A Simple Model for Control of Tumor Cells

Abstract

The Kirschner-Panetta model describes the poblational competition between effector cells and tumor cells. We analize external changes in the parameters and mechanisms to obtain the decreasing of tumor cells. These variations were performed by three different ways: Oscillations, spikes with the natural frequency of the system, and spikes with Normal Distribution. It was observed that the amount of tumor cells decreases to zero if we change simultaneously the parameters properly.

An integrative model of cancer cell differentiation with immunotherapy*

“…As mentioned in the introduction to this work, cancer cell differentiation and the relationship with the immune system are studied separately. In most cases, only generalized populations of cancer cells and immune cells are considered, or only one of the two groups is analysed in depth [39][40][41][42].…”

“…The designed system is mainly related to Shariatpanahi et al [41], Sigal et al [42], and the types of external inputs such as vaccines, under biologically valid ranges, as proposed by Tsygvintsev et al [39], Margarit and Romanelli [40] and Sigal et al [42]. This system is modelled through first-order ordinary differential equations (ODEs).…”

“…In them, generally, there is a single population of cancer cells (without distinguishing the degree of differentiation) and a single population of immune cells (generally effector cells). On other occasions, cancers are only analysed with cytotoxic agents or another population of some of the cells derived from the immune system, both meloid and lymphoid [39,40]. Our goal is to make a preliminary model that is more comprehensive and is a basis for further research.…”

An Optimal Control Problem of Chemotherapy In Presence of Gene and Immunotherapy

“…Lestari et al [43] studied the local stability analysis of the proposed model [33]. In [44], the authors estimated the external parameters of the model [33] for which the growth of tumor cells remains under control. For further study on the applications of gene therapy in cancer treatment models, the authors would like to refer to the works [33,43] to the reader.…”

Estudo de um Modelo Fracionário de Terapia Gênica para o Tratamento de Câncer

“…Para as simulações numéricas utilizamos o método de Grünwald-Letnikov para equações diferenciais fracionárias apresentado e discutido em [13] e os parâmetros do modelo fracionário são os mesmos do modelo de ordem inteira. Com condições iniciais T (0) = 10 5 células e E(0) = 10 3 células [10] e, após várias simulações para diferentes valores de α, exemplificamos com α = 0, 7; 0, 9 e 1. Na simulação 1 (Figura 1) após algum tempo, as oscilações não ocorrem mais, indicando que a população de células cancerosas não cresce devido a atuação das células imunes, caracterizando a dormência tumoral.…”