  Alzheimer's disease (AD) is a common neurodegenerative disorder nowadays.
Amyloid-beta (A$\beta$) and tau proteins are among the main contributors to the
development or propagation of AD. In AD, A$\beta$ proteins clump together to
form plaques and disrupt cell functions. On the other hand, the abnormal
chemical change in the brain helps to build sticky tau tangles that block the
neuron's transport system. Astrocytes generally maintain a healthy balance in
the brain by clearing the A$\beta$ plaques (toxic A$\beta$). However,
over-activated astrocytes release chemokines and cytokines in the presence of
A$\beta$ and react to pro-inflammatory cytokines, further increasing the
production of A$\beta$. In this paper, we construct a mathematical model that
can capture astrocytes' dual behaviour. Furthermore, we reveal that the disease
propagation depends on the current time instance and the disease's earlier
status, called the ``memory effect''. We consider a fractional order network
mathematical model to capture the influence of such memory effect on AD
propagation. We have integrated brain connectome data into the model and
studied the memory effect, the dual role of astrocytes, and the brain's
neuronal damage. Based on the pathology, primary, secondary, and mixed
tauopathies parameters are considered in the model. Due to the mixed tauopathy,
different brain nodes or regions in the brain connectome accumulate different
toxic concentrations of A$\beta$ and tau proteins. Finally, we explain how the
memory effect can slow down the propagation of such toxic proteins in the
brain, decreasing the rate of neuronal damage.
