Fractional optimal control of an HIV/AIDS epidemic model with random testing and contact tracing

Kheiri, Hossein; Jafari, Mohsen A.

doi:10.1007/s12190-018-01219-w

Cited by 43 publications

(30 citation statements)

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“…Now, we utilize the product trapezoidal quadrature formula to approximate (30). Then, the corrector approximation for R(t n+1 ) is obtained as follows:…”

Section: A Numerical Methodsmentioning

confidence: 99%

“…Fractional differential calculus has been used in modeling many phenomena in everyday real-world applications [ 18 , 20 – 23 , 25 ]. Therefore, due to the importance and scope of applications, many efficient numerical methods specific to each of these types of fractional operators have also been introduced [ 3 – 8 , 10 , 11 , 15 , 19 , 24 , 30 , 35 , 37 , 43 ]. However, in [ 41 ] the author has conducted a review to point some possible problems and difficulties arising in the construction of fractional-dynamic model analogs of standard models by using fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

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A fractional system of delay differential equation with nonsingular kernels in modeling hand-foot-mouth disease

Ghanbari

2020

Adv Differ Equ

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In this article, we examine a computational model to explore the prevalence of a viral infectious disease, namely hand-foot-mouth disease, which is more common in infants and children. The structure of this model consists of six sub-populations along with two delay parameters. Besides, by taking advantage of the Atangana–Baleanu fractional derivative, the ability of the model to justify different situations for the system has been improved. Discussions about the existence of the solution and its uniqueness are also included in the article. Subsequently, an effective numerical scheme has been employed to obtain several meaningful approximate solutions in various scenarios imposed on the problem. The sensitivity analysis of some existing parameters in the model has also been investigated through several numerical simulations. One of the advantages of the fractional derivative used in the model is the use of the concept of memory in maintaining the substantial properties of the understudied phenomena from the origin of time to the desired time. It seems that the tools used in this model are very powerful and can effectively simulate the expected theoretical conditions in the problem, and can also be recommended in modeling other computational models in infectious diseases.

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“…Now, we utilize the product trapezoidal quadrature formula to approximate (30). Then, the corrector approximation for R(t n+1 ) is obtained as follows:…”

Section: A Numerical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A fractional system of delay differential equation with nonsingular kernels in modeling hand-foot-mouth disease

Ghanbari

2020

Adv Differ Equ

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“…It is therefore important to implement the control measures to prevent and control the disease spread among the populations. Kheiri and Jafari [35] formulated a fractional optimal control epidemic model of HIV/AIDS with random testing and contact tracing. In their model, they have incorporated the control measures of condom use and antiretroviral therapy for the control of spread of HIV/AIDS in the susceptible population.…”

Section: Introductionmentioning

confidence: 99%

“…The adjoint system(35) i.e., λ S , λ E , λ I 1 , λ I 2 and λ R are obtained from the Hamiltonian H as…”

mentioning

confidence: 99%

Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control

Naik

Owolabi

2020

Chaos, Solitons & Fractals

159

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Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre-including this research content-immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

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“…Fractional optimal control theory has been discussed by Podlubny [20], Matignon [15], Petras [18], Podlubny et al [21], Li and Chen [13], Lin [14], Cao and Ren [4], Sweilam and Al-Mekhlafi [24], Kheiri and Jafari [11], Bonyah [3] with its simulation contributed such effective results. Özbay et al [17] and Hamamci [10] designed a PID controller for a fractional-order system with time delays.…”

Section: Introductionmentioning

confidence: 99%

Fractional order model for yield through diagnosed/undiagnosed soil

Shah

Jayswal

Pandya

2020

São Paulo J. Math. Sci.

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Farming is the basic economy of any country. Soil fertility and water are key resources for yielding. The fractional order compartmental model is prepared in Caputo sense to improve the density of yield through diagnosed and undiagnosed soil. To measure the growing intensity of yield, the basic reproduction number is formulated using the next generation matrix method for integer order non-linear dynamical system. Local stability analysis is described for both the equilibrium points; undiagnosed soil free and optimum equilibrium point. Global stability is exhaustively computed by generating a Lyapunov function. With reference to the basic reproduction number, bifurcation analysis has been defined which expresses the chaotic nature of soil fertility. Moreover, optimal control theory is applied in the present fractional model to optimize yield. And optimality conditions are calculated with the help of Pontryagin maximum principle. The numerical simulation for different fractional orders is performed concerning validated data to analyze the behavior with respect to the order.

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Fractional optimal control of an HIV/AIDS epidemic model with random testing and contact tracing

Cited by 43 publications

References 50 publications

A fractional system of delay differential equation with nonsingular kernels in modeling hand-foot-mouth disease

A fractional system of delay differential equation with nonsingular kernels in modeling hand-foot-mouth disease

Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control

Fractional order model for yield through diagnosed/undiagnosed soil

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