Dynamic analysis and optimal control of a three-age-class hiv/aids epidemic model in china

Hongyong Zhao, Peng Wu, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Based on the fact that HIV/AIDS manifests different transmission characteristics and pathogenesis in different age groups, and the proportions of youth and elderly HIV infected cases in total are increasing in China, we classify the whole population into three age groups, youth (15-24), adult (25-49), and elderly (>50), and establish a three-age-class HIV/AIDS epidemic model to investigate the transmission dynamics of HIV/AIDS in China. We derive the explicit expression for the basic reproduction number via the next generation matrix approach. Qualitative analysis of the model including the local, global behavior and permanence is carried out. In particular, numerical simulations are presented to reinforce these analytical results and demonstrate HIV epidemiological discrepancy among different age groups. We also formulate an optimal control problem and solve it using Pontryagins Maximum Principle and an efficient iterative numerical methods. Our numerical results of optimal controls for the elderly group indicate that increasing the condom use and decreasing the rate of the formerly HIV infected persons converted to AIDS patients are important measures to control HIV/AIDS epidemic among elderly population.

Original languageEnglish (US)
Pages (from-to)3491-3521
Number of pages31
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number9
StatePublished - Sep 2020


  • Optimal control
  • Permanence
  • Sensitivity analysis
  • Three-age-classes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Dynamic analysis and optimal control of a three-age-class hiv/aids epidemic model in china'. Together they form a unique fingerprint.

Cite this