A co-infection model for HPV and syphilis with optimal control and cost-effectiveness analysis

Abstract

A co-infection model for human papillomavirus (HPV) and syphilis with cost-effectiveness optimal control analysis is developed and presented. The full co-infection model is shown to undergo the phenomenon of backward bifurcation when a certain condition is satisfied. The global asymptotic stability of the disease-free equilibrium of the full model is shown not to exist when the associated reproduction number is less than unity. The existence of endemic equilibrium of the syphilis-only sub-model is shown to exist and the global asymptotic stability of the disease-free and endemic equilibria of the syphilis-only sub-model was established, for a special case. Sensitivity analysis is also carried out on the parameters of the model. Using the syphilis associated reproduction number, [Formula: see text], as the response function, it is observed that the five-ranked parameters that drive the dynamics of the co-infection model are the demographic parameter [Formula: see text], the effective contact rate for syphilis transmission, [Formula: see text], the progression rate to late stage of syphilis [Formula: see text], and syphilis treatment rates: [Formula: see text] and [Formula: see text] for co-infected individuals in compartments [Formula: see text] and [Formula: see text], respectively. Moreover, when the HPV associated reproduction number, [Formula: see text], is used as the response function, the five most dominant parameters that drive the dynamics of the model are the demographic parameter [Formula: see text], the effective contact rate for HPV transmission, [Formula: see text], the fraction of HPV infected who develop persistent HPV [Formula: see text], the fraction of individuals vaccinated against incident HPV infection [Formula: see text] and the HPV vaccine efficacy [Formula: see text]. Numerical simulations of the optimal control model showed that the optimal control strategy which implements syphilis treatment controls for singly infected individuals is the most cost-effective of all the control strategies in reducing the burden of HPV and syphilis co-infections.

Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator

“…Goshu and Alebachew [36] created a mathematical model for the spread of CC transmission disease in the presence of vaccination and therapy. Omame et al [37] created and presented a coinfection classical integer-order model for syphilis and HPV with cost-efectiveness analysis and optimal control. While the fractional-order in the Caputo-Fabrizio sense of the coinfection model for HPV and Syphilis is investigated using the nonsingular kernel derivative [38].…”

Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application

“…Mathematical modeling has become the powerful tool for studying the behaviour of infectious diseases ( Egonmwan & Okuonghae, 2019 ; Omame, Okuonghae, Umana, & Inyama, 2020 ; Omame, Okuonghae, Nwafor, & Odionyenma, 2021 ). Different mathematical modeling of COVID-19 with vaccination is studied in ( Gumel, Iboi, Ngonghala, & Ngwa, 2020 ; L. Zhang, Ullah, Al Alwan, Alshehri, & Sumelka, 2021 ; Diagne, Rwezaura, Tchoumi, & Tchuenche, 2021 ; Yavuz, Coşar, Günay, & Özdemir, 2021 ).…”

COVID-19 SIR model: Bifurcation analysis and optimal control

“…Recently, many researchers analyzed their COVID-19 model with backward [16] , forward–backward [17] , [18] , transcritical [19] , Hopf [20] bifurcations. With their model, they used optimal control variables to reduce COVID-19 [21] , [22] such as treatment, infection prevention, and vaccination.…”