Browsing by Author "Assan, Belthasara"

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    Modelling the transmission of Buruli ulcer in fluctuating environments
    (Stellenbosch : Stellenbosch University, 2015-12) Assan, Belthasara; Nyabadza, Farai; Cang, Hui; Stellenbosch University. Faculty of Science. Department Mathematical Sciences (Mathematics)
    ENGLISH ABSTRACT : Buruli ulcer is a disease caused by Mycobacterium ulcerans. The transmission dynamics of this disease largely depends on environmental changes. In this thesis a deterministic model for the transmission converge to the disease free and endemic equilibrium respectively. A very good synergy was obtained between the deterministic model and STELLA model. The STELLA model however, provided flexibility through its ability to accommodate more social dynamics without adding mathematical intractability. The model provides useful insights in the dynamics of Buruli ulcer and has significant implication to the management of disease. of Buruli ulcer in fluctuating environments is proposed. The model incorporates periodicity in the disease transmission pathways and the Mycobacterium ulcerans density, that are thought to vary seasonally. Two reproduction numbers, time-averaged reproduction number [R0] and the basic reproduction number R0, are determined and compared. The time-averaged reproduction number obtained shows that Buruli ulcer epidemic is driven by the dynamics of the environments. It shows inaccuracy in predicting the number of infections. Numerical simulations confirmed that if R0 > 1 the infection is sustained seasonally. The model outcome suggests that environmental fluctuation should be taken into consideration in designing policies aimed at Buruli ulcer control and management. In addition to the deterministic model, a systems dynamic model for the transmission of Buruli ulcer by using STELLA is also proposed with and without periodicity in the disease transmission pathways and the Mycobacterium ulcerans density. The model simulations confirm that when R0 < 1 and R0 > 1 the solutions converge to the disease free and endemic equilibrium respectively. A very good synergy was obtained between the deterministic model and STELLA model. The STELLA model however, provided flexibility through its ability to accommodate more social dynamics without adding mathematical intractability. The model provides useful insights in the dynamics of Buruli ulcer and has significant implication to the management of disease.