A latency fractional order model for HIV dynamics

Pinto, Carla M. A.; Carvalho, Ana R.M.

doi:10.1016/j.cam.2016.05.019

Cited by 109 publications

(54 citation statements)

References 37 publications

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“…In addition, our exact solutions in (54), (66), (105), and (107) are equivalent to that, which were constructed by the exp(−Φ( )) method, in [66] in which they were expressed in (28), (29), (30), and (32), respectively. Furthermore, our exact solutions in (79) and (106) have the same mathematical structure as solution (29) in [67] using the exp-function method. Hence, the novel ( / )-expansion method used in our work have provided more new forms of the exact solutions of (28) since the method gives more free parameters than the existing methods utilized previously.…”

Section: The Exact Solutions Of (28) Obtained Using the Unknown Constmentioning

confidence: 99%

“…Since fractional derivatives [25] such as the RiemannLiouville derivative and the Caputo derivative can describe the memory and hereditary properties of materials and processes which is different from ordinary derivatives, fractional differential equations (FDEs), which are associated with 2 Mathematical Problems in Engineering fractional derivatives and the generalization of the classical differential equations of integer orders, are expansively used to model various complex phenomena in many study fields such as physics [26], engineering [27], finance [28], and biology [29]. It has been found that the above-mentioned methods with their improvements (see, e.g., [30][31][32][33]) are also widely applicable to solve FDEs.…”

Section: Introductionmentioning

confidence: 99%

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Two Reliable Methods for Solving the (3 + 1)‐Dimensional Space‐Time Fractional Jimbo‐Miwa Equation

Sirisubtawee

Koonprasert

Khaopant

et al. 2017

Mathematical Problems in Engineering

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We investigate methods for obtaining exact solutions of the (3 + 1)-dimensional nonlinear space-time fractional Jimbo-Miwa equation in the sense of the modified Riemann-Liouville derivative. The methods employed to analytically solve the equation are the ( / , 1/ )-expansion method and the novel ( / )-expansion method. To the best of our knowledge, there are no researchers who have applied these methods to obtain exact solutions of the equation. The application of the methods is simple, elegant, efficient, and trustworthy. In particular, applying the novel ( / )-expansion method to the equation, we obtain more exact solutions than using other existing methods such as the ( / )-expansion method and the exp(−Φ( ))-expansion method. The exact solutions of the equation, obtained using the two methods, can be categorized in terms of hyperbolic, trigonometric, and rational functions. Some of the results obtained by the two methods are new and reported here for the first time. In addition, the obtained exact explicit solutions of the equation characterize many physical meanings such as soliton solitary wave solutions, periodic wave solutions, and singular multiple-soliton solutions.

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Section: The Exact Solutions Of (28) Obtained Using the Unknown Constmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two Reliable Methods for Solving the (3 + 1)‐Dimensional Space‐Time Fractional Jimbo‐Miwa Equation

Sirisubtawee

Koonprasert

Khaopant

et al. 2017

Mathematical Problems in Engineering

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show abstract

“…In many applications, it has been shown that modeling the behavior of dynamical systems by fractional differential equations has more advantages than integer‐order modeling …”

Section: Introductionmentioning

confidence: 99%

“…They concluded that the integer order and the fractional order models together provide a better understanding of the dynamics of the coinfection. Also, these authors in a previous study considered a latency fractional order model for HIV dynamics where includes latent T helper cells. Jajarmi and Baleanu examined the pathological behavior of HIV‐infection using a new model based on three different operators of fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

A fractional order HIV/AIDS model based on the effect of screening of unaware infectives

Babaei

Jafari

Ahmadi

2019

Math Methods in App Sciences

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In this paper, a fractional order model for the spread of human immunodeficiency virus (HIV) infection is proposed to study the effect of screening of unaware infected individuals on the spread of the HIV virus. For this purpose, local asymptotic stability analysis of the disease‐free equilibrium is investigated. In addition, the model is studied for different values of the fractional order to show the relation between the variations of the reproduction number and the order of the proposed model. Finally, numerical solutions are simulated by using a predictor‐corrector method to illustrate the dynamics between susceptible individuals and unaware infected individuals.

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“…We apply the Grunwald-Letnikov method by using binomial coefficients [48,[56][57][58]. (Figures 14-16).…”

Section: (Iii) Grunwald-letnikov Algorithm (Binomial Coefficients)mentioning

confidence: 99%

A non-integer order dengue internal transmission model

2018

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A non-linear mathematical model with non-integer order γ , 0 < γ ≤ 1, is used to analyze the dengue virus transmission in the human body. Both disease-free F 0 and endemic F * equilibria are calculated. Their stability is also described using the stability theorem of non-integer order. The threshold parameter R 0 demonstrates an important behavior in the stability of a considerable model. For R 0 < 1, the disease-free equilibrium (DFE) F 0 is an attractor. For R 0 > 1, F 0 is not stable, the endemic equilibrium (EE) F * exists, and it is an attractor. Numerical examples of the proposed model are also proven to study the behavior of the system.

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A latency fractional order model for HIV dynamics

Cited by 109 publications

References 37 publications

Two Reliable Methods for Solving the (3 + 1)‐Dimensional Space‐Time Fractional Jimbo‐Miwa Equation

Two Reliable Methods for Solving the (3 + 1)‐Dimensional Space‐Time Fractional Jimbo‐Miwa Equation

A fractional order HIV/AIDS model based on the effect of screening of unaware infectives

A non-integer order dengue internal transmission model

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