A co‐infection model for oncogenic human papillomavirus and tuberculosis with optimal control and Cost‐Effectiveness Analysis

Abstract 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 ( ε 1 ≠ 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.