Optimal control of HIV treatment and immunotherapy combination with state and control delays

Silva, Cristiana J.; Maurer, Helmut

doi:10.1002/oca.2558

Cited by 8 publications

(5 citation statements)

References 29 publications

(124 reference statements)

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“…Analogously to the approach used in [20,21] we use the discretization method developed in [7], discretizing the optimal control problem on a sufficiently fine grid. In these section, we use n = 1000 grid nodes and the Euler's method as integration method, and write the resulting large-scale nonlinear programming problem using the Applied Modeling Programming Language AMPL [6] which is then linked to the optimization solver Interior-Point IPOPT [26], setting the error tolerance to tol = 10 −10 .…”

Section: Numerical Simulations Consider the Initial Conditionsmentioning

confidence: 99%

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Stability and optimal control of a delayed HIV/AIDS-PrEP model

Silva¹

2022

DCDS-S

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In this paper, we propose a time-delayed HIV/AIDS-PrEP model which takes into account the delay on pre-exposure prophylaxis (PrEP) distribution and adherence by uninfected persons that are in high risk of HIV infection, and analyze the impact of this delay on the number of individuals with HIV infection. We prove the existence and stability of two equilibrium points, for any positive time delay. After, an optimal control problem with state and control delays is proposed and analyzed, where the aim is to find the optimal strategy for PrEP implementation that minimizes the number of individuals with HIV infection, with minimal costs. Different scenarios are studied, for which the solutions derived from the Minimum Principle for Multiple Delayed Optimal Control Problems change depending on the values of the time delays and the weights constants associated with the number of HIV infected individuals and PrEP. We observe that changes on the weights constants can lead to a passage from bang-singular-bang to bang-bang extremal controls.

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Section: Numerical Simulations Consider the Initial Conditionsmentioning

confidence: 99%

“…However, not so many papers study delayed differential compartmental models in the framework of optimal control theory, see e.g. [8,15,19,21,22]. Here, we introduce a control function in the delayed differential model and propose an optimal control problem with state and control delays.…”

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confidence: 99%

Stability and optimal control of a delayed HIV/AIDS-PrEP model

Silva¹

2022

DCDS-S

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“…Optimal control with delays is a subject under strong current research [24,25,26], in particular with respect to applications in biological control systems [27,28,29]. Our main aim here is to find the optimal profile u 1 (t) and u 2 (t) to minimize the cost of biopesticides used in pest control.…”

Section: Optimal Controlmentioning

confidence: 99%

Pest control using farming awareness: impact of time delays and optimal use of biopesticides

Abraha,

Basir,

Obsu

et al. 2021

Preprint

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We investigate a mathematical model in crop pest management, considering plant biomass, pest, and the effect of farming awareness. The pest population is divided into two compartments: susceptible pest and infected pest. We assume that the growth rate of self-aware people is proportional to the density of healthy pests present in the crop field. Impacts of awareness is modeled via a saturated term. It is further assumed that self-aware people will adopt biological control methods, namely integrated pest management. Susceptible pests are detrimental to crops and, moreover, there may be some time delay in measuring the healthy pests in the crop field. A time delay may also take place while becoming aware of the control strategies or taking necessary steps to control the pest attack. In agreement, we develop our model incorporating two time delays into the system. The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays. Stability switches occur through Hopf-bifurcation when time delays cross critical values. Optimal control theory has been applied for the cost-effectiveness of the delayed system. Numerical simulations illustrate the obtained analytical results.

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“…The introduction of time delays to mathematical epidemic models has been studied in order to better understand and describe the transmission dynamics of infectious diseases; see, e.g., [14,[19][20][21]. Moreover, time delays may have an important effect on the stability of the equilibrium points, leading, for example, to periodic solutions by Hopf bifurcation; see, e.g., [22] and references cited therein.…”

Section: Introductionmentioning

confidence: 99%