scholarly journals Mathematical model of brain tumour growth with drug resistance

2021 ◽  
pp. 106013
Author(s):  
José Trobia ◽  
Kun Tian ◽  
Antonio M Batista ◽  
Celso Grebogi ◽  
Hai-Peng Ren ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Drug Resistance ◽  
Brain Tumour ◽  
Tumour Growth

scholarly journals Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Caroline W. Kanyiri ◽  
Kimathi Mark ◽  
Livingstone Luboobi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Drug Resistance ◽  
Stability Analysis ◽  
Influenza A ◽  
Reproduction Number ◽  
Critical Value ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
High Morbidity

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

scholarly journals Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer

2018 ◽  
Vol 36 (3) ◽  
pp. 381-410 ◽  
Author(s):  
Angela M Jarrett ◽  
Meghan J Bloom ◽  
Wesley Godfrey ◽  
Anum K Syed ◽  
David A Ekrut ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Immune Response ◽  
Immune System ◽  
Murine Model ◽  
Tumour Growth ◽  
Experimental Approach ◽  
Her2 Breast Cancer ◽  
The Mathematical Model

Abstract The goal of this study is to develop an integrated, mathematical–experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical–experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth—conclusions revealed by the mathematical model that were not deducible from the experimental data alone.

The candidate tumour suppressor protein ING4 regulates brain tumour growth and angiogenesis

Nature ◽  
2004 ◽  
Vol 428 (6980) ◽  
pp. 328-332 ◽  
Author(s):  
Igor Garkavtsev ◽  
Sergey V. Kozin ◽  
Olga Chernova ◽  
Lei Xu ◽  
Frank Winkler ◽  
...  
Keyword(s):  
Brain Tumour ◽  
Tumour Growth ◽  
Tumour Suppressor ◽  
Tumour Suppressor Protein ◽  
Candidate Tumour Suppressor

scholarly journals Mathematical modeling quantifies ERK-activity in response to inhibition of the BRAFV600E-MEK-ERK cascade

2021 ◽  
Author(s):  
Sara Hamis ◽  
Yury Kapelyukh ◽  
Aileen McLaren ◽  
Colin J. Henderson ◽  
C. Roland Wolf ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Drug Resistance ◽  
Chemical Reactions ◽  
Molecular Mechanisms ◽  
Braf Inhibitor ◽  
Mass Action ◽  
Model Parameters ◽  
Mass Action Kinetics ◽  
Erk Activity

AbstractSimultaneous inhibition of multiple components of the BRAF-MEK-ERK cascade (vertical inhibition) has become a standard of care for treating BRAF-mutant melanoma. However, the molecular mechanisms of how vertical inhibition synergistically suppress intracellular ERK activity, and as a consequence cell proliferation, are yet to be fully elucidated.In this study, we develop a mechanistic mathematical model that describes how the mutant BRAF-inhibitor, dabrafenib, and the MEK-inhibitor, trametinib, affect signaling through the BRAFV600E-MEK-ERK cascade. We formulate a system of chemical reactions that describes cascade signaling dynamics and, using mass action kinetics, the chemical reactions are re-expressed as ordinary differential equations. Using model parameters obtained from in vitro data available in the literature, these equations are solved numerically to obtain the temporal evolution of the concentrations of the components in the signaling cascade.Our mathematical model provides a quantitative method to compute how dabrafenib and trametinib can be used in combination to synergistically inhibit ERK activity in BRAFV600E mutant melanoma cells. This work elucidates molecular mechanisms of vertical inhibition of the BRAFV600E-MEK-ERK cascade and delineates how elevated cellular BRAF concentrations generate drug resistance to dabrafenib and trametinib. In addition, the computational simulations suggest that elevated ATP levels could be a factor in drug resistance to dabrafenib. The mathematical model that is developed in this study will have generic application in the improved design of anticancer combination therapies that target BRAF-MEK-ERK pathways.

Analysis of a time-delayed mathematical model for tumour growth with inhibitors

2013 ◽  
Vol 92 (4) ◽  
pp. 703-717
Author(s):  
Shihe Xu ◽  
Xiao Wu ◽  
Meng Bai ◽  
Xiangqing Zhao
Keyword(s):  
Mathematical Model ◽  
Tumour Growth
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