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Analysis of a fuzzy epidemic model with saturated treatment and disease transmission

International Journal of Biomathematics 2018年第1期11卷 23-40页

作者： Swapan Kumar Nandi Soovoojeet Jana manotosh manadal T. K. Kar Department of MathematicsNayabasat P. M. Sikshaniketan Paschim Medinipur 721253 West Bengal India Department of Mathematics Ramsaday College Amta 711501 West Bengal India Department of Mathematics Tamralipta MahavidyalayaTamluk 721636 West Bengal India Department of MathematicsIndian Institute of Engineering Science and Technology Shibpur Howrah 711103 West Bengal India

In this paper, we describe an SIS epidemic model where both the disease transmission rate and treatment function are considered in saturated forms. The dynamical behavior of the system is analyzed. The system is customized by considering the disease transmission rate and treatment control as fuzzy numbers and then fuzzy expected value of the infected individuals is determined. The fuzzy basic reproduction number is investigated and a threshold condition of pathogen is derived at which the system undergoes a backward bifurcation.

关键词：疾病传播流行模型模糊期望浸透在系统动态行为模糊数字 SIS

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Analysis of a fractional-order SIS epidemic model with saturated treatment

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第1期12卷 185-212页

作者： Soovoojeet Jana manotosh Mandal Swapan Kumar Nandi T.K.Kar Department of Mathematics Ramsaday College Amta-711401HowrahWest BengalIndia Department of Mathematics Tamralipta Mahavidyalaya Tamluk-721636West BengalIndia Department of Mathematics Nayabasat P.M.Sikshaniketan Paschim Medinipur-721253West BengalIndia Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur Howrah-711103West BengalIndia

In this paper,we propose and analyze a fractional-order SIS epidemic model with the saturated treatment and disease transmission.The existence and uniqueness,nonnegativity and finiteness of solutions for our suggested model have been studied.Different equilibria of the model are found and their local and global stability analyses are also examined.Furthermore,the conditions for fractional backward and fractional Hopf bifurcation are also analyzed in both the commensurate and incommensurate fractional-order model.We study how the control parameter and the order of the fractional derivative play role in local as well as global stability of equilibrium points and Hopf bifurcation.We have demonstrated the analytical results of our proposed model system through several numerical simulations.

关键词： Caputo fractional differentiation SIS epidemic model global asymptotic stability treatment control fractional Hopf bifurcation fractional backward bifurcation

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Vertical Sediment Concentration Distribution in High-Concentrated Flows:An Analytical Solution Using Homotopy Analysis Method

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Communications in Theoretical Physics 2018年第9期69卷 367-378页

作者： manotosh Kumbhakar Jitraj Saha Koeli Ghoshal Jitendra Kumar Vijay P.Singh Department of Mathematics Indian Institute of Technology Kharagpur Department of Mathematics National Institute of Technology Department of Biological and Agricultural Engineering & Zachry Department of Civil Engineering Texas A&M UniversityCollege Station

Transport of suspended sediment in open channel flow has an enormous impact on real life situations,viz. control and management of reservoir sedimentation, geomorphic evolution such as dunes, rivers, and coastlines etc. Transport entails advection and diffusion. Turbulent diffusion is governed by the concept of Fick’s law, which is based on the molecular diffusion theory, and the equation that represents the distribution of sediment concentration is the advection-diffusion equation. The study uses the existing governing equation which considers different phases for solid and fluid, and then couples the two phases. To deal with high-concentrated flow, sediment and turbulent diffusion coefficients are taken to be different from each other. The effect of hindered settling on sediment particles is incorporated in the governing equation, which makes the equation highly non-linear. This study derives an explicit closed-form analytical solution to the generalized one-dimensional diffusion equation representing the vertical sediment concentration distribution with an arbitrary turbulent diffusion coefficient profile. The solution is obtained by Homotopy Analysis Method, which does not rely on the small parameters present in the equation. Finally, the solution is validated by comparing it with the implicit solution and the numerical solution. A relevant set of laboratory data is selected to check the applicability of the model, and a close agreement shows the potential of the model in the context of application to high-concentrated sediment-laden open channel flow.

关键词：中高度沉积流动分发垂直实验室数据生活状况地球形状

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