Optimal control analysis of hepatitis B virus with treatment and vaccination

Alrabaiah, Hussam; Safi, Mohammad A.; DarAssi, Mahmoud H.; Al-Hdaibat, Bashir; Ullah, Saif; Khan, Muhammad Altaf; Shah, Syed İnayat Ali

doi:10.1016/j.rinp.2020.103599

Cited by 39 publications

(28 citation statements)

References 34 publications

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“…Thus, the following Hamiltonian function is obtained: 𝐻 = (𝑆(𝑡) − 𝑄 𝑃 (𝑡) + The PMP method was used to obtain the adjoint variables [17][18][19][20][21][22][23]. ) , 1)…”

Section: Optimal Control Solutionsmentioning

confidence: 99%

Optimal Control in a Mathematical Model of Smoking

Ilmayasinta

Purnawan

2021

J. Math. Fund. Sci.

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This paper presents a dynamic model of smoking with optimal control. The mathematical model is divided into 5 sub-classes, namely, non-smokers, occasional smokers, active smokers, individuals who have temporarily stopped smoking, and individuals who have stopped smoking permanently. Four optimal controls, i.e., anti-smoking education campaign, anti-smoking gum, anti-nicotine drug, and government prohibition of smoking in public spaces are considered in the model. The existence of the controls is also presented. The Pontryagin maximum principle (PMP) was used to solve the optimal control problem. The fourth-order Runge-Kutta was employed to gain the numerical solutions.

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Section: Optimal Control Solutionsmentioning

confidence: 99%

Optimal Control in a Mathematical Model of Smoking

Ilmayasinta

Purnawan

2021

J. Math. Fund. Sci.

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“…Oud et al [ 13 ] have studied a fractional order mathematical model for COVID-19 dynamics with isolation, quarantine, and environmental viral load. For the study of some interesting models related to COVID-19 pandemic, we refer a reader to [ 14 – 17 ]. From the evaluations so far, we have noticed that isolation plays a huge role in controlling the disease spread.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of a discrete-time compartmental model for hypertensive or diabetic patients exposed to COVID-19

et al. 2021

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In this article, a mathematical model for hypertensive or diabetic patients open to COVID-19 is considered along with a set of first-order nonlinear differential equations. Moreover, the method of piecewise arguments is used to discretize the continuous system. The mathematical system is said to reveal six equilibria, namely, extinction equilibrium, boundary equilibrium, quarantined-free equilibrium, exposure-free equilibrium, endemic equilibrium, and the equilibrium free from susceptible population. Local stability conditions are developed for our discrete-time mathematical system about each of its equilibrium point. The existence of period-doubling bifurcation and chaos is studied in the absence of isolated population. It is shown that our system will become unstable and experiences the chaos when the quarantined compartment is empty, which is true in biological meanings. The existence of Neimark–Sacker bifurcation is studied for the endemic equilibrium point. Moreover, it is shown numerically that our discrete-time mathematical system experiences the period-doubling bifurcation about its endemic equilibrium. To control the period-doubling bifurcation, Neimark–Sacker bifurcation, a generalized hybrid control methodology is used. Moreover, this model is analyzed along with generalized hybrid control in order to eliminate chaos and oscillation epidemiologically presenting the significance of quarantine in the COVID-19 environment.

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“…6,7 Mathematical models have been applied extensively in the study of the dynamics of infectious diseases. [8][9][10][11][12][13][14][15] Particularly, models have recently been studied to understand the transmission dynamics of HPV infection (See Omame et al 16 and the references included therein). For instance, Malik et al 17 investigated an optimal control model for HPV, incorporating optimal vaccination strategies for females in the population.…”

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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Optimal control analysis of hepatitis B virus with treatment and vaccination

Cited by 39 publications

References 34 publications

Optimal Control in a Mathematical Model of Smoking

Optimal Control in a Mathematical Model of Smoking

Bifurcation analysis of a discrete-time compartmental model for hypertensive or diabetic patients exposed to COVID-19

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

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