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Adaptive therapy is a recent paradigm in cancer treatment aiming at indefinite, safe containment of the disease when cure is judged unattainable. In modeling this approach, inherent limitations arise due to the structure of the vector…
In this paper, we study a phase-space analysis of a mathematical model of tumor growth with an immune response. Mathematical analysis of the model equations with multipoint initial condition, regarding to dissipativity, boundedness of…
We formulate the dynamical model for the anti-tumor immune response based on intercellular cytokine-mediated interactions with the interleukin-2 (IL-2) taken into account. The analysis shows that the expression level of tumor antigens on…
This study explores the application potential of a deep learning model based on the CNN-LSTM framework in forecasting the sales volume of cancer drugs, with a focus on modeling complex time series data. As advancements in medical technology…
Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies…
We propose a new model of cancer growth based on nonextensive entropy. The evolution equation depends on the nonextensive parameter q. The exponential, the logistic, and the Gompertz growth laws are particular cases of the generalized…
In this work, we develop a kinetic model of tumour growth taking into account the effects of clinical uncertainties characterising the tumours' progression. The action of therapeutic protocols trying to steer the tumours' volume towards a…
One of the barriers to the development of effective adoptive cell transfer therapies (ACT), specifically for genetically engineered T-cell receptors (TCRs), and chimeric antigen receptor (CAR) T-cells, is target antigen heterogeneity. It is…
Motivated by experimental observations in 3D/organoid cultures derived from glioblastoma, we develop a mathematical model where tumour aggregate formation is obtained as the result of nutrient-limited cell proliferation coupled with…
The problem of the onset and growth of solid tumour in homogeneous tissue is regarded using an approach based on local interaction between the tumoral and the sane tissue cells. The characteristic sizes and growth rates of spherical…
The aim of this study is to investigate the dose-deposition enhancement by alpha-particle irradiation in a cellular model using carbon and oxygen chemical compositions.A simulation study was performed to study dose enhancement due to carbon…
The use of bacteria has been attractive to cancer researchers as drug delivery vehicle because motile bacteria are able to penetrate in tumors. In particular, the combination of therapeutic bacteria and conventional chemotherapy leads to…
We present a theoretical framework based on an extension of dynamical density functional theory (DDFT) for describing the structure and dynamics of cells in living tissues and tumours. DDFT is a microscopic statistical mechanical theory for…
In this work, we consider a diffuse interface model for tumour growth in the presence of a nutrient which is consumed by the tumour. The system of equations consists of a Cahn--Hilliard equation with source terms for the tumour cells and a…
We develop a new four-phase tumor growth model with angiogenesis, derived from a diffuse-interface mixture model composed by a viable, a necrotic, a liquid and an angiogenetic component, coupled with two massless chemicals representing a…
We study a spatially inhomogeneous model of cancer growth based on Michaelis--Menten kinetics, subjected to additive Gaussian noise and multiplicative dichotomous noise. In presence of the latter, we can observe a transition between two…
Treatment of cancer has rapidly evolved over time in quite dramatic ways, for example from chemotherapies, targeted therapies to immunotherapies and chimeric antigen receptor T-cells. Nonetheless, the basic design of early phase I trials in…
In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear…
Research into mechanisms of hematogenous metastasis has largely become genetic in focus, attempting to understand the molecular basis of `seed-soil' relationships. Preceeding this biological mechanism is the physical process of…
Immunotherapy is currently regarded as the most promising treatment to fight against cancer. This is particularly true in the treatment of chronic lymphocytic leukemia, an indolent neoplastic disease of B-lymphocytes which eventually causes…