Doctoral Degrees (Mathematical Sciences)

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Browsing Doctoral Degrees (Mathematical Sciences) by Author "Djiomba Njankou, Sylvie Diane"

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    Mathematical models of Ebola virus disease with socio-economic dynamics
    (Stellenbosch : Stellenbosch University, 2019-04) Djiomba Njankou, Sylvie Diane; Nyabadza, Farai; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics.
    ENGLISH ABSTRACT : West Africa hosted the deadliest Ebola virus disease epidemic from 2013 to 2016 and one of the common characteristics of the affected countries is their status of being developing countries. Poor economic and social living conditions is a reality in these countries and they have deeply affected the fight against Ebola virus disease. In this work, we focus on the potential impact of socio-economic factors on Ebola virus disease dynamics. First, we use a compartmental model to study the dynamics of Ebola virus disease when there is a limited number of beds for patients. We use a non linear hospitalisation rate and formulate the rate at which the time dependent number of available beds evolves. The results suggest that a timely supply of sufficient beds to Ebola treatment units, limits the spread of the disease by keeping the infectious in one place, during their infectious period. Second, we formulate a mathematical model of Ebola virus disease that considers human behaviour through an exponential non linear incidence rate. Suitable Lyapunov functions are built and the proofs of the global stability of equilibria are presented. The results advocate for an immediate and efficacious behaviour change, as a control measure to rapidly control an Ebola virus disease epidemic. Third, we build a mathematical model of Ebola virus disease dynamics, that describes the introduction of a new strain of Ebola virus, through continuous or impulsive immigration of infectives. The results suggest controlled movements of people between countries that have had Ebola outbreaks. Finally, we develop a model of Ebola virus disease that considers two patches with different economic statuses represented by the respective gross-national incomes of these patches. We assume that susceptible, exposed and recovered individuals from the poorer patch move to the rich patch. The results indicate a decrease of the number of infected individuals in the rich patch when movements of populations are limited through the improvement of the economy in the poor patch. We conclude that the improvement of the economy of poorer countries may be critical in avoiding potential outbreaks of Ebola virus disease. The results in this thesis point to the need to consider socio-economic factors in Ebola virus disease epidemic models.