  Coherent activations of brain neuron networks underlay many physiological
functions associated with various behavioral states. These synchronous
fluctuations in the electrical activity of the brain are also referred to as
brain rhythms. At the cellular level, the rhythmicity can be induced by various
mechanisms of intrinsic oscillations in neurons or network circulation of
excitation between synaptically coupled neurons. One of the specific mechanisms
concerns the activity of brain astrocytes that accompany neurons and can
coherently modulate synaptic contacts of neighboring neurons, synchronizing
their activity. Recent studies have shown that coronavirus infection
(Covid-19), entering the central nervous system and infecting astrocytes,
causes various metabolic disorders. Specifically, Covid-19 can depress the
synthesis of astrocytic glutamate and GABA. It is also known that in the
postcovid state, patients may suffer from symptoms of anxiety and impaired
cognitive functions, which may be a consequence of disturbed brain rhythms. We
propose a mathematical model of a spiking neural network accompanied by
astrocytes capable to generate quasi-synchronous rhythmic bursting discharges.
The model predicts that if the astrocytes are infected, and the release of
glutamate is depressed, then normal burst rhythmicity suffers dramatically.
Interestingly, in some cases, the failure of network coherence may be
intermittent with intervals of normal rhythmicity, or the synchronization can
completely disappears.
