Mathematical models has been useful over the years to understand the behavior and impacts of several infectious diseases such as Malaria, Ebola, Cholera, in human and non-human population. In this paper, a modified mathematical model of covid-19 virus in Nigeria is presented. The disease free equilibrium, endemic equilibrium state, threshold behavior 𝑅0 and the bounded region where the model is mathematically and epidemiologically feasible is established. The global stability analysis for the disease-free and endemic equilibria are obtained using Carlos Chavez theorem and LaSalle’s criterion. The results show that the virus will cause devastating impacts (𝑅𝑜>1) in Nigeria if the control and mitigation mechanisms are not adhered to. The numerical approximations of the model via differential transform method illustrate the impacts of the virus dynamical transmission in time/per week. The approximation’s insight raises concern as more people will be susceptible and exposed to the virus, the number of infectious individuals will be on the increase for some time with more hospitalize-isolation individuals in Nigeria. The approximation also shows an increasing rate of recovery for infected individuals.