Smoking is a serious global public health problem.The ability to quit smoking is closely related to age;in addition,personal determination and education usually play an important role in quitting smoking.In order to c...Smoking is a serious global public health problem.The ability to quit smoking is closely related to age;in addition,personal determination and education usually play an important role in quitting smoking.In order to capture such characteristics,we developed a novel age-structured smoking dynamical model.By defining the smoking generation number Ro,the local stability,global stability of the boundary equilibrium and endemic equilibrium are obtained using Lyapunov functions.The uniform persistence and the well-posedness and asymptotic smoothness of the solutions are also studied.Sensitivity analyzes show that the lower the age of onset of smoking and the higher the determination to stop,the greater the likelihood of quitting smoking and numerical studies support the theoretical results.展开更多
We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic repro- duction number R0 〈 1, the disease-free equilibr...We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic repro- duction number R0 〈 1, the disease-free equilibrium （DFE） is globally asymptotically stable, if R0〉 1, the disease is uniformly persistent. The model is then extended to assess the impact of three anti-influenza control measures, precaution, quarantine and treat- ment, by re-formulating the model as an optimal control problem. We focus primarily on controlling disease with a possible minimal the systemic cost. Pontryagin＇s maximum principle is used to characterize the optimal levels of the three controls. Numerical sim- ulations of the optimality system, using a set of reasonable parameter values, indicate that the precaution measure is more effective in reducing disease transmission than the other two control measures. The precaution measure should be emphasized.展开更多
Non-smooth system including impulsive strategies at both fixed and unfixed times are analyzed. For the model with fixed impulsive effects, the global stability of pest eradi- cation periodic solution and the dominance...Non-smooth system including impulsive strategies at both fixed and unfixed times are analyzed. For the model with fixed impulsive effects, the global stability of pest eradi- cation periodic solution and the dominance of dynamic behavior are investigated. This indicates that the model with fixed moments has the potential to protect the natural enemies from extinction, but under some conditions may also serve to extinction of the pest. The second model is constructed according to the practices of IPM, that is, when the pest population reaches the economic injury level, a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is used. Numerical investigations imply that there are several different types of periodic solutions and their maximum amplitudes are always less than the given economic threshold. The results also show that the time series at which the IPM strategies are applied are quite complex, which means that the application and realization of IPM in practice are very difficult.展开更多
基金supported by the National Natural Science Foundation of China(NSFC:11961024,11801047)the Natural Science Foundation of Chongqing under Grant(cstc2019jcyj-msxmX0755,cstc2018jcyjAX0606)+1 种基金the Team Building Project for Graduate Tutors in Chongqing(JDDSTD201802)Group Building Scientific Innovation Project for universities in Chongqing(CXQT21021).
文摘Smoking is a serious global public health problem.The ability to quit smoking is closely related to age;in addition,personal determination and education usually play an important role in quitting smoking.In order to capture such characteristics,we developed a novel age-structured smoking dynamical model.By defining the smoking generation number Ro,the local stability,global stability of the boundary equilibrium and endemic equilibrium are obtained using Lyapunov functions.The uniform persistence and the well-posedness and asymptotic smoothness of the solutions are also studied.Sensitivity analyzes show that the lower the age of onset of smoking and the higher the determination to stop,the greater the likelihood of quitting smoking and numerical studies support the theoretical results.
文摘We develop an influenza pandemic model with quarantine and treatment, and analyze the dynamics of the model. Analytical results of the model show that, if basic repro- duction number R0 〈 1, the disease-free equilibrium （DFE） is globally asymptotically stable, if R0〉 1, the disease is uniformly persistent. The model is then extended to assess the impact of three anti-influenza control measures, precaution, quarantine and treat- ment, by re-formulating the model as an optimal control problem. We focus primarily on controlling disease with a possible minimal the systemic cost. Pontryagin＇s maximum principle is used to characterize the optimal levels of the three controls. Numerical sim- ulations of the optimality system, using a set of reasonable parameter values, indicate that the precaution measure is more effective in reducing disease transmission than the other two control measures. The precaution measure should be emphasized.
文摘Non-smooth system including impulsive strategies at both fixed and unfixed times are analyzed. For the model with fixed impulsive effects, the global stability of pest eradi- cation periodic solution and the dominance of dynamic behavior are investigated. This indicates that the model with fixed moments has the potential to protect the natural enemies from extinction, but under some conditions may also serve to extinction of the pest. The second model is constructed according to the practices of IPM, that is, when the pest population reaches the economic injury level, a combination of biological, cultural, and chemical tactics that reduce pests to tolerable levels is used. Numerical investigations imply that there are several different types of periodic solutions and their maximum amplitudes are always less than the given economic threshold. The results also show that the time series at which the IPM strategies are applied are quite complex, which means that the application and realization of IPM in practice are very difficult.
