Enriched spatiotemporal dynamics of a model of Ebola transmission with a composite incidence function and density-independent treatment

In this work, we are concerned with the mathematical modeling and analysis of Ebola virus disease dynamics. Firstly, we design and analyze a nonlinear ordinary differential equations model integrating both direct and indirect transmission pathways with density-independent treatment and a composite nonlinear incidence function. We begin the analysis by proving the global existence of a unique positive and bounded solution. Then we compute the basic reproduction number on which relies the global dynamics of the model. We precisely show the existence of a unique disease-free equilibrium and that of a unique endemic equilibrium, and prove their global stability under appropriate assumptions on the basic reproduction number. Moreover, we perform the global sensitivity analysis of the basic reproduction number to assess the variability in the model predictions. We find that the forecasts closely agree with the 2014 outbreaks of the disease in Liberia and Sierra Leone. Secondly, we enrich this first model by extending it to a partially degenerate reaction–diffusion system via the inclusion of Fickian diffusion for susceptible and non-hospitalized infectious individuals in order to understand the dynamics of the disease transmission in a spatially homogeneous environment. We prove the global stability of the disease-free equilibrium and the uniform persistence when the basic reproduction number lies below and above one, respectively. Finally, numerical simulations are performed to illustrate some theoretical results obtained.