A type of SEIR epidemic model with media coverage and temporary immunity is investigated in this paper. The existence and uniqueness of the global positive solution with any positive initial value is proved. Under the...A type of SEIR epidemic model with media coverage and temporary immunity is investigated in this paper. The existence and uniqueness of the global positive solution with any positive initial value is proved. Under the condition R0s> 1, we prove that the disease is persistent in the mean for a long run. Furthermore, by constructing suitable Lyapunov functions, some sufficient conditions that guarantee the existence of stationary distribution are derived. We also obtain that, if the condition R0e< 1 is satisfied, then the disease is extinct with an exponential rate. As a consequence, some examples and numerical simulation are demonstrated to show the validity and feasibility of the theoretical results.展开更多
In this paper,the dynamic behaviors are studied for a stochastic delayed avian influenza model with mutation and temporary immunity.First,we prove the existence and uniqueness of the global positive solution for the s...In this paper,the dynamic behaviors are studied for a stochastic delayed avian influenza model with mutation and temporary immunity.First,we prove the existence and uniqueness of the global positive solution for the stochastic model.Second,we give two different thresholds R_(01)^(s) and,R_(02)^(s) and further establish the sufficient conditions of extinction and persistence in the mean for the avian-only subsystem and avian-human system,respectively.Compared with the corresponding deterministic model,the thresholds affected by the white noises are smaller than the ones of the deterministic system.Finally,numerical simulations are carried out to support our theoretical results.It is concluded that the vaccination immunity period can suppress the spread of avian influenza during poultry and human populations,while prompt the spread of mutant avian influenza in human population.展开更多
An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the ...An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the community when the number of infectives is getting larger. The distributed delay is derived to describe the dynamics of infectious diseases with varying immunity. Lyapunov functionals are used to show that the diseasefree equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one. Moreover, it is shown that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions under which the endemic equilibrium is locally and globally asymptotically stable are obtained.展开更多
基金This work was supported by NSFC under grant 61911530398Natural Science Foundation of Fujian Province of China under grant 2016J01015.
文摘A type of SEIR epidemic model with media coverage and temporary immunity is investigated in this paper. The existence and uniqueness of the global positive solution with any positive initial value is proved. Under the condition R0s> 1, we prove that the disease is persistent in the mean for a long run. Furthermore, by constructing suitable Lyapunov functions, some sufficient conditions that guarantee the existence of stationary distribution are derived. We also obtain that, if the condition R0e< 1 is satisfied, then the disease is extinct with an exponential rate. As a consequence, some examples and numerical simulation are demonstrated to show the validity and feasibility of the theoretical results.
基金The research was supported by Ningxia Natural Science Foundation Project(2019AAC03069).
文摘In this paper,the dynamic behaviors are studied for a stochastic delayed avian influenza model with mutation and temporary immunity.First,we prove the existence and uniqueness of the global positive solution for the stochastic model.Second,we give two different thresholds R_(01)^(s) and,R_(02)^(s) and further establish the sufficient conditions of extinction and persistence in the mean for the avian-only subsystem and avian-human system,respectively.Compared with the corresponding deterministic model,the thresholds affected by the white noises are smaller than the ones of the deterministic system.Finally,numerical simulations are carried out to support our theoretical results.It is concluded that the vaccination immunity period can suppress the spread of avian influenza during poultry and human populations,while prompt the spread of mutant avian influenza in human population.
文摘An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the community when the number of infectives is getting larger. The distributed delay is derived to describe the dynamics of infectious diseases with varying immunity. Lyapunov functionals are used to show that the diseasefree equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one. Moreover, it is shown that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions under which the endemic equilibrium is locally and globally asymptotically stable are obtained.
