Mathematical models on Alzheimer's disease and its treatment: A review.

Alzheimer's disease is a gradually advancing neurodegenerative disease. According to the report by "World Health Organization (WHO)", there are over 55 million individuals currently living with Alzheimer's disease and other dementia globally, and the number of sufferers is increasing every day. In absence of effective cures and preventive measures, this number is predicted to triple by 2050.

Roles of astrocytes and prions in Alzheimer's disease: insights from mathematical modeling.

We present a mathematical model that explores the progression of Alzheimer's disease, with a particular focus on the involvement of disease-related proteins and astrocytes. Our model consists of a coupled system of differential equations that delineates the dynamics of amyloid beta plaques, amyloid beta protein, tau protein, and astrocytes. Amyloid beta plaques can be considered fibrils that depend on both the plaque size and time.