Survey on $SEIRD$ epidemic models with different focuses

This study is a survey of several extended models based on $SEIRD$ epidemics. The main contribution of the review is a modification of the classical $SEIRD$ epidemic model, from single-layer to multi-layer to super-exposure, and from general vaccine to pre-emptive vaccine to two-stage evolutionary-epidemic model. Assuming the presence of two viruses in a population, simultaneous and non-simultaneous occurrence of the two viruses was compared; assuming super-exposure between multiple viruses, general and pre-emptive vaccines were compared; and assuming that individuals have decision-making power over vaccination, the effect of the basic number of infections on the evolutionary stabilisation strategy was investigated. A series of numerical experiments support the theoretical results obtained.