Mathematical analysis of a two-sex Human Papillomavirus (HPV) model

Ukanwoke

et al. 2020

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This paper presents an SVEIRT epidemiological model in the human population with Chlamydia trachomatis. The model incorporated the vaccination class and investigated the role played by some control strategies in the dynamics of the disease (Chlamydia tracomatis). The reproduction number which helps in determining the rate of spread of the disease, was calculated using the method proosed by van den Driessche and Watmough. The local and global stability of the equilibrium points where established, where it was observed that the model is locally asymptotically stable if the reproduction number is less than unity, and globally stable if a certain threshold value is greater than unity or the re-infection rate is zero. The effect of the re-infection rate on the global stability suggests the exhibition of the phenomenon of backward bifurcation of the model. The backward bifurcation of the system was later studied, and it shows that backward bifurcation will occur if the value of the bifurcation parameter a is positive. The optimal control of the model shows the effect of different strategies in the transmission dynamicsof the disease and the cost effectivenes of each control pair. It was observed that the treatment and control effort gives the most cost effective combinations and at the same time the highest rate of disease avertion when compared to other stratagies. Sensitivity analysis of the parameters as shown in model, shows parameters that have high impact on the chosen classes.

Section: Introductionmentioning

confidence: 99%

Optimal Control of Chlamydia Model with Vaccination

Odionyenma

Ukanwoke

et al. 2020

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“…For the oncogenic HPV-TB co-infection model (1) to be meaningful in the concept of epidemiological sense, it is necessary to prove that all its state variables are non-negative over time. The approach adopted by Omame et al [23] will be used to establish the results below .…”

Section: Model Formulation and Basic Properties Of The Modelmentioning

confidence: 99%

“…Mathematical models have recently been studied to understand the transmission dynamics of human papillomavirus infection (See Omame et al [23] and the references included therein). Malik et al [17] investigated an optimal control model for HPV, incorporating optimal vaccination strategies for females in the population.…”

Section: Introductionmentioning

confidence: 99%

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A co-infection model for Oncogenic HPV and TB with Optimal Control and Cost-Effectiveness Analysis

Okuonghae

2020

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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.

“…Many mathematical modelling studies have been carried out to understand the dynamics of transmission of the Human papillomavirus [4, 21, 22, 29, 37]. Malik et al .…”

Section: Introductionmentioning

confidence: 99%

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

Okuonghae

Nwafor

et al. 2020

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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.