Cancer as Multifaceted Disease

Abstract

Abstract. Cancer has recently overtaken heart disease as the world's biggest killer. Cancer is initiated by gene mutations that result in local proliferation of abnormal cells and their migration to other parts of the human body, a process called metastasis. The metastasized cancer cells then interfere with the normal functions of the body, eventually leading to death. There are two hundred types of cancer, classified by their point of origin. Most of them share some common features, but they also have their specific character. In this article we review mathematical models of such common features and then proceed to describe models of specific cancer diseases.

Existence and Stability of Limit Cycles in a Two-delays Model of Hematopoiesis Including Asymmetric Division

“…While normal hematopoiesis is characterized by the production of healthy blood cells controlled by complex feedback mechanisms, pathological hematopoiesis involves some abnormal functioning of the hematopoietic system and consequently, can lead to blood disease. The ratio between annual deaths to annual new cases for leukemia is 58% [19]. A very common and intensively studied type of blood disease is Chronic Myelogenous Leukemia (CML).…”

“…The importance of the study of mathematical models of CML resides on two major facts: the molecular mechanisms involved in the disease initiation are well known and understood and the current treatment scheme with Imatinib is maybe the most efficient cancer therapy. Because of these particularities, many authors studied and modeled the evolution of leukemia, using different mathematical tools and various biological hypotheses: ordinary differential equations (ODEs); delay differential equations (DDEs) with a constant time delay that consider the resting stem cell population [26], [32], [6]; DDEs with distributed parameters: it is taken into consideration the fact that the cells do not divide at the same age and it is supposed that the delays (proliferating phase time duration) obey a low of uniform distribution on an interval [2], [3], [6], [31] and DDE with state dependent delay [6].Models that involve partial differential equations for tumors are described in [19], [4]. Previous mathematical models of hematopoietic stem cell dynamics are analyzed in [7], [11], [12], [24], [26], [27], [37].…”

Stability Analysis of a Feedback Model for the Action of the Immune System in Leukemia

“…Other authors ( [17], [18]) used the more simple model from [21] for the dynamics of hematopoietic stem cells (HSC). Other approaches can be found in [3], [14], [24] [27].…”

Modeling of Tumor Occurrence and Growth - I

“…В первом параграфе статьи приведены различные подходы к описанию поведения злокачественной опухоли [1]. Сравнивая новую литературу с той, что была разработана десять лет назад, можно понять, что не только значительно возросло внимание исследовательского сообщества к моделированию раковых опухолей, но и типы разработанных моделей существенно эволюционировали.…”