一类细菌毒素依赖性发病模型的动力学性质

Dynamic Properties of a Class of Bacterial Toxin-Dependent Pathogenesis Model

讨论一类细菌毒素依赖性发病模型的动力学性质.首先,用上下解方法和抛物方程的比较定理,证明该系统解的全局存在性、耗散性、持续性和边界稳态解的全局渐近稳定性;其次,基于Lyapunov泛函方法,得到正常值稳态解的全局渐近稳定性;最后,通过数值模拟验证所得结果的有效性.结果表明,适当调节病原体内禀增长率和免疫效应器消灭病原体的速率,可预防疾病的爆发.

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.