A mathematical model described the propagation of information including rumor and truth presented and its properties investigated. We explored exists of the equilibria, local stability and global asymptotical stabilit...A mathematical model described the propagation of information including rumor and truth presented and its properties investigated. We explored exists of the equilibria, local stability and global asymptotical stability, and obtained the propagation threshold of rumor spreading. Numerical simulation is shown to demonstrate our results. Uncertainty and sensitivity analysis shows the importance of the parameters in our model.展开更多
In this paper, an impulsive epidemic model with time delay is proposed, which susceptible population is divided into two groups: high risk susceptibles and non-high risk susceptibles. We introduce two thresholds R1, R...In this paper, an impulsive epidemic model with time delay is proposed, which susceptible population is divided into two groups: high risk susceptibles and non-high risk susceptibles. We introduce two thresholds R1, R2 and demonstrate that the disease will be extinct if R11 . Our results show that larger pulse vaccination rates or a shorter the period of pulsing will lead to the eradication of the disease. The conclusions are confirmed by numerical simulations.展开更多
From the lifecycle of schistosome, the phenomenon of time delay is widespread. In this paper, a two-dimensional system is studied that incorporates two time delays which are the incubation period of human and snail, r...From the lifecycle of schistosome, the phenomenon of time delay is widespread. In this paper, a two-dimensional system is studied that incorporates two time delays which are the incubation period of human and snail, respectively. Our purpose is to demonstrate that the time delays are harmless for stability of equilibria of the system. Further, sufficient conditions of stability of equilibria are obtained.展开更多
In this paper, a nonautonomous eco-epidemiological model with disease in the predator is formulated and analyzed, in which saturated predation rate is taken into consideration. Under quite weak assumptions, sufficient...In this paper, a nonautonomous eco-epidemiological model with disease in the predator is formulated and analyzed, in which saturated predation rate is taken into consideration. Under quite weak assumptions, sufficient conditions for the permanence and extinction of the disease are obtained. Moreover, by constructing a Liapunov function, the global attractivity of the model is discussed. Finally, numerical simulations verified these results.展开更多
In this paper, the SECIR rumor spreading model is formulated and analyzed, in which the social education level and the counterattack mechanism are taken into consideration. The results show that improving education le...In this paper, the SECIR rumor spreading model is formulated and analyzed, in which the social education level and the counterattack mechanism are taken into consideration. The results show that improving education level and increasing the ratio of counter are effective in reducing the risk of rumor propagation and enhancing the resistance to rumor propagation.展开更多
In this paper, a Schistosomiasis japonicum model incorporating time delay is proposed which represents the developmental time from cercaria penetration through skins of human hosts to egg laying. By linearizing the sy...In this paper, a Schistosomiasis japonicum model incorporating time delay is proposed which represents the developmental time from cercaria penetration through skins of human hosts to egg laying. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equations, the local stability of the equilibria is investigated. And it proves that Hopf bifurcations occur when the time delay passes through a sequence of critical value. Furthermore, the explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using techniques from the normal form theory and Center Manifold Theorem. Some numerical simulations which support our theoretical analysis are also conducted.展开更多
Huanglongbing(HLB)is an incurable disease that affects citrus trees.To better understand the transmission of HLB,the mathematical model is developed to investigate the transmission dynamics of the disease between Asia...Huanglongbing(HLB)is an incurable disease that affects citrus trees.To better understand the transmission of HLB,the mathematical model is developed to investigate the transmission dynamics of the disease between Asian citrus psyllid(ACP)and citrus trees.Through rigorous mathematical derivations,we derive the expression of the basic reproduction number(R_(0))of HLB.The findings show that the disease-free equilibrium is locally asymptotically stable if R_(0)<1,and if R_(0)>1 the system is uniformly persistent.By applying the global sensitivity analysis of R_(0),we can obtain some parameters that have the greatest influence on the HLB transmission dynamics.Additionally,the optimal control theory is used to explore the corresponding optimal control problem of the HLB model.Numerical simulations are conducted to reinforce the analytical results.These theoretical and numerical results provide useful insights for understanding the transmission dynamics of HLB and may help policy makers to develop intervention strategies for the disease.展开更多
文摘A mathematical model described the propagation of information including rumor and truth presented and its properties investigated. We explored exists of the equilibria, local stability and global asymptotical stability, and obtained the propagation threshold of rumor spreading. Numerical simulation is shown to demonstrate our results. Uncertainty and sensitivity analysis shows the importance of the parameters in our model.
文摘In this paper, an impulsive epidemic model with time delay is proposed, which susceptible population is divided into two groups: high risk susceptibles and non-high risk susceptibles. We introduce two thresholds R1, R2 and demonstrate that the disease will be extinct if R11 . Our results show that larger pulse vaccination rates or a shorter the period of pulsing will lead to the eradication of the disease. The conclusions are confirmed by numerical simulations.
文摘From the lifecycle of schistosome, the phenomenon of time delay is widespread. In this paper, a two-dimensional system is studied that incorporates two time delays which are the incubation period of human and snail, respectively. Our purpose is to demonstrate that the time delays are harmless for stability of equilibria of the system. Further, sufficient conditions of stability of equilibria are obtained.
文摘In this paper, a nonautonomous eco-epidemiological model with disease in the predator is formulated and analyzed, in which saturated predation rate is taken into consideration. Under quite weak assumptions, sufficient conditions for the permanence and extinction of the disease are obtained. Moreover, by constructing a Liapunov function, the global attractivity of the model is discussed. Finally, numerical simulations verified these results.
文摘In this paper, the SECIR rumor spreading model is formulated and analyzed, in which the social education level and the counterattack mechanism are taken into consideration. The results show that improving education level and increasing the ratio of counter are effective in reducing the risk of rumor propagation and enhancing the resistance to rumor propagation.
文摘In this paper, a Schistosomiasis japonicum model incorporating time delay is proposed which represents the developmental time from cercaria penetration through skins of human hosts to egg laying. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equations, the local stability of the equilibria is investigated. And it proves that Hopf bifurcations occur when the time delay passes through a sequence of critical value. Furthermore, the explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using techniques from the normal form theory and Center Manifold Theorem. Some numerical simulations which support our theoretical analysis are also conducted.
基金The research has been supported by the Natural Science Foundation of China(11961003,11901110)The Natural Science Foundation of Jiangxi Province(20192ACBL20004)The Science and Technology Project of Education Department of Jiangxi Province(GJJ190740,GJJ201406).
文摘Huanglongbing(HLB)is an incurable disease that affects citrus trees.To better understand the transmission of HLB,the mathematical model is developed to investigate the transmission dynamics of the disease between Asian citrus psyllid(ACP)and citrus trees.Through rigorous mathematical derivations,we derive the expression of the basic reproduction number(R_(0))of HLB.The findings show that the disease-free equilibrium is locally asymptotically stable if R_(0)<1,and if R_(0)>1 the system is uniformly persistent.By applying the global sensitivity analysis of R_(0),we can obtain some parameters that have the greatest influence on the HLB transmission dynamics.Additionally,the optimal control theory is used to explore the corresponding optimal control problem of the HLB model.Numerical simulations are conducted to reinforce the analytical results.These theoretical and numerical results provide useful insights for understanding the transmission dynamics of HLB and may help policy makers to develop intervention strategies for the disease.
