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School Mathematics, Statistics and Computer Science

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Browsing School Mathematics, Statistics and Computer Science by Author "Abdalla, Suliman Jamiel Mohamed."

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    Mathematical modelling of the Ebola virus disease.
    (2024) Abdalla, Suliman Jamiel Mohamed.; Govinder, Keshlan Sathasiva.; Chirove, Faraimunashe.
    Despite the numerous modelling efforts to advise public health physicians to understand the dynamics of the Ebola virus disease (EVD) and control its spread, the disease continued to spread in Africa. In the current thesis, we systematically review previous EVD models. Further, we develop novel mathematical models to explore two important problems during the 2018-2020 Kivu outbreak: the impact of geographically targeted vaccinations (GTVs) and the interplay between the attacks on Ebola treatment centres (ETCs) and the spread of EVD. In our systematic review, we identify many limitations in the modelling literature and provide brief suggestions for future work. Our modelling findings underscore the importance of considering GTVs in areas with high infections. In particular, we find that implementing GTVs in regions with high infections so that the total vaccinations are increased by 60% decreases the cumulative cases by 15%. On the other hand, we need to increase the vaccinations to more than 1000% to achieve the 15% decrease in EVD cases if we implement GTVs in areas with low infections. On the impact of the attacks on ETCs, we find that due to the attacks on ETCs, the cumulative cases increased by more than 17% during the 2018-2020 Kivu outbreak. We also find that when 10% of the hospitalised individuals flee the attacks on ETCs after spending only three days under treatment, the cumulative cases increased by more than 30% even if these individuals all returned to the ETCs three days later. On the other hand, if only half of these individuals returned to ETCs for treatment, the cumulative cases increase by approximately 50%. Further, when these patients spend one more day in the community, after which they all return to ETCs, the cumulative cases rise by an additional 10%. Global sensitivity analysis also confirmed these findings. To conclude, our literature systematic review is used to identify many critical factors which were overlooked in previous EVD models. Our modelling findings show that the attacks on ETCs can be destructive to the efforts of EVD response teams. Hence, it is important for decision-makers to tackle the reasons for community distrust and address the roots of the hostility towards ETCs. We also find that GTVs can be used to contain the spread of EVD when ring vaccinations, contact tracing and antiviral treatments cannot successfully control the spread of EVD.
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    Matrix models of population theory.
    (2013) Abdalla, Suliman Jamiel Mohamed.; Banasiak, Jacek.
    Non-negative matrices arise naturally in population models. In this thesis, we first study Perron- Frobenius theory of non-negative irreducible matrices. We use this theory to investigate the asymptotic behaviour of discrete time linear autonomous models. Then we discuss an application for this in age structured population. Furthermore, we study Liapunov stability of a general non-linear autonomous model. We consider a general nonlinear autonomous model that arises in structured population. We assume that the associated nonlinear matrix of this model is non-increasing at all density levels. Then, we show the existence of global extinction. In addition, we show the stability condition of the extinction equilibrium of the this model in the Liapunov sense.