| Despite the commitment of national governments and collaborative efforts by the world Health Organization(WHO)toward the eradication of Ebola Virus disease(EVD)in Ebola torn countries in Africa,many people are still not aware of some possible modes of transmission of EVD.Many researchers also fail to include these possible modes of EVD transmission,co-infection of EVD with other diseases,relapse of EVD after recovery and re-infection of Ebola virus by recovered Ebola victims in their studies.In this thesis,we present a novel but realistic dynamics of Ebola virus disease(EVD)transmission.We present introduction of the thesis,Ebola virus ecology and transmission,Recurrence(Relapse)and Reinfection of Ebola Virus Disease,Ebola and Malaria Co-infections,life cycle of Ebola virus,Ebola virus species,prevention of EVD,treatment of EVD,Ebola vaccine,review of related literature,objectives of the thesis and Organization of the thesis in Chapter 1,Chapter 2 is devoted to study the various modes of transmission of EVD,incorporated with possible reinfection of EVD after recovery,permanently and temporally recovered Ebola victims.We evaluated R0,discussed the existence and stability of Ebola-free and endemic equilibria.The Ebola-free equilibrium was asymptotically stable if R0<1 but unstable if R0>1.Global stability of the Ebola free and endemic equilibria was discussed in the model,using Lasalle's Invariance Principle.We performed numerical simulations to confirm our ana-lytic results.Next,we used optimal control to prove that there exists an optimal control,which is effective in controlling Ebola disease outbreak in a cost-effective way.Finally,our studies show that EVD can be controlled by reducing contact with infected people and animals,educating the public about reinfection of Ebo-la,vaccinating recovered Ebola victims,intensifying educational program against funeral practices like bathing of dead bodies and environmental contamination of Ebola virus.In Chapter 3.we used a non-linear SITR mathematical model to study the dynamics of Ebola virus disease transmission with relapse and reinfection.We estimated the basic reproduction number,discussed the existence and stability of the Ebola-free equilibrium,endemic equilibrium and also performed the sen-sitivity analysis.The Ebola-free equilibrium was locally asymptotically stable if R0<1 and unstable if R0>1.Global stability of the Ebola-free equilibrium was also considered in the model using the Lassalle's invariance principle.We further analysed the model and established that our model exhibits the backward bifur-cation.We therefore proved the asymptotic stability of the model by applying the centre manifold theory.Finally,our study shows that Ebola virus disease can be controlled by increasing the infectious people who go for treatment,reducing the effective contact rate of susceptible individuals through intensive educational campaign and vaccination of susceptible individualsIn Chapter 4,we examined the Ebola-Malaria co-infection model,incorporated with reinfection of both diseases after recovery and the contribution of Ebola virus pathogens in the environment of deceased Ebola victims in the model.We first considered the analysis of the single infection states of Ebola and Malaria respectively,derived the basic reproduction number using the next generation approach and then study the existence of the disease-free and endemic equilibria of the two models.Secondly,we analyzed the Ebola-Malaria co-infection model and established that the co-infection model exhibits the backward bifurcation.The asymptotic stability of the co-infection model was then proved using the center manifold theory.We also investigate the impact of Ebola and its treatment on the dynamics of Malaria and vice versa.Our numerical results suggest that the best strategy to minimize Ebola,Malaria and their co-infections is to controls the two diseases together.Finally,we ended the thesis by drawing conclusions,made some suggestions for future work and recommendations in Chapter 5. |
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