A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

中文翻译：

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在最佳控制策略下模拟蠕虫感染对结核分枝杆菌传播动力学的影响

介绍了蠕虫和结核病共同相互作用的传播和控制的确定性数学模型，以检查蠕虫对结核病的影响和控制策略的影响。建立平衡点，计算有效再生数。当有效繁殖数小于单位时，无病平衡点被证实是渐近稳定的。有效繁殖数的分析表明，蠕虫病例的增加会增加结核病病例，表明控制蠕虫感染对控制结核病动态具有积极影响。使用中心流形定理研究分岔的可能性。进行敏感性分析以确定每个参数对两种疾病传播的影响。该模型被扩展以包含控制措施，并应用庞特里亚金的最大原理来推导出最佳控制的必要条件。通过考虑为婴儿接种 Mtb 疫苗、治疗活动性结核病患者、使用常规抗蠕虫药物进行大规模给药以及卫生控制策略，通过迭代方案以数值方式解决了最优控制问题。结果表明，教育活动、活动性结核病患者的治疗、大规模药物管理和卫生相结合是控制蠕虫-Mtb 合并感染的最有效策略。因此，为了有效控制蠕虫-Mtb 共感染，