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Threshold and Sensitivity Analysis of an Ebola Model with Case detection, Vaccination and Environmental Transmission |
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PP: 11-21 |
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Author(s) |
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Opeyemi Odetunde,
Victor Aduragbemi Adekunle,
Mohammed Olanrewaju Ibrahim,
Samuel Tosin Akinyemi,
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Abstract |
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| Ebola hemorrhagic fever, also known as Ebola virus disease (EVD) is a viral infection, usually with high fatality rate whenever there is a breakout. EVD has multiple transmission pathways, ranging from human-human, animal-human, human- environment and environment-human. With these multiple pathways, lots of preventive mechanisms have to be observed whenever there is a break-out so that the number of new cases can be minimized. Of such mechanisms are case detection, environmental sanitation, vaccination and other precautionary motives. Thus, a new mathematical model for EVD was proposed by incorporating case detection at each stage, with environmental contamination and vaccination impact on EVD transmission also considered. The aim of these measures is to check their effectiveness in reducing the number of EVD secondary cases. The model was qualitatively examined by establishing the region of feasible solution, which was found to exist and bounded. The non-negativity of solution for the model system of equation was established by using appropriate theorem. Equilibrium points of the system was analyzed at steady state, which was found to exist as disease free (DFE) and endemic equilibrium (EE). Basic reproduction number (R0) of the model was computed by using the next generational matrix approach. Local stability analysis of the model was computed to show the region of solution for both the DFE and EE points. The global stability analysis was obtained by constructing a unique and appropriate Lyapunov function. The result shows that the DFE is stable globally (G.A.S) if R0 < 1. Sensitivity analysis of the model was carried out to establish the effect of each parameter of the model on the (R0). It was discovered from the sensitivity index table that contact rate is the most sensitive parameter in disease transmission because of its large positive value. Numerical simulation for the sensitivity analysis was obtained graphically by varying the values of each parameter. The study concluded that case-detection, quarantining and proper disposal (burial) of dead infective are effective measures in reducing the number of new case(s) of the infection.
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