Steady States and Stability Analysis of Brain Tumour Growth Model


Authors : Ibrahim Jamiu Omotola

Volume/Issue : Volume 8 - 2023, Issue 10 - October

Google Scholar : https://tinyurl.com/26t8ysjx

Scribd : https://tinyurl.com/2p9ffrmz

DOI : https://doi.org/10.5281/zenodo.10254812

Abstract : Brain tumors have been reported to be among the highest causes of mortality. Based on the information from the Central Brain Tumor Registry of the United States (CBTRUS), it was projected that about 84,000 new cases of primary malignant and non-malignant brain and other central nervous system tumors were expected to be diagnosed in the United states in 2021. Brain Tumour is one of the illness that affect the Central Nervous System (CNS). Its effects are so critical and thereby requires an overhauling treatment. Over the years, different treatments have been employed to remove or alleviate the effects of this tumour. One of such treatments is the Chemotherapy approach. In this work, growth of brain tumour together with its treatment was modeled as a system of nonlinear ordinary differential equations. The existence and uniqueness of solution of this system were established. The steady states (equilibrium points) of this system were obtained and used to analyze its stability.

Keywords : Brain, Tumour, Chemotherapy, Steady States, Stability.

Brain tumors have been reported to be among the highest causes of mortality. Based on the information from the Central Brain Tumor Registry of the United States (CBTRUS), it was projected that about 84,000 new cases of primary malignant and non-malignant brain and other central nervous system tumors were expected to be diagnosed in the United states in 2021. Brain Tumour is one of the illness that affect the Central Nervous System (CNS). Its effects are so critical and thereby requires an overhauling treatment. Over the years, different treatments have been employed to remove or alleviate the effects of this tumour. One of such treatments is the Chemotherapy approach. In this work, growth of brain tumour together with its treatment was modeled as a system of nonlinear ordinary differential equations. The existence and uniqueness of solution of this system were established. The steady states (equilibrium points) of this system were obtained and used to analyze its stability.

Keywords : Brain, Tumour, Chemotherapy, Steady States, Stability.

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