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在研究人类免疫缺陷性病毒HIV和丙肝病毒C(HCV)中,数学模型起到了非常重要的作用.感染T细胞在人体内潜伏若干年后才转化为病毒,在这期间,感染T细胞的丢失不是简单的线性作用关系.本文报道了一类具有饱和丢失率的数学模型,得到了基本再生数R0.R0完全决定T细胞的全局动力学性质,即如果R0≤1,感染T细胞消失,如果R0>1, 感染变为慢性的,在可行区域内,惟一流行病平衡点是全局渐近稳定的.同时,还考虑了在饱和丢失感染T细胞下的药物的影响.
Mathematical models play a very important role in the study of human immunodeficiency virus HIV and hepatitis C virus C (HCV), and infected T cells turn into viruses only after they have been dormant for years in the human body, during which time the loss of infected T cells Is not a simple linear relationship.This paper reports a mathematical model with saturation loss rate and obtains the basic reproductive number R0.R0 completely decides the global dynamics of T cells, that is, if R0≤1, the infected T cells disappear if R0> 1, the infection becomes chronic, and in the feasible region, the only equilibrium point of the epidemic is globally asymptotically stable. Meanwhile, the influence of drugs under the condition of saturated loss of infected T cells is also considered.