Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability

Majee, Suvankar; Jana, Soovoojeet; Das, Dhiraj Kumar; Kar, Tapan Kumar

doi:10.1016/j.chaos.2022.112291

Cited by 28 publications

(9 citation statements)

References 39 publications

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“…In the context of a pandemic, various uncertain factors have a particularly significant impact on disease transmission. Therefore, a large number of deterministic infectious disease models can be further extended to random environments [40,41]. In the above section, we have obtained that if R 0 > 1, then the system (19) has a unique endemic equilibrium P * (S * , E * , Q * , I * ) and is asymptotically stable.…”

Section: Stochastic Stability Analysis Around the Endemic Equilibriummentioning

confidence: 90%

Stability and Optimal Control of a Fractional SEQIR Epidemic Model with Saturated Incidence Rate

Sun

Zhao

2023

Fractal Fract

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The fractional differential equation has a memory property and is suitable for biomathematical modeling. In this paper, a fractional SEQIR epidemic model with saturated incidence and vaccination is constructed. Firstly, for the deterministic fractional system, the threshold conditions for the local and global asymptotic stability of the equilibrium point are obtained by using the stability theory of the fractional differential equation. If R0<1, the disease-free equilibrium is asymptotically stable, and the disease is extinct; when R0>1, the endemic equilibrium is asymptotically stable and the disease persists. Secondly, for the stochastic system of integer order, the stochastic stability near the positive equilibrium point is discussed. The results show that if the intensity of environmental noise is small enough, the system is stochastic stable, and the disease will persist. Thirdly, the control variables are coupled into the fractional differential equation to obtain the fractional control system, the objective function is constructed, and the optimal control solution is obtained by using the maximum principle. Finally, the correctness of the theoretical derivation is verified by numerical simulation.

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Section: Stochastic Stability Analysis Around the Endemic Equilibriummentioning

confidence: 90%

Stability and Optimal Control of a Fractional SEQIR Epidemic Model with Saturated Incidence Rate

Sun

Zhao

2023

Fractal Fract

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“…Therefore, it is necessary to study the influence of various parameters on the basic reproduction number to make a control policy. A model's most sensitive parameters are calculated using the sensitivity index approach [16,38,39]. The data collection process and presumed parameter values are usually error-prone.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…ODE is used frequently in the mathematical models in the field of epidemiology to analyze a biological system. In the real world, many biological systems have memory effects (see [16,17]), but ODE is unable to take into account this memory. Fractional order differential equations can reflect this memory [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…Hence, it is logical to consider a mathematical model with the help of fractional order differential equations to study the memory effect of the monkeypox. In recent years, fractional differential equations have been widely employed epidemiology to describe both infectious and non-infectious diseases [16,17,25,26]. Very few studies have been conducted on monkeypox that discusses memory.…”

Section: Introductionmentioning

confidence: 99%

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Transmission dynamics of monkeypox virus with treatment and vaccination controls: a fractional order mathematical approach

Majee¹,

Jana²,

Barman³

et al. 2023

Phys. Scr.

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Presently, monkeypox virus infection has spread worldwide in the ongoing outbreak that began in the UK. To study the transmission dynamics of monkeypox, we formulate here a seven-compartmental (five compartments for the human population and two compartments for animals or rodents) fractional-order mathematical model. The existence and uniqueness of the solution of the proposed fractional order model are examined here. The basic reproduction number for humans ($\mathfrak{R}_0^h$) and animals ($\mathfrak{R}_0^a$) are obtained through the next-generation matrix approach. Depending on the values of $\mathfrak{R}_0^h$ and $\mathfrak{R}_0^a$, we observed that the fractional order model has three equilibria, namely, monkeypox-free equilibrium, animal-free endemic equilibrium, and endemic equilibrium. Also, the stability of all equilibria is checked in this present article. We found that the model goes through transcritical bifurcation at $\mathfrak{R}_0^a=1$ for any values of $\mathfrak{R}_0^h$ and at $\mathfrak{R}_0^h=1$ for $\mathfrak{R}_0^a<1$. Best of our knowledge, this is the first work where the fractional order optimal control for monkeypox is formulated and solved considering vaccination and treatment controls. Several feasible parameter values are used in the simulations to visualize and verify the findings, from which the results show that fractional order is more appropriate. Finally, parameters involved in the expression of $\mathfrak{R}_0^h$ and $\mathfrak{R}_0^a$ are scaled using the sensitivity index approach.

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“…Fractional derivatives provide a more versatile way to model and describe the behavior of complex systems, especially those with non-local and memory-dependent characteristics [22][23][24]. They offer advantages in modeling biological phenomena by providing a more nuanced representation of complex processes, particularly in cases where memory and nonlocal effects play a crucial role [25][26][27]. This enhanced modeling capability allows for a more accurate portrayal of disease dynamics, contributing to improved understanding, diagnosis, and treatment strategies [28,29].…”

Section: Introductionmentioning

confidence: 99%

Modeling the dynamical behavior of the interaction of T-cells and human immunodeficiency virus with saturated incidence

Boulaaras,

Jan,

Khan

et al. 2024

Commun. Theor. Phys.

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In the last forty years, the rise of HIV has undoubtedly become a major concern in the field of public health, imposing significant economic burdens on affected regions. Consequently, it becomes imperative to undertake comprehensive investigations into themechanisms governing the dissemination of HIV within the human body. In this work, we devise a mathematical model that elucidates the intricate interplay between CD4+ Tcells and viruses of HIV, employing the principles of fractional calculus. The productionrate of CD4+ T-cells, like other immune cells depends on factors like age, health status, and the presence of infections or diseases. Therefore, we incorporate a variable source term in the dynamics of HIV infection with saturated incidence rate to enhance the precision of our findings. We introduce the fundamental concepts of fractional operators as a means of scrutinizing the proposed HIV model. To facilitate a deeper understanding of our system, we represent an iterative scheme that elucidates the trajectories of solution pathways of the system. We present the time series analysis of our model through numerical findings to conceptualize and understand the key factors of the system. In addition to this, we present the phase portrait and the oscillatory behavior of the systemwith the variation of different input parameters. These information can be utilized to predict the long-term behavior of the system, including whether it will converge to a steady state or exhibit periodic or chaotic oscillations.

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Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability

Cited by 28 publications

References 39 publications

Stability and Optimal Control of a Fractional SEQIR Epidemic Model with Saturated Incidence Rate

Stability and Optimal Control of a Fractional SEQIR Epidemic Model with Saturated Incidence Rate

Transmission dynamics of monkeypox virus with treatment and vaccination controls: a fractional order mathematical approach

Modeling the dynamical behavior of the interaction of T-cells and human immunodeficiency virus with saturated incidence

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