COVID-19, declared a pandemic by the World Health Organization (WHO) [25] on 11 March 2020, is still spreading around the world up to date 26 September 2020. The number of people infected is beyond 32 million on 26 September 2020 with 989,380 deaths [24]. In Senegal, the number of cumulative cases is currently 14839 with 2624 individuals undergoing treatment on 25 September 2020[13]. The first cases, from Wuhan, were notified to WHO on 31 December 2019 [25, 26] while, Senegal notified its first case on 02 March 2020 [13]. Because of its limited resources, as in many sub-Saharan African countries, it is therefore valuable to understand the growth and the timing in responding to the logistic needs of their health system. We note that several developed countries that nevertheless have high-capacity health structures have been overwhelmed and this considerably impacted negatively in the combat against the pandemic.

We consider a compartmental model from which we incorporate a time-dependent health care capacity having a logistic growth. This allows us to take into account the Senegalese authorities response in anticipating the growing number of infected cases. We highlight the importance of anticipation and timing to avoid overwhelming that could impact considerably the treatment of patients and the well-being of health care workers. A condition, depending on the health care capacity and the flux of new hospitalized individuals, to avoid possible overwhelming is provided. We also use machine learning approach to project forward the cumulative number of cases from March 02, 2020, until 1st December, 2020.