Research Articles (Mathematical Sciences)

Permanent URI for this collection

https://scholar.sun.ac.za/handle/10019.1/4832

Browse

Browsing Research Articles (Mathematical Sciences) by Author "Bonyah, Ebenezer"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    On the transmission dynamics of Buruli ulcer in Ghana : insights through a mathematical model
    (BioMed Central, 2015-11-06) Nyabadza, Farai; Bonyah, Ebenezer
    Background: Mycobacterium ulcerans is know to cause the Buruli ulcer. The association between the ulcer and environmental exposure has been documented. However, the epidemiology of the ulcer is not well understood. A hypothesised transmission involves humans being bitten by the water bugs that prey on mollusks, snails and young fishes. Methods: In this paper, a model for the transmission of Mycobacterium ulcerans to humans in the presence of a preventive strategy is proposed and analysed. The model equilibria are determined and conditions for the existence of the equilibria established. The model analysis is carried out in terms of the reproduction number R0. The disease free equilibrium is found to be locally asymptotically stable for R0 < 1. The model is fitted to data from Ghana. Results: The model is found to exhibit a backward bifurcation and the endemic equilibrium point is globally stable when R0 > 1. Sensitivity analysis showed that the Buruli ulcer epidemic is highly influenced by the shedding and clearance rates of Mycobacterium ulcerans in the environment. The model is found to fit reasonably well to data from Ghana and projections on the future of the Buruli ulcer epidemic are also made. Conclusions: The model reasonably fitted data from Ghana. The fitting process showed data that appeared to have reached a steady state and projections showed that the epidemic levels will remain the same for the projected time. The implications of the results to policy and future management of the disease are discussed.
  • Thumbnail Image
    Item
    A Theoretical model for the transmission dynamics of the Buruli Ulcer with saturated treatment
    (Hindawi Publishing Corporation, 2014-08) Bonyah, Ebenezer; Dontwi, Isaac; Nyabadza, Farai
    The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.