International Journal of Innovation and Development

ON SITR THEORETICAL MODEL OF EBOLA VIRUS PROPAGATION WITH RELAPSE AND REINFECTION

Isaac Kwasi Adu

Kumasi Technical University

Fredrick Asenso Wireko

Kwame Nkrumah University of Science and Technology

Keywords: STIR model, reproduction ratio, backward bifurcation, asymptotically stable, global stability

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Abstract

Despite the national government’s commitment to eradicating the Ebola virus epidemic and the WHO’s combined efforts in this regard in Ebola-torn countries in Africa, many people are still not aware of some possible modes of transmission of Ebola. Many researchers also failed to include these possible modes of transmission, reinfection, and relapse of EVD in their studies. We studied the dynamics of Ebola infection with relapse and reinfection by employing a non-linear SITR mathematical model. We computed the fundamental reproduction ratio, examined the model equilibria, and carried out a sensitivity analysis. Lassalle’s invariance principle was employed to examine the global stability of the Ebola-free equilibrium. Further analysis indicates that the model exhibits a backward bifurcation. We therefore employed the centre manifold theorem to prove the model’s asymptotic stability. Our analysis indicates that Ebola-free equilibrium was locally asymptotically stable if and unstable if . The global analysis conducted on the model revealed that the Ebola-free equilibrium was globally stable if . Our model revealed that Ebola can be controlled by increasing the number of infectious people who go for treatment and reducing the transmission rate of people who are prone to the disease through an intensive educational campaign and vaccination of susceptible individuals.

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Author Biographies

Isaac Kwasi Adu, Kumasi Technical University

Department of Mathematical Sciences

Fredrick Asenso Wireko, Kwame Nkrumah University of Science and Technology

Department of Mathematics, Kwame Nkrumah University of Science and Technology