【摘要】 本文建立一类HIV病毒-细胞感染模型,考虑潜伏感染细胞再激活以及缺陷病毒到完整病毒的转化.首先,讨论系统解的全局存在性以及最终有界性,定义系统疾病的基本再生数R0,讨论系统平衡点(无病平衡点,地方病平衡点)的存在性.其次,通过计算R0> 1与R0<1时平衡点处的Jacobian矩阵建立系统平衡点局部渐近稳定性准则,通过构造恰当的Lyapunov函数和运用La Salle变原理,建立系统平衡点的全局渐近稳定性判别准则.最后,用数值模拟检验理论结果,研究发现缺陷病毒转化率在基本再生数中起关键作用,两者成正比,其更进一步的加剧了HIV的传播.更多还原

【Abstract】 This paper establishes a class of HIV virus-cell infection model, considering latent infected cell reactivation and conversion of defective virus to intact virus. Firstly, the global existence and ultimate boundedness of the system solutions are discussed, the basic reproduction number R0 of the system is defined, and the existence of system equilibria（disease-free equilibrium point, endemic equilibrium point） is discussed. Secondly, the criteria for local asymptotic stability of system equilibrium points are established by computing the Jacobian matrix at equilibrium points when R₀ > 1 and R₀ < 1,and the global asymptotic stability criteria of system equilibrium points are established by constructing appropriate Lyapunov functions and applying the La Salle invariance principle. Finally, theoretical results are verified by numerical simulations, revealing that the rate of defective virus conversion plays a crucial role in the basic reproduction number, being directly proportional to each other, further exacerbating the transmission of HIV.更多还原