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...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.展开更多
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 custo...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 trans- mission rate and treatment control as fuzzy numbers and then fuzzy expected value of the infected individuals is determined. The fuzzy basic reproduction number is investi- gated and a threshold condition of pathogen is derived at which the system undergoes a backward bifurcation.展开更多
基金The work of S.J.is financially supported by the Department of Science&Technology and Biotechnology,Government of West Bengal(vide memo no.201(Sanc.)/ST/P/S&T/16G-12/2018 dt 19-02-2019)。
文摘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.
文摘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 trans- mission rate and treatment control as fuzzy numbers and then fuzzy expected value of the infected individuals is determined. The fuzzy basic reproduction number is investi- gated and a threshold condition of pathogen is derived at which the system undergoes a backward bifurcation.
