The COVID-19 epidemic is an emerging infectious disease of the viral zoonosis type caused by the corona-virus strain SARS-CoV-2, is classified as a human-to-human communicable disease and is currently a pandemic worldwide. In this paper, we propose conceptual mathematical models the epidemic dynamics of four compartments. We have collected data from the Djibouti health ministry. We define the positivity, boundedness of solutions and basic reproduction number. Then, we study local and global stability and bifurcation analysis of equilibrium to examine its epidemiological relevance. Finally, we analyze the fit of the data in comparison with the result of our mathematical results, to validate the model and estimating the important model parameters and prediction about the disease, we consider the real cases of Djibouti from 23th March to 10th June, 2020.

The Covid-19 epidemic is an emerging infectious disease of the viral zoonosis type caused by the coronavirus strain SARS-CoV-2, it is classified as a human-to-human communicable disease and is currently a pandemic worldwide. In this paper, we propose conceptual mathematical models of the epidemic dynamics of four compartments. We have collected data from the Djibouti health ministry. We study the positivity, boundedness, existence and uniqueness of the weak solution. Next, we define the Basic reproduction number by the method of the DFE and EEP. Then, we study the local and global stability and the bifurcation analysis of equilibrium to examine its epidemiological relevance. Finally, we analyze the fit of the data in comparison with the result of our mathematical results, to validate the model and estimate the important model parameters and prediction about the disease. We consider the real cases of Djibouti from 15th March to 15th May 2021.