Mbalilo V M, Nyabadza F, Gatyeni S P
Department of Mathematics and Applied Mathematics, University of Johannesburg, South Africa.
Institute of Applied Research and Technology, Emirates Aviation University, Dubai International Academic City, United Arab Emirates.
Infect Dis Model. 2025 Jun 2;10(4):1037-1054. doi: 10.1016/j.idm.2025.05.010. eCollection 2025 Dec.
Tuberculosis (TB) continues to be a major global health challenge, with millions of new cases and deaths each year despite the massive efforts and funding put in the fight against the disease. In this paper, we develop a mathematical model to evaluate the impact of TB-funded prevention programs on the transmission dynamics of TB. The model incorporates stages of TB infection (latent and active), and accounts for the effects of treatment, funding and TB-funded prevention programs. Our analysis shows that increased funding and enhanced prevention programs reduce the number of active TB cases, thereby decreasing the reproduction number and TB endemicity. Specifically, higher funding rates lead to improved prevention and treatment outcomes, resulting in the lowering of the effective reproduction number and reduced transmission. The model's steady states are determined and it is shown that the model has a disease-free equilibrium that is locally asymptotically stable whenever and multiple endemic equilibria for and a unique endemic equilibrium for . The model is shown to exhibit a backward bifurcation that vanishes as the funding for TB is increased. The paper also highlights that treatment alone, while beneficial, is less effective than a combined strategy involving funding and prevention. Numerical simulations are carried out and the influences of various parameters on the effective reproduction number are investigated. The implications of TB-funded prevention programs on TB dynamics and control of TB are discussed and valuable insights for policymakers in designing effective TB control programs are highlighted.
结核病（TB）仍然是一项重大的全球卫生挑战，尽管在抗击该疾病方面投入了巨大努力和资金，但每年仍有数百万新发病例和死亡病例。在本文中，我们建立了一个数学模型，以评估由结核病资助的预防项目对结核病传播动态的影响。该模型纳入了结核病感染的各个阶段（潜伏性和活动性），并考虑了治疗、资金以及由结核病资助的预防项目的影响。我们的分析表明，增加资金投入和加强预防项目可减少活动性结核病病例数，从而降低繁殖数和结核病的地方流行程度。具体而言，更高的资金投入率会带来更好的预防和治疗效果，进而降低有效繁殖数并减少传播。确定了该模型的稳态，结果表明，当 时，该模型具有一个局部渐近稳定的无病平衡点，对于 有多个地方病平衡点，对于 有一个唯一的地方病平衡点。该模型显示出一种随着结核病资金投入增加而消失的向后分支现象。本文还强调，仅靠治疗虽然有益，但不如涉及资金投入和预防的联合策略有效。进行了数值模拟，并研究了各种参数对有效繁殖数的影响。讨论了由结核病资助的预防项目对结核病动态和结核病控制的影响，并强调了为政策制定者设计有效的结核病控制项目提供的宝贵见解。
