Kinetic Properties Of A Class Of Bacterial Toxin-dependent Pathogenesis Models

Bacterial toxin infection has caused immeasurable harm and loss to human life and social economy,so it is very necessary to prevent disease outbreaks in advance.In recent years,the study of infectious disease models has become an important topic in medicine and biomathematics.Since the toxin infection of host cells may be a bilinear function or a nonlinear function.Based on this,we mainly studies the kinetic properties of a class of bacterial toxin-dependent disease model subject to Neumann boundary conditions.In this paper,the global existence,dissipation,persistence of the solutions and the global stability of constant-valued stationary solutions for the bacterial toxin-dependent disease model with the Allee effect and the Holling II type are discussed,discussing the nonexistence of nonconstant positive steady-state solutions,then the global existence,boundedness of solutions and local stability of constant-valued stationary solutions for bacterial toxin-dependent disease model with time delays are analyzed,the existence,stability and direction of Hopf bifurcation are shown.Our studies show that Allee effect,Holling II and time delay can make bacterial toxin-dependent disease model exhibit more complex dynamic properties.