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More than 20 outbreaks of Ebola virus disease have occurred in Africa since 1976, and yet no adequate treatment is available. Hence, prevention, control measures and supportive treatment remain the only means to avoid the disease. Among these measures, contact tracing occupies a prominent place. In this paper, we propose a simple mathematical model that incorporates imperfect contact tracing, quarantine and hospitalization (or isolation). The control reproduction number ℛ c of each sub-model and for the full model are computed. Theoretically, we prove that when ℛ c is less than one, the corresponding model has a unique globally asymptotically stable disease-free equilibrium. Conversely, when ℛ c is greater than one, the disease-free equilibrium becomes unstable and a unique globally asymptotically stable endemic equilibrium arises. Furthermore, we numerically support the analytical results and assess the efficiency of different control strategies. Our main observation is that, to eradicate EVD, the combination of high contact tracing (up to 90%) and effective isolation is better than all other control measures, namely: (1) perfect contact tracing, (2) effective isolation or full hospitalization, (3) combination of medium contact tracing and medium isolation. [ABSTRACT FROM AUTHOR]

A mathematical model presented in Berge T, Lubuma JM-S, Moremedi GM, Morris N Shava RK, A simple mathematical model for Ebola in Africa, J Biol Dyn 11(1): 42-74 (2016) for the transmission dynamics of Ebola virus is extended to incorporate vaccination and change of behavior for self-protection of susceptible individuals. In the new setting, it is shown that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than or equal to unity and unstable when . In the latter case, the model system admits at least one endemic equilibrium point, which is locally asymptotically stable. Using the parameters relevant to the transmission dynamics of the Ebola virus disease, we give sensitivity analysis of the model. We show that the number of infectious individuals is much smaller than that obtained in the absence of any intervention. In the case of the mass action formulation with vaccination and education, we establish that the number of infectious individuals decreases as the intervention efforts increase. In the new formulation, apart from supporting the theory, numerical simulations of a nonstandard finite difference scheme that we have constructed suggests that the results on the decrease of the number of infectious individuals is valid. [ABSTRACT FROM AUTHOR]