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    Université de Fribourg

    Positive periodic solutions of an epidemic model with seasonality

    Sun, Gui-Quan ; Bai, Zhenguo ; Zhang, Zi-Ke ; Zhou, Tao ; Jin, Zhen

    In: The Scientific World Journal, 2013, vol. 2013, p. -

    An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction Rd number is obtained. Moreover, only the basic reproduction number R0 cannot ensure the existence of the positive equilibrium, which needs...

    Université de Fribourg

    Spatial dynamics of a vegetation model in an arid flat environment

    Sun, Gui-Quan ; Li, Li ; Zhang, Zi-Ke

    In: Nonlinear Dynamics, 2013, vol. 73, no. 4, p. 2207–2219

    Self-organized vegetation patterns in space were found in arid and semi-arid areas. In this paper, we modelled a vegetation model in an arid flat environment using reaction-diffusion form and investigated the pattern formation. By using Hopf and Turing bifurcation theory, we obtain Turing region in parameters space. It is found that there are different types of stationary patterns including...