In this paper,a reaction-diffusion system is proposed to investigate avian-human influenza.Two free boundaries are introduced to describe the spreading frontiers of the avian influenza.The basic reproduction numbers r...In this paper,a reaction-diffusion system is proposed to investigate avian-human influenza.Two free boundaries are introduced to describe the spreading frontiers of the avian influenza.The basic reproduction numbers rF0(t)and RF0(t)are defined for the bird with the avian influenza and for the human with the mutant avian influenza of the free boundary problem,respectively.Properties of these two time-dependent basic reproduction numbers are obtained.Sufficient conditions both for spreading and for vanishing of the avian influenza are given.It is shown that if rF0(0)<1 and the initial number of the infected birds is small,the avian influenza vanishes in the bird world.Furthermore,if rF0(0)<1 and RF0(0)<1,the avian influenza vanishes in the bird and human worlds.In the case that rF0(0)<1 and RF0(0)>1,spreading of the mutant avian influenza in the human world is possible.It is also shown that if rF0(t0)>1 for any t0>0,the avian influenza spreads in the bird world.展开更多
In this paper, analytical result of avian-human influenza epidemic model has been inves- tigated by applying homotopy analysis method （HAM） and by expanding it to hybrid numeric-analytic method which is known as mul...In this paper, analytical result of avian-human influenza epidemic model has been inves- tigated by applying homotopy analysis method （HAM） and by expanding it to hybrid numeric-analytic method which is known as multistage HAM （MSHAM）. HAM is an algorithm which gives us the approximate solution of the problem in an arrangement of time interims and by modifying it to multistage one. Some advantages such as flexibility of picking the auxiliary linear operator and the auxiliary parameter are emerged, that leads us to achieve some excellent results in this work. Furthermore, in this analyti- cal work, obtained results are compared and reported with numerical ones which were obtained previously from methods such as the Runge-Kutta （RK4） method.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11071209)Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(Grant No.2010-0025700)Natural Science Foundation of the Higher Education Institutions of Jiangsu Province(Grant No.12KJD110008)
文摘In this paper,a reaction-diffusion system is proposed to investigate avian-human influenza.Two free boundaries are introduced to describe the spreading frontiers of the avian influenza.The basic reproduction numbers rF0(t)and RF0(t)are defined for the bird with the avian influenza and for the human with the mutant avian influenza of the free boundary problem,respectively.Properties of these two time-dependent basic reproduction numbers are obtained.Sufficient conditions both for spreading and for vanishing of the avian influenza are given.It is shown that if rF0(0)<1 and the initial number of the infected birds is small,the avian influenza vanishes in the bird world.Furthermore,if rF0(0)<1 and RF0(0)<1,the avian influenza vanishes in the bird and human worlds.In the case that rF0(0)<1 and RF0(0)>1,spreading of the mutant avian influenza in the human world is possible.It is also shown that if rF0(t0)>1 for any t0>0,the avian influenza spreads in the bird world.
文摘In this paper, analytical result of avian-human influenza epidemic model has been inves- tigated by applying homotopy analysis method （HAM） and by expanding it to hybrid numeric-analytic method which is known as multistage HAM （MSHAM）. HAM is an algorithm which gives us the approximate solution of the problem in an arrangement of time interims and by modifying it to multistage one. Some advantages such as flexibility of picking the auxiliary linear operator and the auxiliary parameter are emerged, that leads us to achieve some excellent results in this work. Furthermore, in this analyti- cal work, obtained results are compared and reported with numerical ones which were obtained previously from methods such as the Runge-Kutta （RK4） method.
