Optimal Control Analysis of HIV-TB Co-infection Model

2020 ◽  
pp. 259-273
Author(s):  
Tanvi ◽  
Rajiv Aggarwal
Keyword(s):  
Optimal Control ◽  
Infection Model ◽  
Control Analysis

scholarly journals Optimal Control and Cost-effectiveness Analysis of an HPV-Chlamydia Trachomatis co-infection model

2020 ◽  
Author(s):  
Andrew Omame ◽  
Celestine Uchenna Nnanna ◽  
Simeon Chioma Inyama
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Chlamydia Trachomatis ◽  
Reproduction Number ◽  
Population Level ◽  
Backward Bifurcation ◽  
Infection Model ◽  
Control Analysis ◽  
Number Of Individuals ◽  
Positive Population

In this work, a co-infection model for human papillomavirus (HPV) and Chlamydia trachomatis with cost-effectiveness optimal control analysis is developed and analyzed. The disease-free equilibrium of the co-infection model is \textbf{shown not to} be globally asymptotically stable, when the associated reproduction number is less unity. It is proven that the model undergoes the phenomenon of backward bifurcation when the associated reproduction number is less than unity. It is also shown that HPV re-infection ($\varepsilon\sst{p} \neq 0$) induced the phenomenon of backward bifurcation. Numerical simulations of the optimal control model showed that: (i) focusing on HPV intervention strategy alone (HPV prevention and screening), in the absence of Chlamydia trachomatis control, leads to a positive population level impact on the total number of individuals singly infected with Chlamydia trachomatis, (ii) Concentrating on Chlamydia trachomatis intervention controls alone (Chlamydia trachomatis prevention and treatment), in the absence of HPV intervention strategies, a positive population level impact is observed on the total number of individuals singly infected with HPV. Moreover, the strategy that combines and implements HPV and Chlamydia trachomatis prevention controls is the most cost-effective of all the control strategies in combating the co-infections of HPV and Chlamydia trachomatis.

scholarly journals Mathematical Analysis of a model for Chlamydia and Gonorrhea Codynamics with Optimal Control

2020 ◽  
Author(s):  
Eziaku Chinomso Chukukere ◽  
Simeon Chioma Inyama ◽  
Andrew Omame
Keyword(s):  
Optimal Control ◽  
Chlamydia Trachomatis ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Intervention Strategy ◽  
Infection Model ◽  
Control Analysis ◽  
Existence Of Optimal Control ◽  
The Impact ◽  
Disease Free

Abstract A model for Chlamydia trachomatis (CT) and Gonorrhea codynamics, with optimal control analysis is studied and analyzed to assess the impact of targetted treatment for each of the diseases on their co-infections in a population. The model exhibits the dynamical feature of backward bifurcation when the associated reproduction number is less than unity. 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. Simulations of the optimal control model reveal that the intervention strategy which implements female Chlamydia trachomatis treatment and male gonorrhea treatment is the most effective in combating the co-infections of Chlamydia trachomatis and gonorrhea.

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

2020 ◽  
Author(s):  
Andrew Omame ◽  
Daniel Okuonghae ◽  
Ugochukwu Emmanuel Nwafor ◽  
Benedict Udoka Odionyenma
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Control Strategies ◽  
Cost Effective ◽  
Infection Model ◽  
Control Analysis ◽  
Optimal Control Strategy ◽  
Disease Free

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.

scholarly journals An optimal control analysis of a COVID-19 model

2021 ◽  
Vol 60 (3) ◽  
pp. 2875-2884
Author(s):  
Muhammad Zamir ◽  
Thabet Abdeljawad ◽  
Fawad Nadeem ◽  
Abdul Wahid ◽  
Ali Yousef
Keyword(s):  
Optimal Control ◽  
Control Analysis

scholarly journals Discrete-time inverse optimal control for a reaction wheel pendulum: a passivity-based control approach

2020 ◽  
Vol 19 (4) ◽  
pp. 123-132 ◽  
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Federico Martin Serra
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Point Of View ◽  
Control Analysis ◽  
Inverse Optimal Control ◽  
Reaction Wheel ◽  
Control Approach ◽  
Control Functions ◽  
Passivity Based Control ◽  
The Time Domain

In this paper it is presented the design of a controller for a reaction wheel pendulum using a discrete-time representation via optimal control from the point of view of passivity-based control analysis. The main advantage of the proposed approach is that it allows to guarantee asymptotic stability convergence using a quadratic candidate Lyapunovfunction. Numerical simulations show that the proposed inverse optimal control design permits to reach superiornumerical performance reported by continuous approaches such as Lyapunov control functions and interconnection,and damping assignment passivity-based controllers. An additional advantageof the proposed inverse optimal controlmethod is its easy implementation since it does not employ additional states. It is only required a basic discretizationof the time-domain dynamical model based on the backward representation. All the simulations are carried out inMATLAB/OCTAVE software using a codification on the script environment.

scholarly journals Analysis of Atangana–Baleanu fractional-order SEAIR epidemic model with optimal control

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chernet Tuge Deressa ◽  
Gemechis File Duressa
Keyword(s):  
Numerical Simulation ◽  
Optimal Control ◽  
Fractional Order ◽  
Control Strategy ◽  
Epidemic Model ◽  
Numerical Scheme ◽  
Order Derivative ◽  
Control Analysis ◽  
Fractional Order Derivative ◽  
Fractional Orders

AbstractWe consider a SEAIR epidemic model with Atangana–Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Optimal control analysis and simulation show that the control strategy designed is operative in reducing the number of cases in different compartments. Moreover, simulating the optimal profile revealed that reducing the fractional-order from 1 leads to the need for quick starting of the application of the designed control strategy at the maximum possible level and maintaining it for the majority of the period of the pandemic.

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