A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number is calculated. It is shown that this number characterizes the disease transmission dynamic...A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number is calculated. It is shown that this number characterizes the disease transmission dynamics: if, there only exists the disease-free equilibrium which is globally asymptotically stable;if, there is a unique endemic equilibrium and the disease persists, sufficient cond- itions are obtained for the global asymptotic stability of the endemic equilibrium.展开更多
In this paper,we propose a deterministic model to study the transmission dynamics of anthrax disease,which includes live animals,carcasses,spores in the environment and vectors.We derive three biologically plausible a...In this paper,we propose a deterministic model to study the transmission dynamics of anthrax disease,which includes live animals,carcasses,spores in the environment and vectors.We derive three biologically plausible and insightful quantities(reproduction numbers)that determine the stability of the equilibria.We carry out rigorous mathematical analysis on the model dynamics,the global stability of the disease-free and vector-free equilibrium,the disease-free equilibrium and the vector-free disease equilibrium is proved.The global stability of the endemic equilibrium as the basic reproduction number is greater than one is derived in the special case in which the disease-related death rate is zero.The possibility of backward bifurcation is briefly discussed.Numerical analyses are carried out to understand the transmission dynamics of anthrax and investigate effective control strategies for the outbreaks of the disease.Our studies suggest that the larval vector control measure should be taken as early as possible to control the vector population size,a vaccination policy and an animal carcass removal policy are useful methods to control the prevalence of the diseases in infected animal populations,the adult vector control measure is also necessary to prevent the transmission of anthrax.展开更多
文摘A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number is calculated. It is shown that this number characterizes the disease transmission dynamics: if, there only exists the disease-free equilibrium which is globally asymptotically stable;if, there is a unique endemic equilibrium and the disease persists, sufficient cond- itions are obtained for the global asymptotic stability of the endemic equilibrium.
基金This work was supported by the National Natural Science Foundation of China(11801431)the Natural Science Basic Research Plan in Shaanxi Province of China(2021JM-445,2022JM-023).
文摘In this paper,we propose a deterministic model to study the transmission dynamics of anthrax disease,which includes live animals,carcasses,spores in the environment and vectors.We derive three biologically plausible and insightful quantities(reproduction numbers)that determine the stability of the equilibria.We carry out rigorous mathematical analysis on the model dynamics,the global stability of the disease-free and vector-free equilibrium,the disease-free equilibrium and the vector-free disease equilibrium is proved.The global stability of the endemic equilibrium as the basic reproduction number is greater than one is derived in the special case in which the disease-related death rate is zero.The possibility of backward bifurcation is briefly discussed.Numerical analyses are carried out to understand the transmission dynamics of anthrax and investigate effective control strategies for the outbreaks of the disease.Our studies suggest that the larval vector control measure should be taken as early as possible to control the vector population size,a vaccination policy and an animal carcass removal policy are useful methods to control the prevalence of the diseases in infected animal populations,the adult vector control measure is also necessary to prevent the transmission of anthrax.
