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 ( p ≠ 0 and t ≠ 0) as well as TB exogenous re-infection term ( 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.

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

“…The relative infectiousness of co-infected individuals when compared to singly infected individuals with COVID-19 is still unknown; we have therefore assumed . COVID-19 induced death rate was set to be 0.015, following the work in [23] , so that . The total population of New Delhi is estimated to be 30,291,000 [8] .…”

“…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.…”

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.…”

An optimal control model for COVID‐19, zika, dengue, and chikungunya co‐dynamics with reinfection

“…To understand the dynamics of co‐interaction between diseases, a lot of models have been proposed in the literature. 22 , 23 , 24 , 25 , 26 , 27 , 28 The authors in Reference 22 considered a dynamical model for SARS‐CoV‐2 and zika virus, incorporating the assumption of incident co‐infection with the two diseases. They showed that under this scenario, the qualitative behavior of the complete co‐infection model is not driven by that of the sub‐models.…”

“…They also investigated the Lyapunov stability of both infection‐free and endemic equilibria when the causes of backward bifurcation are removed from the model. Omame and Okuonghae 23 used optimal control to investigate the co‐interaction of oncogenic human papillomavirus and tuberculosis. Using optimal control, Bonyah et al 24 analyzed a co‐dynamical model for dengue fever and zika virus.…”