A co-infection model for oncogenic human papillomavirus (HPV) and tuberculosis (TB), with optimal control and cost-effectiveness analysis is studied and analyzed to assess the impact of controls against incident infection and against infection with HPV by TB-infected individuals as well as optimal TB treatment in reducing the burden of the co-infection of the two diseases in a population. The co-infection model exhibits backward bifurcation when the associated reproduction number is less than unity. Furthermore, it is shown that TB and HPV re-infection parameters (ϕ_p ≠ 0 and ) as well as TB exogenous re-infection term (ε₁ ≠ 0) induced the phenomenon of backward bifurcation in the oncogenic HPV-TB co-infection model. The global asymptotic stability of the disease-free equilibrium of the co-infection model is shown not to exist, when the associated reproduction number is below unity. The necessary conditions for the existence of optimal control and the optimality system for the co-infection model is established using the Pontryagin's Maximum Principle. Numerical simulations of the optimal control model reveal that the intervention strategy which combines and implements control against HPV infection by TB infected individuals as well as TB treatment control for dually infected individuals is the most cost-effective of all the control strategies for the control and management of the burden of oncogenic HPV and TB co-infection.

中文翻译：

---

具有最佳控制和成本效益分析的致癌人乳头瘤病毒和结核病的共感染模型

研究并分析了致癌性人乳头瘤病毒 (HPV) 和结核病 (TB) 的共感染模型，并进行了最佳控制和成本效益分析，以评估控制措施对突发感染和 HPV 感染的影响。以及在减少人群中两种疾病合并感染负担方面的最佳结核病治疗。当相关的繁殖数小于 1 时，共感染模型表现出向后分叉。此外，还表明 TB 和 HPV 再感染参数（ϕ _p  ≠ 0 和）以及 TB 外源性再感染项（ε ₁ ≠ 0) 在致癌 HPV-TB 共感染模型中诱导后向分叉现象。当相关的繁殖数低于 1 时，表明共感染模型的无病平衡的全局渐近稳定性不存在。利用庞特里亚金最大原理建立了最优控制存在的必要条件和共感染模型的最优系统。最优控制模型的数值模拟表明，将结核病感染者的HPV感染控制与双重感染者的结核病治疗控制相结合并实施的干预策略是所有控制和管理控制策略中最具成本效益的。致癌性 HPV 和 TB 合并感染的负担。