Dynamics of host-reservoir transmission of Ebola with spillover potential to humans

Ebola virus disease (EVD) is a zoonotic disease (i.e. disease that is spread from animals to people). Therefore human beings can be infected through direct contact with an infected animal (fruit-eating bat or great ape). It has been demonstrated that fruit-eating bats of pteropodidae family are potential reservoir of EVD. Moreover, it has been biologically shown that fruit-eating bats do not die due to EVD and bear the Ebola viruses lifelong. We develop in this paper, a mathematical model to assess the impact of the reservoir on the dynamics of EVD. Our model couples a bat-to-bat model with a human-to-human model and the indirect environmental contamination through a spillover process (i.e. process by which a zoonotic pathogen moves (regardless of transmission mode) from an animal host (or environmental reservoir) to a human host) from bats to humans. The sub-models and the coupled models exhibit each a threshold behavior with the corresponding basic reproduction numbers being the bifurcation parameters. Existence of equilibria, their global stability are established by combining monotone operator theory, Lyapunov-LaSalle techniques and graph theory. Control strategies are assessed by using the target reproduction numbers. The efforts required to control EVD are assessed as well through S-control. The spillover event is shown to be highly detrimental to EVD by allowing the disease to switch from bats to humans even though the disease was not initially endemic in the human population. Precisely, we show that the spillover phenomenon contributes to speed up the disease outbreak. This suggests that the manipulation and consumption of fruit-bats play an important role in sustaining EVD in a given environment.