Mathematical models of leukaemia and its treatment: a review

Abstract

Leukaemia accounts for around 3% of all cancer types diagnosed in adults, and is the most common type of cancer in children of paediatric age (typically ranging from 0 to 14 years). There is increasing interest in the use of mathematical models in oncology to draw inferences and make predictions, providing a complementary picture to experimental biomedical models. In this paper we recapitulate the state of the art of mathematical modelling of leukaemia growth dynamics, in time and response to treatment. We intend to describe the mathematical methodologies, the biological aspects taken into account in the modelling, and the conclusions of each study. This review is intended to provide researchers in the field with solid background material, in order to achieve further breakthroughs in the promising field of mathematical biology.

Comparison of Predator-Prey Model and Hawk-Dove Game for Modelling Leukemia

“…By considering the data of a patient who has been diagnosed with leukemia, the two-dimensional Leslie predator prey model of equation (10). Shows in Figure 7…”

“…Miguel [8] & Rodriguesa et.al [9], also contributed their results for cancer metabolism and presented a detailed mathematical model for chemoimmunotherapy for lymphocytic leukemia describing its normal conditions and stability analysis of immunotherapy. Leukemia and tumor based on several other mathematical models were studied by a few more researchers such as [10][11][12][13]. On the other hand, many other models related to differential equations were studied recently by several authors, see [14][15][16][17][18][19][20][21][22][23][24][25][26].…”

AML consolidation therapy: timing matters

“…A large variety of mathematical models have been proposed for different purposes in oncology, see (Sager 2023 ; Chulián et al. 2022 ; Stiehl and Marciniak-Czochra 2012 ; Michor and Beal 2015 ; Brady and Enderling 2019 ; Clairambault 2009 ) for surveys and further references. We trained and cross-validated a previously published mathematical model (Jost et al.…”