The　global　impact　of　corona　virus　(COVID-19)　has　been　profound,　and　the　public　health　threat　it　represents　is　the　most　serious　seen　in　a　respiratory　virus　since　the　1918　influenza　A(H1N1)　pandemic.　In　this　paper,　we　have　focused　on　reviewing　the　results　of　epidemiological　modelling　especially　the　fractional　epidemic　model　and　summarized　different　types　of　fractional　epidemic　models　including　fractional　Susceptible-Infective-Recovered　(SIR),　Susceptible-Exposed-Infective-Recovered　(SEIR),　Susceptible-Exposed-Infective-Asymptomatic-Recovered　(SEIAR)　models　and　so　on.　Furthermore,　we　propose　a　general　fractional　SEIAR　model　in　the　case　of　single-term　and　multi-term　fractional　differential　equations.　A　feasible　and　reliable　parameter　estimation　method　based　on　modified　hybrid　Nelder-Mead　simplex　search　and　particle　swarm　optimisation　is　also　presented　to　fit　the　real　data　using　fractional　SEIAR　model.　The　effective　methods　to　solve　the　fractional　epidemic　models　we　introduced　construct　a　simple　and　effective　analytical　technique　that　can　be　easily　extended　and　applied　to　other　fractional　models,　and　can　help　guide　the　concerned　bodies　in　preventing　or　controlling,　even　predicting　the　infectious　disease　outbreaks.　©　2021　Elsevier　Inc.