Related papers: Discrete and continuum models for the coevolutiona…
We present a spatial hybrid discrete-continuum modelling framework for the interaction dynamics between tumour cells and cytotoxic T cells, which play a pivotal role in the immune response against tumours. In this framework, tumour cells…
We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context…
Intra-tumour heterogeneity (ITH) has a strong impact on the efficacy of the immune response against solid tumours. The number of sub-populations of cancer cells expressing different antigens and the percentage of immunogenic cells (i.e.…
We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of…
The interactions between tumor cells and the immune system play a crucial role in cancer evolution. In this study, we explore how these interactions influence cancer progression by modeling the relationships among naive T cells, effector T…
We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell, $s$, that determines its proliferative…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
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…
Cancer is a disease that takes millions of lives every year. Then, to propose treatments, avoid recurrence, and improve the patient's life quality, we need to analyze this disease from a biophysical perspective with a solid mathematical…
Chimeric antigen receptor (CAR) T cell therapy has shown remarkable success in hematological malignancies, yet patient responses remain highly variable and the roles of CD4+ and CD8+ subsets are not fully understood. We present an extended…
Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type which have so far been proposed, though, is that cells in the…
The recent advances in cancer immunotherapy boosted the development of tumor-immune system models aiming to provide mechanistic understanding and indicate more efficient treatment regimes. However, the complexity of such models, their…
Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally…
This paper presents a mathematical model for tumour-immune response interactions in the perspective of immunotherapy by immune checkpoint inhibitors ICIs. The model is of the nonlocal integro-differential Lotka-Volterra type, in which…
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However,…
Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or…
In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in…
We present a mathematical model, based on ordinary differential equations, for the evolution of solid tumors and their response to treatment. Specifically the effects of a cytotoxic agent and a monoclonal antibody are included as control…
Tumor-immune interactions are central to cancer progression and treatment outcomes. In this study, we present a stochastic agent-based model that integrates cellular heterogeneity, spatial cell-cell interactions, and drug resistance…