Mathematical analysis of the Cancitis model and the role of inflammation in blood cancer progression

Zamra Sajid; Morten Andersen; Johnny T. Ottesen; Zamra Sajid; Morten Andersen; Johnny T. Ottesen

doi:10.3934/mbe.2019418

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 8268-8289. doi: 10.3934/mbe.2019418

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Mathematical analysis of the Cancitis model and the role of inflammation in blood cancer progression

IMFUFA, Department of Science and Environment, Roskilde University, Denmark

Received: 30 May 2019 Accepted: 04 September 2019 Published: 16 September 2019

Recently, a tight coupling has been observed between inflammation and blood cancer such as the Myeloproliferative Neoplasms (MPNs). A mechanism based six-dimensional model-the Cancitis model-describing the progression of blood cancer coupled to the inflammatory system is analyzed. An analytical investigation provides criteria for the existence of physiological steady states, trivial, hematopoietic, malignant and co-existing steady states. The classification of steady states is explicitly done in terms of the inflammatory stimuli. Several parameters are crucial in determining the attracting steady state(s). In particular, increasing inflammatory stimuli may transform a healthy state into a malignant state under certain circumstances. In contrast for the co-existing steady state, increasing inflammatory stimuli may reduce the malignant cell burden. The model provides an overview of the possible dynamics which may inform clinical practice such as whether to use inflammatory inhibitors during treatment.
- cancer,
- inflammation,
- mathematical modelling,
- steady states,
- stability
Citation: Zamra Sajid, Morten Andersen, Johnny T. Ottesen. Mathematical analysis of the Cancitis model and the role of inflammation in blood cancer progression[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 8268-8289. doi: 10.3934/mbe.2019418

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Abstract

Recently, a tight coupling has been observed between inflammation and blood cancer such as the Myeloproliferative Neoplasms (MPNs). A mechanism based six-dimensional model-the Cancitis model-describing the progression of blood cancer coupled to the inflammatory system is analyzed. An analytical investigation provides criteria for the existence of physiological steady states, trivial, hematopoietic, malignant and co-existing steady states. The classification of steady states is explicitly done in terms of the inflammatory stimuli. Several parameters are crucial in determining the attracting steady state(s). In particular, increasing inflammatory stimuli may transform a healthy state into a malignant state under certain circumstances. In contrast for the co-existing steady state, increasing inflammatory stimuli may reduce the malignant cell burden. The model provides an overview of the possible dynamics which may inform clinical practice such as whether to use inflammatory inhibitors during treatment.

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