An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered.A system with diffusion under the homogeneous Neumann boundary condition is studied.The existence for a p...An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered.A system with diffusion under the homogeneous Neumann boundary condition is studied.The existence for a positive solution of the corresponding steady state problem is mainly discussed.First,a prior estimates（positive upper and lower bounds） of the positive steady states of the reaction-diffusion system is given by the maximum principle and the Harnack inequation.Then,the non-existence of non-constant positive steady states by using the energy method is given.Finally,the existence of non-constant positive steady states is obtained by using the topological degree.展开更多
The peer-to-peer（P2P） file-sharing network as a vehicle of disseminating files has become very popular. The appearance of dozens of kinds of passive worms on this network has, however, made it unsecured. This proble...The peer-to-peer（P2P） file-sharing network as a vehicle of disseminating files has become very popular. The appearance of dozens of kinds of passive worms on this network has, however, made it unsecured. This problem has been paid attention and a few of models for passive worm propagation has been presented. Unfortunately, the dynamic properties of this network are ignored in these models. Given the fact, the characteristics of both this network and the passive worm are identified, and on this basis a new mathematical model of passive worm propagation on the P2P network is presented in applying epidemiology in this paper. Note that the dynamic properties of this network are considered in the presented model. The model has been validated by large scale simulation experiments, which demonstrates that the presented model may be used for analyzing the behaviors of passive worms and predicting the trend of their propagation.展开更多
Mathematical models are increasingly being used in the evaluation of control strategies for infectious disease such as the vaccination program for the Human PapiUomavirus （HPV）. Here, an ordinary differential equati...Mathematical models are increasingly being used in the evaluation of control strategies for infectious disease such as the vaccination program for the Human PapiUomavirus （HPV）. Here, an ordinary differential equation （ODE） transmission dynamic model for HPV is presented and analyzed. Parameter values for a gender and risk structured model are estimated by calibrating the model around the known prevalence of infection. The effect on gender and risk sub-group prevalence induced by varying the epidemiological parameters are investigated. Finally, the outcomes of this model are applied using a classical mathematical method for calculating R0 in a heterogeneous mixing population. Estimates for R0 under various gender and mixing scenarios are presented.展开更多
基金The National Natural Science Foundation of China (No.10601011)
文摘An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered.A system with diffusion under the homogeneous Neumann boundary condition is studied.The existence for a positive solution of the corresponding steady state problem is mainly discussed.First,a prior estimates（positive upper and lower bounds） of the positive steady states of the reaction-diffusion system is given by the maximum principle and the Harnack inequation.Then,the non-existence of non-constant positive steady states by using the energy method is given.Finally,the existence of non-constant positive steady states is obtained by using the topological degree.
文摘The peer-to-peer（P2P） file-sharing network as a vehicle of disseminating files has become very popular. The appearance of dozens of kinds of passive worms on this network has, however, made it unsecured. This problem has been paid attention and a few of models for passive worm propagation has been presented. Unfortunately, the dynamic properties of this network are ignored in these models. Given the fact, the characteristics of both this network and the passive worm are identified, and on this basis a new mathematical model of passive worm propagation on the P2P network is presented in applying epidemiology in this paper. Note that the dynamic properties of this network are considered in the presented model. The model has been validated by large scale simulation experiments, which demonstrates that the presented model may be used for analyzing the behaviors of passive worms and predicting the trend of their propagation.
文摘Mathematical models are increasingly being used in the evaluation of control strategies for infectious disease such as the vaccination program for the Human PapiUomavirus （HPV）. Here, an ordinary differential equation （ODE） transmission dynamic model for HPV is presented and analyzed. Parameter values for a gender and risk structured model are estimated by calibrating the model around the known prevalence of infection. The effect on gender and risk sub-group prevalence induced by varying the epidemiological parameters are investigated. Finally, the outcomes of this model are applied using a classical mathematical method for calculating R0 in a heterogeneous mixing population. Estimates for R0 under various gender and mixing scenarios are presented.
