Qualitative and quantitative analysis of the transmission dynamics of Ebola with convex incidence rates: a case study of Guinea

Ebola infection poses severe threats due to its high mortality rate, potential for rapid spread, and devastating impact on both individual health and public safety, particularly in regions with limited healthcare infrastructure. In this study, we develop a mathematical model of the transmission dynamics of Ebola to investigate the key factors responsible for the spread and control of the infection. The model utilizes convex incidence rates to represent multiple exposures, extending the classical Susceptible-Exposed-Infected-Removed (SEIR) epidemic compartmental model. This extended model is referred to as the Susceptible-Exposed-Infected-Removed-Dead-Bacteria (SEIRD-B) model. We calculate the basic reproduction number, \({\mathcal {R}}_0\) ${\mathcal{R}}_0$ , and demonstrate that the disease-free equilibrium is locally and conditionally globally stable whenever \({\mathcal {R}}_0 < 1\) ${\mathcal{R}}_0<1$ . Furthermore, we establish the existence of a unique endemic equilibrium and prove its global stability under certain conditions when \({\mathcal {R}}_0 > 1\) ${\mathcal{R}}_0>1$ by constructing a Lyapunov function. The theoretical results are validated through numerical simulations. Using real data from Guinea, we calibrate the model by performing a model estimation analysis. This allows us to estimate the basic reproduction number, \({\mathcal {R}}_0 \approx 37.9709\) ${\mathcal{R}}_0\approx 37.9709$ , which is significantly higher than values reported in the literature. With these model parameter values, we also predict the progression of the disease in Guinea. Our findings suggest that multiple pandemic waves could occur, indicating that sustained Ebola control measures are necessary to protect the population in Guinea.