Nyabadza Farai, Bonyah Ebenezer
Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland, 7602, South Africa.
Department of Mathematics and Statistics, Kumasi Polytechnic, P. O. Box 854, Kumasi, Ghana.
BMC Res Notes. 2015 Nov 6;8:656. doi: 10.1186/s13104-015-1619-5.
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.
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 [Formula: see text]. The disease free equilibrium is found to be locally asymptotically stable for [Formula: see text] The model is fitted to data from Ghana.
The model is found to exhibit a backward bifurcation and the endemic equilibrium point is globally stable when [Formula: see text] 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.
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.
已知溃疡分枝杆菌会引发布氏溃疡。溃疡与环境暴露之间的关联已有文献记载。然而，该溃疡的流行病学尚未得到充分了解。一种假设的传播途径是人类被捕食软体动物、蜗牛和幼鱼的水生昆虫叮咬。
本文提出并分析了一种在存在预防策略的情况下溃疡分枝杆菌向人类传播的模型。确定了模型的平衡点，并建立了平衡点存在的条件。根据繁殖数[公式：见原文]对模型进行分析。发现当[公式：见原文]时，无病平衡点局部渐近稳定。该模型与来自加纳的数据进行拟合。
发现该模型呈现后向分岔，当[公式：见原文]时，地方病平衡点全局稳定。敏感性分析表明，布氏溃疡疫情受环境中溃疡分枝杆菌的脱落和清除率影响很大。发现该模型与来自加纳的数据拟合得相当好，并且还对布氏溃疡疫情的未来进行了预测。
该模型与来自加纳的数据拟合合理。拟合过程显示数据似乎已达到稳定状态，预测表明在预测期内疫情水平将保持不变。讨论了结果对该疾病政策和未来管理的影响。
