A hybrid computational model of thalamocortical circuitry and basal ganglia is proposed to investigate the relation between the fractional amplitude of low-frequency fluctuations (fALFF) in the resting-state functional magnetic resonance imaging (rs-fMRI) in the striatum and electroencephalogram (EEG) changes within the alpha frequency bands in thalamic region in the case of Alzheimer's disease (AD). For that purpose, an Izikhevich neuron model-based network of the basal ganglia region is constructed and connected with the thalamic region which is modeled as neural mass. By considering the neurodegenerative changes in AD, the network dynamics are analyzed. The relation between the neural activity of basal ganglia and AD is investigated by modeling the blood oxygenation level-dependent (BOLD) signal. Decrease in fALFF of slow-4 band in the simulated BOLD signal of the striatum is observed. As the thalamic region receives inhibitory connections from basal ganglia over globus pallidus internal segment (GPi), the parameter changes emulating AD degenerations in the striatum increased the inhibitory effect on the thalamic network, and as a result, slowing in alpha rhythms is observed. It is observed that the decrease in the synaptic strength between the neurons in the striatum has a dominant effect on the slowing in alpha rhythm and also causes a decrease in fALFF of slow-4 band in striatum. This demonstrates a close and causal relation between the decrease in fALFF in the striatum and the slowing in alpha rhythms in the thalamic region in AD.