Related papers: Tumor containment for Norton-Simon models

Tumors are defined by their intense proliferation, but sometimes cancer cells turn senescent and stop replicating. In the stochastic cancer model in which all cells are tumorigenic, senescence is seen as the result of random mutations,…

The long-term efficacy of targeted therapeutics for cancer treatment can be significantly limited by the type of therapy and development of drug resistance, inter alia. Experimental studies indicate that the factors enhancing acquisition of…

Adaptive therapy improves cancer treatment by controlling the competition between sensitive and resistant cells through treatment holidays. This study highlights the critical role of treatment-holiday thresholds in adaptive therapy for…

We formulate and analyze a mathematical model describing immune response to avascular tumor under the influence of immunotherapy and chemotherapy and their combinations as well as vaccine treatments. The effect of vaccine therapy is…

Chemotherapy is one of the most important therapeutic options used to treat human cancers, either alone or in combination with radiation therapy and surgery. Recent studies have indicated that intra-tumoural heterogeneity has a significant…

Tumor recurrence, driven by the evolution of drug resistance is a major barrier to therapeutic success in cancer. Resistance is often caused by genetic alterations such as point mutation, which refers to the modification of a single genomic…

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…

Cancer is a heterogeneous disease and tumours of the same type can differ greatly at the genetic and phenotypic levels. Understanding how these differences impact sensitivity to treatment is an essential step towards patient-specific…

Mutation-induced drug resistance in cancer often causes the failure of therapies and cancer recurrence, despite an initial tumor reduction. The timing of such cancer recurrence is governed by a balance between several factors such as…

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…

Cancer cells are known to modify their micro-environment such that it can sustain a larger population, or, in ecological terms, they construct a niche which increases the carrying capacity of the population. It has however been argued that…

We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully…

We are keenly interested in finding the limiting behaviors of total tumor size when tumor cells are subject to the periodic repetition of therapy and rest periods, called intermittent cyclic therapy. We hypothesize that each tumor cell can…

In this study, we develop consistent estimators for key parameters that govern the dynamics of tumor cell populations when subjected to pharmacological treatments. While these treatments often lead to an initial reduction in the abundance…

Recent clinical trials have shown that the adaptive drug therapy can be more efficient than a standard MTD-based policy in treatment of cancer patients. The adaptive therapy paradigm is not based on a preset schedule; instead, the doses are…

Currently, most of the basic mechanisms governing tumor-immune system interactions, in combination with modulations of tumor-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of…

In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor…

While cancer has traditionally been considered a genetic disease, mounting evidence indicates an important role for non-genetic (epigenetic) mechanisms. Common anti-cancer drugs have recently been observed to induce the adoption of…

Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor…

The uncontrolled proliferation of cancer cells and their interaction with healthy tissue poses a major challenge in oncology. This manuscript develops and analyzes mathematical models that describe tumor response to radiotherapy by…