Aldila Dipo, Fardian Basyar Lauzha, Chukwu Chidozie Williams, Hifzhudin Noor Aziz Muhamad, Kamalia Putri Zahra
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia.
Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, USA.
R Soc Open Sci. 2024 Jun 19;11(6):231715. doi: 10.1098/rsos.231715. eCollection 2024 Jun.
Tuberculosis (TB) remains a significant global health concern, necessitating effective control strategies. This article presents a mathematical model to evaluate the comparative effectiveness of medical mask usage and case detection in TB control. The model is constructed as a system of ordinary differential equations and incorporates crucial aspects of TB dynamics, including slow-fast progression, medical mask use, case detection, treatment interventions and differentiation between symptomatic and asymptomatic cases. A key objective of TB control is to ensure that the reproduction number, , remains below unity to achieve TB elimination or persistence if exceeds 1. Our mathematical analysis reveals the presence of a transcritical bifurcation when the signifies a critical juncture in TB control strategies. These results confirm that the effectiveness of case detection in diminishing the endemic population of symptomatic individuals within a TB-endemic equilibrium depends on exceeding a critical threshold value. Furthermore, our model is calibrated using TB yearly case incidence data per 100 000 population from Indonesia, India, Lesotho and Angola. We employed the bootstrap resampling residual approach to assess the uncertainty inherent in our parameter estimates which provides a comprehensive distribution of the parameter values. Despite a declining trend in new incidence, these four countries exhibit a reproduction number greater than 1, indicating persistent TB cases in the presence of ongoing TB control programmes. We employ the partial rank correlation coefficient in conjunction with the Latin hypercube sampling method to conduct a global sensitivity analysis of the parameter for each fitted parameter in every country. We find that the medical mask use is more sensitive to reduce compared with the case detection implementation. To further gain insight into the necessary control strategy, we formulated an optimal control and studied the cost-effectiveness analysis of our model to investigate the impact of case detection and medical mask use as control measures in TB spread. Cost-effectiveness analysis demonstrates that combining these interventions emerges as the most cost-effective strategy for TB control. Our findings highlight the critical importance of medical masks and their efficacy coupled with case detection in shaping TB control dynamics, elucidating the primary parameter of concern for managing the control reproduction number. We envisage our findings to have implications and be vital for TB control if implemented by policymakers and healthcare practitioners involved in TB control efforts.
结核病（TB）仍然是一个重大的全球卫生问题，需要有效的控制策略。本文提出了一个数学模型，以评估医用口罩使用和病例检测在结核病控制中的相对有效性。该模型构建为一个常微分方程组，并纳入了结核病动态的关键方面，包括快慢进展、医用口罩使用、病例检测、治疗干预以及有症状和无症状病例之间的区分。结核病控制的一个关键目标是确保繁殖数(R)保持在1以下，以实现结核病消除；如果(R)超过1，则实现结核病持续存在。我们的数学分析表明，当(R)表示结核病控制策略中的一个关键节点时，存在一个跨临界分岔。这些结果证实，在结核病流行平衡点减少有症状个体的流行人群方面，病例检测的有效性取决于超过一个临界阈值。此外，我们使用印度尼西亚、印度、莱索托和安哥拉每10万人口的结核病年度病例发病率数据对模型进行了校准。我们采用自助重采样残差方法来评估参数估计中固有的不确定性，该方法提供了参数值的全面分布。尽管新发病率呈下降趋势，但这四个国家的繁殖数大于1，表明在实施结核病控制计划的情况下仍有持续的结核病病例。我们结合拉丁超立方采样方法使用偏秩相关系数，对每个国家的每个拟合参数进行(R)参数的全局敏感性分析。我们发现，与实施病例检测相比，使用医用口罩对降低(R)更敏感。为了进一步深入了解必要的控制策略，我们制定了一个最优控制，并研究了我们模型的成本效益分析，以调查病例检测和医用口罩使用作为结核病传播控制措施的影响。成本效益分析表明，结合这些干预措施是结核病控制最具成本效益的策略。我们的研究结果突出了医用口罩的关键重要性及其功效，以及病例检测在塑造结核病控制动态中的作用，阐明了管理控制繁殖数的主要关注参数。我们设想，如果参与结核病控制工作的政策制定者和医疗从业者实施我们的研究结果，将对结核病控制产生影响并至关重要。
