A Co-infection model for HPV and Syphilis with Optimal Control and Cost-Effectiveness Analysis

Abstract

In this work, we develop and present a co-infection model for human papillomavirus (HPV) and syphilis with cost-effectiveness optimal control analysis. 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 \textbf{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 both the syphilis-only sub-model and HPV-only sub-model were established. The global asymptotic stability of disease-free equilibrium of the HPV-only sub-model is also proven. 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.

A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative

“…Many of the research works that have been carried out on the epidemiology of diseases using integer order models, such as those in [13] , [17] , [20] , [21] , [22] , [23] , [24] have so much limitations as they could not capture the effect of memory as a result the integer nature of the order. These limitations have created a big vacuum for other methodologies to come up, such as fractional differential operators which involve both non-local and singular kernel and uses the power law function as its kernel.…”