Alzheimer's disease is an age-related, progressive and chronic neurodegenerative disorder caused by neuronal cell death and attributed to memory loss. Recent studies have shown that glutamate has an important role in learning, memory formation and synaptic plasticity. A disruption to glutamatergic neurotransmission has been suggested to lead to Alzheimer's Dementia. As a main objective, this study computational models the glutamate pathway to relate molecular mechanisms of how glutamate links to neural activity and predict the involvement in Alzheimer's disease. Simulations was by numerical solving ordinary differential equations as rate equations based on biochemical systems theory. Results suggest in normal or control condition there was an increase in astrocyte calcium levels. Our simulations showed a lower level of GluN2B level in control suggesting a reduced production of amyloid beta compared to the diseased condition. Simulating diseased state, increased IP3 levels lead to the release of TNFα, released glutamine synthase that converted glutamine to glutamate. The results also demonstrated the elevation in extracellular glutamate concentration that activated NMDAR. Through modeling, we show that increased production of amyloid beta that forms amyloid plaques elucidating the main component of neurodegeneration occurred in Alzheimer's disease.