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We consider the $SEIRS$ epidemiology model with such features of the COVID-19outbreak as: abundance of unidentified infected individuals, limited time ofimmunity and a possibility of vaccination. Within a compartmental realizationof this model, we found the disease-free and the endemic stationary states.They exist in their respective restricted regions of the le via linearstability analysis. The expression for the basic reproductive number isobtained as well. The positions and heights of a first peak for the fractionsof infected individuals are obtained numerically and are fitted to simplealgebraic forms, that depend on model rates. Computer simulations of alattice-based realization for this model was performed by means of the cellularautomaton algorithm. These allowed to study the effect of the quarantinemeasures explicitly, via changing the neighbourhood size. The attempt is madeto match both quarantine and vaccination measures aimed on balanced solutionfor effective suppression of the pandemic.

Compartmental and cellular automaton $SEIRS$ epidemiology models for the COVID-19 pandemic with the effects of temporal immunity and vaccination