In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solu...In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented and a discrete-time finite difference scheme is constructed using the nonstandard finite difference (NSFD) method. A comparative study of the classical Runge-Kutta method and ODE45 is presented in the case of integer order derivatives. The solutions obtained are presented graphically.展开更多
Definition of ecological integrity based on community analysis has long been a critical issue in risk assessment for sustainable ecosystem management. In this work, two indices （i.e., Shannon index and exergy） were ...Definition of ecological integrity based on community analysis has long been a critical issue in risk assessment for sustainable ecosystem management. In this work, two indices （i.e., Shannon index and exergy） were selected for the analysis of community properties of benthic macroinvertebrate community in streams in Korea. For this purpose, the means and variances of both indices were analyzed. The results found an extra scope of structural and functional properties in communities in response to environmental variabilities and anthropogenic disturbances. The combination of these two parameters （four indices） was feasible in identification of disturbance agents （e.g., industrial pollution or organic pollution） and specifying states of communities. The four-aforemen- tioned parameters （means and variances of Shannon index and exergy） were further used as input data in a self- organizing map for the characterization of water quality. Our results suggested that Shannon index and exergy in combination could be utilized as a suitable reference system and would be an efficient tool for assessment of the health of aquatic ecosystems exposed to environmental disturbances.展开更多
文摘In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented and a discrete-time finite difference scheme is constructed using the nonstandard finite difference (NSFD) method. A comparative study of the classical Runge-Kutta method and ODE45 is presented in the case of integer order derivatives. The solutions obtained are presented graphically.
文摘Definition of ecological integrity based on community analysis has long been a critical issue in risk assessment for sustainable ecosystem management. In this work, two indices （i.e., Shannon index and exergy） were selected for the analysis of community properties of benthic macroinvertebrate community in streams in Korea. For this purpose, the means and variances of both indices were analyzed. The results found an extra scope of structural and functional properties in communities in response to environmental variabilities and anthropogenic disturbances. The combination of these two parameters （four indices） was feasible in identification of disturbance agents （e.g., industrial pollution or organic pollution） and specifying states of communities. The four-aforemen- tioned parameters （means and variances of Shannon index and exergy） were further used as input data in a self- organizing map for the characterization of water quality. Our results suggested that Shannon index and exergy in combination could be utilized as a suitable reference system and would be an efficient tool for assessment of the health of aquatic ecosystems exposed to environmental disturbances.
