Papers by Stefano Pedarra
The term "cancer" refers to a group of diseases which can affect almost any tissue and ... more The term "cancer" refers to a group of diseases which can affect almost any tissue and organ and are characterised by the uncontrolled growth of abnormal cells, whose cell cycle is much faster than the one of a healthy cell. The carcinogenesis, i.e. the production of a cancer, is due to mutations that occur physiologically during the DNA replication process. From a mathematical point of view, many aspects can be studied. In this thesis, we focus on tumour initial developement, modelling the oncogenesis through a system of ordinary differential equations (ODEs), taking into account the possibility that a mutation occurs and the competition among healthy cells and cancer cells for the available resource, such as physical space to develop, nutrients and oxygen. The model is later analysed: it is done analitically when we are differentiating between healthy cells and cancer ones; otherwise, if we want to consider n different genotypes, the study is numerical. Some biological i...
Trends in Mathematics, 2019
Cancer appears as a result of mutation of normal tissue cells. In this paper, we consider the ini... more Cancer appears as a result of mutation of normal tissue cells. In this paper, we consider the initial stage of the cancer appearance and development. In particular, we study the conditions that are necessary for an initial fixation of the mutant cells in a patient tissue and their further successful development. In order to do this, we are using a reasonably simple mutation-selection model composed of two interacting populations, namely, the normal cells and the mutant cells. Conditions for persistence of the mutant cells are found.
Trends in Mathematics, 2019
In this paper, we suggest a discrete variant space model of cancer evolution. The model is reason... more In this paper, we suggest a discrete variant space model of cancer evolution. The model is reasonably simple, deterministic, and is formulated as a system of ordinary differential equations. The model is based on the concept of “multi-strain modeling” (or quasi-species), which is successfully applied in modeling of the infectious disease dynamics and viral dynamics. The model constructed in this paper is mechanistic; that is, it is based upon a set of explicitly stated assumptions and hypothesis (“the first principles”). This implies that model’s parameters, as well as results obtained, can be immediately interpreted, and that a further model development, e.g., incorporation into the model factors such as anticancer therapies, immune response, etc., is a reasonably straightforward procedure. To illustrate this model applicability, results of numerical simulations, as well as their biological interpretations, are provided.
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Papers by Stefano Pedarra