Dynamical transmission and effect of smoking in society

Ahmad, et al.

doi:10.21833/ijaas.2018.02.012

Cited by 14 publications

(10 citation statements)

References 26 publications

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“…8,9 Ahmad et al examine the behavior of smoking effects in the society. 10 The outlines memory and transmitted properties of various mathematical models are the well-known features of fractional differential equations. Fractional-order models are more convincing and useful than the classical-order models.…”

Section: Introductionmentioning

confidence: 99%

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

et al. 2020

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In recent year, the world has witnessed the arrival of deadly diseases like cancer over all the global levels. To fight back this disease or control the spread, mankind relies on modeling and medicine to control, cure, and behavior of the cancer diseases. We developed the fractional‐order immunotherapy bladder cancer model and used the BCG vaccine for treatment by using the Caputo fractional derivative operator φɛ(0,1]. A mathematical model has four variables B,E, Ti, Tu which represent the vaccine for the immune system, effector cells, total population of affected, and unaffected cells, respectively. In this model, we have two cases according to the growth rate of cells. The fractional‐order system is stable in both cases and gives the solution infeasible region for uniqueness, positivity, and boundedness to illustrate the treatment of cancer. The effect of fractional parameter on our obtained solutions is presented, and a comparison is made with the classical ordinary derivative operator. It is worthy to observe that fractional derivatives show significant changes and memory effects as compared with ordinary derivatives to control the disease at the initial stage to overcome the risk of living with cancer.

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Section: Introductionmentioning

confidence: 99%

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

et al. 2020

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“…Norbert Wiener's cybernetics to study biological control mechanisms [5], mathematical research on the nervous system [6] and recent use of mathematics to study consciousness [7,8]. Examine the Dynamical transmission and effect of smoking in society [15]. The distinguished features of fractional differential equations are that it outlines memory and transmitted properties of numerous mathematical models.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Analysis of Fractional Order Co-Infection TB and HIV Model

Farman¹,

Usman²,

Ahmad

et al. 2020

ijaa

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A mathematical model of HIV/AIDS and TB including its co-infections is formulated. We find the Equilibrium points and with the help of numerical simulation, we have analyzed that the sub-models of TB, HIV/AIDS and its co-infections. The Caputo and Caputo Febrizo fractional derivative operator of order α ∈ (0, 1] is employed to obtain the system of fractional differential equations. Laplace Adomian Decomposition Method was successfully used for solving the different differential equations.Laplace transform is a perfect technique in various field of biological science,engineering,pure and applied mathematics. The latest technique Laplace Adomian Decomposition Method is employed on the developed fractional order model for the numerical solutions. Finally numerical simulations are also established to investigate the influence of the system parameter on the spread of disease and which show effect of fractional parameter α on our obtained solutions.

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“…These people do not develop symptoms, even though they harbor the virus and can transmit it to other people. More than 240 million people have chronic liver infections [1,3,6].…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Analysis and Modelling of Hepatitis B Model with Non-Integer Time Fractional Derivative

Farman

Ahmad

Saleem

et al. 2019

Comm. Math. & Appl.

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In this paper, we develop time fractional Hepatitis B model and analyze qualitatively. The Caputo fractional derivative operator of order α ∈ (0, 1] is employed to obtain the system of fractional differential equations. The stability and sensitivity analysis of fractional order model has been made and verify the non-negative unique solution. LADM was successfully used for solving different problems. Laplace transform method is a useful technique in different field of biological science, engineering and applied mathematics. The latest technique (LADM) is employed on the developed fractional order model for numerical solutions. Finally, numerical simulations are also established to investigate the influence of the system parameter on the spread of the disease and which show the effect of fractional parameter α on our obtained solutions.

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Dynamical transmission and effect of smoking in society

Cited by 14 publications

References 26 publications

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

Mathematical Analysis of Fractional Order Co-Infection TB and HIV Model

A Mathematical Analysis and Modelling of Hepatitis B Model with Non-Integer Time Fractional Derivative

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