to chemotherapy is presented. A study of the existence and local stability of the solutions, as …
View article: Dynamics of the tumor-immune-virus interactions: Convergence conditions to tumor-only or tumor-free equilibrium points
Dynamics of the tumor-immune-virus interactions: Convergence conditions to tumor-only or tumor-free equilibrium points Open
In the present paper convergence dynamics of one tumor-immune-virus model is examined with help of the localization method of compact invariant sets and the LaSalle theorem. This model was elaborated by Eftimie et al. in 2016. It is shown …
View article: The four-dimensional Kirschner-Panetta type cancer model: How to obtain tumor eradication?
The four-dimensional Kirschner-Panetta type cancer model: How to obtain tumor eradication? Open
In this paper we examine ultimate dynamics of the four-dimensional model describing interactions between tumor cells, effector immune cells, interleukin -2 and transforming growth factor-beta. This model was elaborated by Arciero et al. an…
View article: Modeling cancer evolution: evolutionary escape under immune system control
Modeling cancer evolution: evolutionary escape under immune system control Open
It can be expected that adequate immune response should be able to annihilate cancer at a very early stage of its appearance. However, in some cases cancer is able to persist avoiding immune response. One can conject that cancer is able to…
View article: Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy
Dynamical properties and tumor clearance conditions for a nine-dimensional model of bladder cancer immunotherapy Open
Understanding the global interaction dynamics between tumor and the immune system plays a key role in the advancement of cancer therapy. Bunimovich-Mendrazitsky et al. (2015) developed a mathematical model for the study of the immune syste…
View article: Estudio de la dinámica global para un modelo de Evasión-Inmune de un tumor cancerígeno
Estudio de la dinámica global para un modelo de Evasión-Inmune de un tumor cancerígeno Open
En este artículo se estudia la dinámica global del modelo de Evasión-Inmune presentado por Arciero, Jackson y Kirschner [1], el cual describe la interacción entre células efectoras, células cancerígenas y las citocinas IL - 2 y TGF -β en e…