该文研究了一类具有空间异质性HIV潜伏感染的非局部扩散动力学模型. 克服了非局部算子引起的非紧性困难并利用更新方程得到了下一代再生算子的泛函表达式, 进而得到模型基本再生数, 即下一代再生算子的谱半径. 然后对系统进行阈值动力学分析. 具体地, 通过构造合适的Lyapunov泛函证明了当时, 未感染平衡态是全局渐近稳定的; 利用点耗散系统的一致持久性理论证明了当时, 系统是一致持久的并且系统至少存在一个正平衡态.
Abstract
In this paper, a nonlocal dispersal dynamic model of HIV latent infection with spatial heterogeneity is studied. We overcome the difficulty of non compactness caused by the nonlocal dispersal operator, and obtain the functional expression of the next generation operator by using the renewal equation. Then, the basic reproduction number of the model is obtained, which is defined by the spectral radius of the next generation regeneration operator . Finally, the threshold dynamics of the system is analyzed. Specifically, by constructing appropriate Lyapunov functional, it is proved that the uninfected steady state is globally asymptotically stable when ; Applying the consistent persistence theory of point dissipative systems, we prove that the system is uniformly persistent and has at least one positive steady state when .
关键词
HIV /
潜伏感染 /
非局部扩散模型 /
空间异质性 /
下一代再生算子 /
阈值动力学
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Key words
HIV /
latent infection /
nonlocal dispersal model /
spatial heterogeneity /
the next generation operator /
threshold dynamics
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中图分类号：
O175
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脚注
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基金
国家自然科学基金(12201557)、浙江省属高校基本科研业务费专项资金(GK249909299001-20)资助项目.
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