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• COVID-19 modeling transmission using known theory concerning the disease transmission and control strategies. • Formulation of a mathematical model for the COVID-19 that incorporates some key epidemiological and biological features. • Sensitivity analysis of the model. • Theoretical studies and numerical simulations. In this paper, we formulated a general model of COVID-19 model transmission using biological features of the disease and control strategies based on the isolation of exposed people, confinement (lock-downs) of the human population, testing people living risks area, wearing of masks and respect of hygienic rules. We provide a theoretical study of the model. We derive the basic reproduction number R 0 which determines the extinction and the persistence of the infection. It is shown that the model exhibits a backward bifurcation at R 0 = 1. The sensitivity analysis of the model has been performed to determine the impact of related parameters on outbreak severity. It is observed that the asymptomatic infectious group of individuals may play a major role in the spreading of transmission. Moreover, various mitigation strategies are investigated using the proposed model. A numerical evaluation of control strategies has been performed. We found that isolation has a real impact on COVID-19 transmission. When efforts are made through the tracing to isolate 80% of exposed people the disease disappears about 100 days. Although partial confinement does not eradicate the disease it is observed that, during partial confinement, when at least 10% of the partially confined population is totally confined, COVID-19 spread stops after 150 days. The strategy of massif testing has also a real impact on the disease. In that model, we found that when more than 95% of moderate and symptomatic infected people are identified and isolated, the disease is also really controlled after 90 days. The wearing of masks and respecting hygiene rules are fundamental conditions to control the COVID-19. [ABSTRACT FROM AUTHOR]