A co-infection model for Oncogenic HPV and TB 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 is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. Furthermore, it is shown that TB and HPV re-infection parameters (ϕp ≠ 0 and σT ≠ 0) as well as TB exogenous re-infection term (ϵ1 ≠ 0) oncogenic HPV-TB co-infection model. The global asymptotic stability of the disease-free equilibrium of the co-infection model is also proven 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. Uncertainty and global sensitivity analysis are also carried out to determine the top ranked parameters that drive the dynamics of the co-infection model, when the associated reproduction numbers as well as the infected populations are used as response functions. 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.

A fractional-order multi-vaccination model for COVID-19 with non-singular kernel

“…Recent trends in epidemiological research revealed that applying non-integer order differential equations is vital in obtaining good results for dynamical systems. The classical mathematical models of the integer-order derivatives have been greatly employed in studying infectious diseases [10] , [11] , [12] , [13] , [16] , [17] , [18] , [19] , [47] , [27] , [28] , [23] , [24] , [25] . For instance, Omame et al [9] considered and analyzed an integer-order model for the dynamics of Human papillomavirus and Chlamydia trachomatis using optimal control.…”

“…They examined the impact of various non-pharmaceutical interventions on the control of the disease. In [47] , the authors considered a mathematical model for the co-dynamics of COVID-19 and Dengue in Brazil, with optimal control and cost-effectiveness analysis. Furthermore, Bonyah et al [18] considered and analyzed a mathematical model for the co-infection of dengue fever and Zika virus.…”

A Mathematical Model for the Study of Effectiveness in Therapy in Tuberculosis Taking into Account Associated Diseases

“…A. Omame et al [16] presented and studied a model of human papillomavirus (HPV) and Chlamydia trachomatis co-infection and showed that trachomatis prevention controls are the most cost-effective strategies to combat HPV and Chlamydia trachomatis co-infections. A. Omamea and D. Okuonghaeb [17] presented a co-infection model for Oncogenic HPV and TB with cost-effectiveness optimal control analysis and showed that the combination of HPV prevention and TB treatment positively impacts the reduction of oncogenic HPV and co-infection.…”

Mathematical models for the study of adherence to tuberculosis treatment taking into account the effects of HIV/AIDS and diabetes

“…In recent years, the use of mathematical models with different techniques to predict the behavior of epidemics has been increasing [18,93,94]. For example, Farman et al [18] used evolutionary computational techniques and the Padé approach to study a nonlinear model of Hepatitis B.…”

“…A. Omame et al [93] introduced and analyzed a model of human papillomavirus (HPV) and Chlamydia trachomatis co-infection, and studied different control strategies to eliminate HPV and Chlamydia trachomatis co-infections. Omame and Okuonghae [94] proposed a co-infection model for oncogenic HPV and tuberculosis with an optimal control analysis and proved that the combination of HPV prevention and tuberculosis treatment has a positive impact on the reduction of oncogenic HPV and co-infection [80].…”