JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (10): 67-73.doi: 10.6040/j.issn.1671-9352.1.2019.037

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Study on nonlinear HIV/AIDS model with two infection stages treatment and incidence rate

WANG Fei1*, YANG Ya-li1, JIN Ying-ji2, CAO Shu-miao3   

  1. 1. Department of Applied Mathematics and Military Cryptography, Air Force Engineering University, Xian 710051, Shaanxi, China;
    2. College of Education, Tibetan University for Nationalities, Xianyang 712082, Shaanxi, China;
    3. Xian University of Architecture and Technology, Shaanxi Key Laboratory of Environmental Engineering, School of Environmental and Municipal Engineering, Xian 710055, Shaanxi, China
  • Published:2019-10-12

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Abstract: Based on the actual transmission and treatment, a mathematical model of HIV/AIDS with two infection stages, treatment and non-linear incidence is established in this paper.Then the range of the feasible region of the system is discussed by using the limit theory.Secondly, the basic regeneration number is obtained by constructing regeneration matrix, and the range of the basic regeneration number is discussed. The existence and number of equilibrium points are obtained.Finally, the local and global properties of equilibrium point are proved by constructing Lyapunov function, using Lasalle invariant set, Boosenberg theorem and Van den Lacy principle.

Key words: HIV/AIDS, nonlinear incidence, basic regeneration number, LaSalle invariant set principle, Lyapunov function

CLC Number: 

  • O175.1
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