Stochastic dynamics of hepatitis B epidemics

Din, Anwarud; Li, Yongjin; Khan, Tahir; Anwar, Khurshaid; Zaman, Gul

doi:10.1016/j.rinp.2020.103730

Cited by 25 publications

(17 citation statements)

References 30 publications

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“…The methodology used to establish the above lemma can be found in Zhao and Jiang's work, readers are welcome to check references [27]. To avoid repetition, we will omit the proof here as it is similar to what has been done in [27][28][29][30][31][32].…”

Section: Extinction For Criticismmentioning

confidence: 99%

Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?

Atangana

2021

Adv Differ Equ

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Fractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to become a centre of interest for many researchers from various backgrounds. As a result, multiple innovative ideas had emerged, which caused significant divisions regarding fractional calculus in the past three years. Therefore, this work is aimed at developing a mathematical model that could be used to depict the survival of fractional calculus. Six classes are herein considered to construct a mathematical model with six ordinary differential equations. All elementary analysis have been performed. Additionally, a new analysis including strength number that accounts for the accelerative information of nonlinear and linear parts of a given epidemiological model is introduced. An analysis of the second derivative of the Lyapunov function as well as an analysis of the second derivative of each class is applied to assess how a wave could be detected. It is strongly believed that this new analysis will particularly open new doors within the field of epidemiological modelling, which will aid researchers to better understand the spread of infectious diseases. The stochastic version of the suggested model was also investigated, and numerical simulations were performed. The obtained reproductive number, strength number, extinction of criticism together with numerical simulation, revealed that the field of fractional calculus will be stable will therefore have no significant effect soon.

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Section: Extinction For Criticismmentioning

confidence: 99%

Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?

Atangana

2021

Adv Differ Equ

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“…Whereas, the Lie symmetry approach allows us to find complete local one-parameter transformation groups that can be used to find exact solutions or to reduce nonlinear DEs to linear DEs. Concerning the relationship between Lie symmetry methods and financial mathematics and economic models, we would like to note the presence of several recent studies [12][13][14][15][16][17][18][19][20][21][22], which represent the applications and utility of well-known concepts of Lie theory to several problems from mathematical finance.…”

Section: Theory and Backgroundmentioning

confidence: 99%

“…where K � 8f(t) and k j (j � 1, 2, 3, 4) are the integration constants and β can take any value as given in equation (22). Substituting the values from equation ( 23) to equation ( 16), the equivalence transformations which give the reduction of CIR equation ( 4) into the heat equation (after performing some lengthy and tedious calculation) are given as…”

Section: Casementioning

confidence: 99%

On the Resolution of a Remarkable Bond Pricing Model from Financial Mathematics: Application of the Deductive Group Theoretical Technique

Aziz

2021

Mathematical Problems in Engineering

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The classical Cox–Ingersoll–Ross (CIR) bond-pricing model is based on the evolution space-time dependent partial differential equation (PDE) which represents the standard European interest rate derivatives. In general, such class of evolution partial differential equations (PDEs) has generally been resolved by classical methods of PDEs and by ansatz-based techniques which have been previously applied in a similar context. The author here shows the application of an invariant approach, a systematic method based on deductive group-theoretical analysis. The invariant technique reduces the scalar linear space-time dependent parabolic PDE to one of the four classical Lie canonical forms. This method leads us to exactly solve the scalar linear space-time dependent parabolic PDE representing the CIR model. It was found that CIR PDE is transformed into the first canonical form, which is the heat equation. Under the proper choice of emerging parameters of the model, the CIR equation is also reduced to the second Lie canonical form. The equivalence transformations which map the CIR PDE into the different canonical forms are deduced. With the use of these equivalence transformations, the invariant solutions of the underlying model are found by using some well-known results of the heat equation and the second Lie canonical form. Furthermore, the Cauchy initial-value model of the CIR problem along with the terminal condition is discussed and closed-form solutions are deduced. Finally, the conservation laws associated with the CIR equation are derived by using the general conservation theorem.

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“…Similarly, another study has been performed to investigate the effects of information as well as to forecast the control of disease [43]. More recently, the extinction as well as the persistence analysis of an epidemic model for hepatitis B have been performed by Khan and their co-authors [44]. However, to the best of our knowledge, no one incorporates HBV epidemic model with information intervention as well as variable-order fractional network.…”

Section: Introductionmentioning

confidence: 99%

Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

Din

Yusuf

et al. 2022

Eur. Phys. J. Spec. Top.

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This paper aims at analyzing the dynamical behavior of a SIR hepatitis B epidemic stochastic model via a novel approach by incorporating the effect of information interventions and random perturbations. Initially, we demonstrate the positivity and global existence of the solutions. Afterward, we derive the stochastic threshold parameter Rs, followed by the fact that this number concludes the transmission of hepatitis B from the population. By increasing the intensity of noise, we get Rs less than one, inferring that ultimately hepatitis B will lapse. While decreasing the intensity of noise to a sufficient level, we have Rs > 1. For the case Rs > 1, adequate results for the presence of stationary distribution are achieved, showing the prevalence of hepatitis B. The present study also involves the derivation of the necessary conditions for the persistence of the epidemic. Finally, the main theoretical solutions are plotted through simulations. Discussion on theoretical and numerical results shows that utilizing random perturbations and information interventions have a pronounced impact on the syndrome's dynamics. Furthermore, since most communities interact with each other, and the disease spread rate is affected by this factor, a new variable-order fractional network of the stochastic hepatitis B model is offered. Subsequently, this study will provide a robust theoretical basis for comprehending worldwide SIR stochastic and variable-order fractional network-related case studies.

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Stochastic dynamics of hepatitis B epidemics

Cited by 25 publications

References 30 publications

Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?

Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?

On the Resolution of a Remarkable Bond Pricing Model from Financial Mathematics: Application of the Deductive Group Theoretical Technique

Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

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