Abstract: We discussed the dynamic properties of a class of bacterial toxin-dependent pathogenesis models. Firstly, by using the upper and lower solution method and the comparison theorem of parabolic equation, the global existence of solutions of the systems, dissipation, continuity and global asymptotic stability of boundary steady-state solutions were proved. Secondly, based on Lyapunov functional method, the global asymptotic stability of the positive normal steady-state solution was obtained. Finally, the effectiveness of results was verified by numerical simulation. The results show that proper regulation of the intrinsic growth rate of pathogens and the rate of elimination of pathogens by immune effectors can prevent disease outbreaks.

Key words: bacterial toxin-dependent pathogenesis model, global asymptotic stability, Lyapunov functional, numerical simulation