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Simple Summary: COVID-19 is a rapidly spreading and mutating pandemic. In the case of some people the disease can be fatal It has been observed that weight and age are parameters of comorbidity If it is difficult to take into account the uncertainties related to the combination of the two parameters to build up a model of simulation. Therefore, we propose in this article a SIR/SIH model with fuzzy parameters which allows us to simulate the pandemic in the absence of barrier actions and vaccines. In this paper, we propose a multi-group SIR to simulate the spread of COVID-19 in an island context. The multi-group aspect enables us to modelize transmissions of the virus between non-vaccinated individuals within an age group as well as between different age groups. In addition, fuzzy subsets and aggregation operators are used to account for the increased risks associated with age and obesity within these different groups. From a conceptual point of view, the model emphasizes the notion of Hospitalization which is the major stake of this pandemic by replacing the compartment R (Removed) by compartment H (Hospitalization). The experimental results were carried out using medical and demographic data from the archipelago, Guadeloupe (French West Indies) in the Caribbean. These results show that without the respect of barrier gestures, a first wave would concern the elderly then a second the adults and the young people, which conforms to the real data. [ABSTRACT FROM AUTHOR]