Mathematical analysis of the effects of precarious health system on COVID-19 transmission dynamics: case of Burkina Faso

Abstract

n the early moments of the pandemic of coronavirus disease 2019 (COVID-19), the level of effectiveness in treatment and management of patients was limited due to the lack of effective medications and adapted infrastructures in several countries especially in most developing countries. In this study, we propose an SIR-pattern model to investigate the epidemiological effect of delay in hospitalization and case managements. After computing the basic reproduction number thanks to the Next Generation Matrix method, we proved that the model has a locally asymptotically stable disease-free equilibrium whenever the basic reproduction number is less than one, and condition which ensure the appearance of two endemic equilibria indicating the possibility of having backward bifurcation is determined. When the basic reproduction number exceeds one, Lyapunov functional technique is used to establish the global stability of the unique endemic equilibrium point. Also, we presented a local sensitivity analysis that gives better understanding of the role of each model parameter appearing in the basic reproduction number. Numerical simulation of the model is also performed to corroborate the analytical results. Finally, we fitted our model by using reported data for Burkina Faso, and the results showed that it can be used for predicting the disease outcomes.