Optimal control of HIV resistance and tuberculosis co-infection using treatment intervention

Fatmawati, Fatmawati; Tasman, Hengki

doi:10.12980/apjtd.7.2017d6-400

Cited by 9 publications

(7 citation statements)

References 12 publications

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“…Since the bifurcation coefficient b is positive, it follows from Theorem 4.1 in [6] that the model (1), or the transformed model (8), will undergo a backward bifurcation if the backward bifurcation coefficient, a, given by (11) is positive. Setting the HPV and TB re-infection paramters ϕp = 0, σt = 0 and the TB exogenous re-infection term ε t 1 = 0, the bifurcation coefficient, a < 0 (since (1 − ξ t 2 )ν8 > ξ t 2 ν9 > 0 and (1 − ξ t 3 )ν10 > ξ t 3 ν11 > 0, based on the definition of the components in (9), and also noting that all other components of the left and right eigenvectors occuring in the coefficient, a, are positive, including the parameters of the model. Hence, backward bifurcation does not occur in the Oncogenic HPV-TB co-infection model, in the absence of HPV and TB re-infection and in the absence of exogenous re-infection.…”

Section: Letmentioning

confidence: 99%

“…Lately, mathematical models have been developed to consider the optimal control strategies for the dynamics of infectious diseases including their co-infections [1, 9, 11, 20, 26, 27, 31, 32, 34]. Agusto and Adekunle [1] studied the optimal control and cost-effectiveness analysis of the co-infection of drug-resistant tuberculosis and HIV/AIDS.…”

Section: Introductionmentioning

confidence: 99%

“…They showed that the strategy that combines Pneumonia treatment and Typhoid fever prevention is the most cost-effective in reducing the burden of the co-infections of Pnemonia and Typhoid fever. The researchers in [9] analyzed an optimal control model for HIV and TB co-infection, capturing resistance of HIV to anti-retroviral therapy. The authors showed that a combination of TB treatment and anti-retroviral therapy for HIV is the most effective in reducing the burden of the co-infection of the two diseases.…”

Section: Introductionmentioning

confidence: 99%

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

Omame

Okuonghae

2020

Preprint

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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.

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Section: Letmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Omame

Okuonghae

2020

Preprint

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“…Lately, mathematical models have been developed, incorporating optimal control strategies for the dynamics of infectious diseases, including their co-infections. [25][26][27][28][29][30][31][32][33][34] More recently, Egeonu et al 27 studied a co-infection model for drug-resistant malaria and cholera with optimal control. Numerical simulations of their model revealed that malaria drug resistance can greatly influence the co-infection cases averted, even in the presence of treatment controls for co-infected individuals.…”

Section: Introductionmentioning

confidence: 99%

A co‐infection model for oncogenic human papillomavirus and tuberculosis with optimal control and Cost‐Effectiveness Analysis

Omame

Okuonghae

2021

Optim Control Appl Methods

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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 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.

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“…Mathematical models are needed to understand the dynamics of epidemic infection [4][5][6][7][8]. At present many models have been proposed to describe the dynamics of HIV/ AIDS infection [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A Fractional-Order Model for HIV Dynamics in a Two-Sex Population

Fatmawati

Shaiful

Utoyo

2018

International Journal of Mathematics and Mathematical Sciences

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Human Immunodeficiency Virus (HIV) is a virus that attacks or infects cells in the immune system that causes immune decline. Acquired Immunodeficiency Syndrome (AIDS) is the most severe stage of HIV infection. AIDS is the rapidly spreading and becoming epidemic diseases in the world of almost complete influence across the country. A mathematical model approach of HIV/AIDS dynamic is needed to predict the spread of the diseases in the future. In this paper, we presented a fractionalorder model of the spread of HIV and AIDS diseases which incorporates two-sex population. The fractional derivative order of the model is in the interval (0, 1]. We compute the basic reproduction number and prove the stability of the equilibriums of the model. The sensitivity analysis also is done to determine the important factor controlling the spread. Using the Adamstype predictor-corrector method, we then perform some numerical simulations for variation values of the order of the fractional derivative. Finally, the effects of various antiretroviral therapy (ART) treatments are studied and compared with numerical approach.

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Optimal control of HIV resistance and tuberculosis co-infection using treatment intervention

Cited by 9 publications

References 12 publications

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

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

A co‐infection model for oncogenic human papillomavirus and tuberculosis with optimal control and Cost‐Effectiveness Analysis

A Fractional-Order Model for HIV Dynamics in a Two-Sex Population

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