Moualeu-Ngangue Dany Pascal, Röblitz Susanna, Ehrig Rainald, Deuflhard Peter
Institute of Horticultural Production Systems, Leibniz Universität Hannover, Hannover, Germany.
Department of Numerical Mathematics, Zuse Institute Berlin (ZIB), Berlin, Germany.
PLoS One. 2015 Apr 13;10(4):e0120607. doi: 10.1371/journal.pone.0120607. eCollection 2015.
A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.
设计并分析了喀麦隆结核病的确定性模型，以研究其传播动力学。该模型包括难以获得治疗、诊断能力薄弱以及频率依赖和密度依赖的传播方式。结果表明，该模型在数学上是适定的，在流行病学上是合理的。当初始值非负时，解是非负且有界的。对模型参数进行了敏感性分析，并通过先进的高斯-牛顿法确定了最敏感的参数。特别是，代表有机会获得医疗设施的个体比例的参数对疾病动态有很大影响。该模型预测，这些参数的逐步增加可能在未来15年内显著减轻人群的疾病负担。
