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Dynamics of a Generalized Model for Ebola Virus Disease

  • Zineb El Rhoubari
  • Hajar Besbassi
  • Khalid Hattaf
  • Noura Yousfi
Chapter

Abstract

Ebola virus can be transmitted from an infected individual who is still alive or from dead to the living during funerals. In this study, we propose a new generalized mathematical model that describes the dynamics of Ebola virus disease and takes into account the two modes of transmission. In the proposed model, the transmission process for both modes is modeled by two general incidence functions that include many types of incidence rates existing in the literature. We first prove that the proposed model is epidemiologically and mathematically well-posed by showing the existence, positivity, and boundedness of solutions. By analyzing the characteristic equations, the local stability of equilibria is investigated. The global stability of equilibria is obtained by constructing suitable Lyapunov functionals. Numerical simulations are carried out to support the theoretical results.

Keywords

Ebola General incidence rate Global stability 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Zineb El Rhoubari
    • 1
  • Hajar Besbassi
    • 1
  • Khalid Hattaf
    • 1
    • 2
  • Noura Yousfi
    • 1
  1. 1.Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Science Ben M’sikHassan II UniversitySidi OthmanMorocco
  2. 2.Centre Régional des Métiers de l’Education et de la Formation (CRMEF)Derb GhalefMorocco

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