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要旨

In this paper, we propose and analyse a compartmental model of COVID-19 to predict and control the outbreak. We first formulate a comprehensive mathematical model for the dynamical transmission of COVID-19 in the context of sub-Saharan Africa. We provide the basic properties of the model and compute the basic reproduction number R0 when the parameter values are constant. After, assuming continuous measurement of the weekly number of newly COVID-19 detected cases, newly deceased individuals and newly recovered individuals, the Ensemble of Kalman filter (EnKf) approach is used to estimate the unmeasured variables and unknown parameters, which are assumed to be time-dependent using real data of COVID-19. We calibrated the proposed model to fit the weekly data in Cameroon and Gabon before, during and after the lockdown. We present the forecasts of the current pandemic in these countries using the estimated parameter values and the estimated variables as initial conditions. During the estimation period, our findings suggest that R0≈1.8377 in Cameroon, while R0≈1.0379 in Gabon meaning that the disease will not die out without any control measures in theses countries. Also, the number of undetected cases remains high in both countries, which could be the source of the new wave of COVID-19 pandemic. Short-term predictions firstly show that one can use the EnKf to predict the COVID-19 in Sub-Saharan Africa and that the second vague of the COVID-19 pandemic will still increase in the future in Gabon and in Cameroon. A comparison between the basic reproduction number from human individuals R0h and from the SARS-CoV-2 in the environment R0v has been done in Cameroon and Gabon. A comparative study during the estimation period shows that the transmissions from the free SARS-CoV-2 in the environment is greater than that from the infected individuals in Cameroon with R0h = 0.05721 and R0v = 1.78051. This imply that Cameroonian apply distancing measures between individual more than with the free SARS-CoV-2 in the environment. But, the opposite is observed in Gabon with R0h = 0.63899 and R0v = 0.39894. So, it is important to increase the awareness campaigns to reduce contacts from individual to individual in Gabon. However, long-term predictions reveal that the COVID-19 detected cases will play an important role in the spread of the disease. Further, we found that there is a necessity to increase timely the surveillance by using an awareness program and a detection process, and the eradication of the pandemic is highly dependent on the control measures taken by each government.