An S-A-I-Q-R epidemic model is investigated for Covid-19 as a class of infectious diseases that can be transmitted through carriers, not only infected individuals who are contagious but do not show any disease symptoms but through air which contained the virus droplets. Mathematical analysis is carried out that determines the global dynamics of the Modified Compartmental Epidemiological Model describing the transmission of the SARS-CoV-2 virus. The impacts of disease carriers on the transmission dynamics are analyze with emphasis on infected migrant, asymptomatic infected and social interacting people. We presented our discussion through the basic reproduction number as well as numerical simulations. We derived the condition for boundedness was obtained. Results: It was discovered that when Π δ λ and ρ are increased withing the first week of consideration, the reproduction number asymptotically approaches zero while a sudden increase in τ was observed to result into a sudden increase in reproduction number within the first week of the outbreak and thereafter decreases with further increment in τ. The result also showed that, population under quarantine are rarely infected with the virus except if already infected before being quarantined.