The accumulation of amyloid β peptide \(\left( {\text{A}}\beta \right) \) is assumed to be one of the main causes of Alzheimer’s disease \(\left( {\text{AD}}\right) \) . There is increasing evidence that astrocytes are the primary targets of Aβ. Aβ can cause abnormal synaptic glutamate, aberrant extrasynaptic glutamate, and astrocytic calcium dysregulation through astrocyte glutamate transporters facing the synaptic cleft (GLT-syn), astrocyte glutamate transporters facing the extrasynaptic space (GLT-ess), metabotropic glutamate receptors in astrocytes (mGluR), N-methyl-D-aspartate receptors in astrocytes (NMDAR), and glutamatergic gliotransmitter release (Glio-Rel). However, it is difficult to experimentally identify the extent to which each pathway affects synaptic glutamate, extrasynaptic glutamate, and astrocytic calcium signaling. Motivated by these findings, this work established a concise mathematical model of astrocyte \({\text{Ca}}^{2+}\) dynamics, including the above Aβ-mediated glutamate-related multiple pathways. The model results presented the extent to which five mechanisms acted upon by Aβ affect synaptic glutamate, extrasynaptic glutamate, and astrocytic intracellular \({\text{Ca}}^{2+}\) signals. We found that GLT-syn is the main pathway through which Aβ affects synaptic glutamate. GLT-ess and Glio-Rel are the main pathways through which A \(\beta \) affects extrasynaptic glutamate. GLT-syn, mGluR, and NMDAR are the main pathways through which Aβ affects astrocytic intracellular \({\text{Ca}}^{2+}\) signals. Additionally, we discovered a strong, monotonically increasing relationship between the mean glutamate concentration and the mean \({\text{Ca}}^{2+}\) oscillation amplitude (or frequency). Our results may have therapeutic implications for slowing cell death induced by the combination of glutamate imbalance and \({\text{Ca}}^{2+}\) dysregulation in AD.
