Mushayabasa S, Bhunu C P
Department of Mathematics, University of Zimbabwe, PO Box MP 167, Harare, Zimbabwe.
J Biol Phys. 2013 Sep;39(4):723-47. doi: 10.1007/s10867-013-9328-6. Epub 2013 Aug 23.
Effective tuberculosis (TB) control depends on case findings to discover infectious cases, investigation of contacts of those with TB, as well as appropriate treatment. Adherence and successful completion of the treatment are equally important. Unfortunately, due to a number of personal, psychosocial, economic, medical, and health service factors, a significant number of TB patients become irregular and default from treatment. In this paper, a mathematical model is developed to assess the impact of early therapy for latent TB and non-adherence on controlling TB transmission dynamics. Equilibrium states of the model are determined and their local stability is examined. With the aid of the center manifold theory, it is established that the model undergoes a backward bifurcation. Qualitative mathematical analysis of the model suggests that a high level of latent tuberculosis case findings, coupled with a decrease of defaulting rate, may be effective in controlling TB transmission dynamics in the community. Population-level effects of organized campaigns to improve early therapy and to guarantee successful completion of each treatment are evaluated through numerical simulations and presented in support of the analytical results.
有效的结核病控制依赖于病例发现以找出感染病例、对结核病患者接触者进行调查以及进行适当治疗。坚持治疗并成功完成治疗同样重要。不幸的是，由于一些个人、心理社会、经济、医学和卫生服务因素，大量结核病患者治疗变得不规律并中断治疗。本文建立了一个数学模型，以评估潜伏性结核病早期治疗和不坚持治疗对控制结核病传播动态的影响。确定了模型的平衡状态并研究了其局部稳定性。借助中心流形理论，确定该模型经历向后分岔。对该模型的定性数学分析表明，高水平的潜伏性结核病例发现，再加上违约率的降低，可能有效地控制社区中的结核病传播动态。通过数值模拟评估了有组织的运动对改善早期治疗和确保每次治疗成功完成的人群水平影响，并展示这些结果以支持分析结果。
