Analysis Of Two Types Of Anthrax Propagation Models With Age Structure

Anthrax is acute and septic infectious disease of human being and animals caused by Bacillus anthracis.The spread of anthrax is wide,the prevalence is fast,and the harm is great,not only brings immeasurable economic losses to the aquaculture industry,but also endangers human health and life safety.Therefore,the study of the spread of anthrax is of practical significance.In this paper two kinds of anthrax epidemic dynamics models with infection-age structure are es-tablished and analyzed.One is the transmission dynamics model with anthrax infection age structure,the other is anthrax epidemic model with age of infection and antibiotic therapy are considered.By means of the theory and methods in differential equations and stability analysis,the explicit expres-sion of the basic reproductive numbers of two model are given,and the conditions for the existence and uniqueness of the disease-free equilibrium and the endemic equilibrium are investigated.It is shown that that if the basic reproduction number R0 ?1 the disease-free equilibrium E0 is locally asymptotically stable,if R0>1,the disease-free equilibrium E0 is locally unstable,the endemic equilibrium E*is locally asymptotically stable.The persistence of the system are anlayzed.By using the Lyapunov functional method,it is proved that the disease-free equilibrium E0 is global-ly asymptotically stable if R0<1,the endemic equilibrium E*is globally asymptotically stable if R0>1.