COVID-19 is currently affecting over 215 countries worldwide and poses serious threats to public health not only the health system but also economics, education, transportation, politics. The objective of this paper was modeling the evolution COVID-19 data using deterministic and stochastic models and investigates how the model parameters depend on the population sizes in Ethiopia and we extend the deterministic SEIR (Susceptible, Exposed, Infectious, Recovered) model to simulate disease outbreak scenarios and to quantify the potential impact of a host-based early warning capability to mitigate pathogen transmission during an outbreak. Here, we show that real-time predictions of COVID-19 infections are extremely complex to errors in data collection and crucially depend on the last available data. We test these ideas in both using deterministic and stochastic models (susceptible–exposed–infected–recovered) models that are currently used to forecast the evolution of the COVID-19 epidemic. Our goal is to show how uncertainties arising from both poor data quality and inadequate estimations of model parameters (incubation, infection, and recovery rates) promulgate to long-term extrapolations of infection counts. Finally is to be better to understand the evolution of COVID-19 in Ethiopia, we apply a susceptible–exposed–infected–recovered (SEIR) model to the analysis of data from the Ethiopian Department of Health. Based on systematic and numerical results, as well on the data, the basic reproduction number is estimated to R_0= 1.12, we have analyzed SEIR model and concluded with saturated incidence rate and we observed that the reproduction number plays an important role to control the disease, when R_0 1, the endemic equilibrium is locally asymptotically stable, so based on the analysis of the result was indicates the diseases was reached outbreak time so that the responsible body will create more awareness in the society for the seriousness of the diseases