Modelling the transmission of Buruli ulcer in fluctuating environments

Assan, Belthasara (2015-12)

Thesis (MSc)--Stellenbosch University, 2015

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

AFRIKAANSE OPSOMMING : Buruli ulkus is ‘n siekte wat veroorsaak word deur Mycobacterium ulcerans. Die oordrag dinamika van hierdie siekte hang grootliks van omgewingsveranderinge af. In hierdie tesis word ‘n deterministiese model vir die oordrag van Buruli ulkus in wisselende omgewings voorgestel. Die model inkorporeer periodisiteit in die siekte oordrag paaie en die Mycobacterium ulcerans digtheid, wat seisoenaal wissel. Twee reproduksie syfers, tyd-gemiddelde reproduksie syfer [R0] en die basiese reproduksie syfer R0, word bepaal en vergelyk. Die tyd-gemiddelde reproduksie syfer wat verkry word toon dat die Buruli ulkus epidemie deur die dinamika van die omgewing gedryf word. Dit toon ‘n mate van onakkuraatheid in die voorspelling van die aantal infeksies. Numeriese simulasie bevestig dat, as R0 > 1, dan word die infeksie seisoenaal opgedoen. Die uitkomste van die model stel voor dat fluksuasies in die omgewing in ag geneem moet word in die ontwerp van beleide gemik op Buruli ulkus beheer en bestuur. Bykomend tot die deterministiese model, word ’n stelsel dinamika model vir die oordrag van Buruli ulkus wat STELLA gebruik ook voorgestel met en sonder periodisiteit in die siekte oordrag paaie en die Mycobacterium ulcerans digtheid. Die model simulasies bevestig dat as R0 < 1 en R0 > 1, die oplossings na die siekte-vry en endemiese ewewigte, onderskeidelik, konvergeer. ‘n Baie goeie sinergie was verkry tussen die deterministiese model en die STELLA model. Die STELLA model verskaf egter buigsaamheid deur sy vermoë om meer sosiale dinamika, sonder om wiskundige onregeerbaarheid by te voeg, te akkomodeer. Die model verskaf nuttige insigte in die dinamika van BU en het beduidende implikasie tot die bestuur van die siekte.

Thesis

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/98144
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