On the bifurcations and multiple endemic states of a single strain HIV model

  • Lindley Kent M. FainaEmail author
  • Lorna S. Almocera
  • Polly W. Sy


The dynamics of a single strain HIV model is studied. The basic reproduction number R 0 used as a bifurcation parameter shows that the system undergoes transcritical and saddle-node bifurcations. The usual threshold unit value of R 0 does not completely determine the eradication of the disease in an HIV infected person. In particular, a sub-threshold value R c is established which determines the system’s number of endemic states: multiple if R c < R 0 < 1, only one if R c = R 0 = 1, and none if R 0 < R c < 1.


single strain HIV model multiple endemic states transcritical bifurcation saddle-node bifurcation hysteresis 

2000 MR Subject Classification

34C23 34C55 34D20 


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Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Lindley Kent M. Faina
    • 1
    Email author
  • Lorna S. Almocera
    • 2
  • Polly W. Sy
    • 3
  1. 1.College of Arts and SciencesUniversity of the Philippines VisayasMiagao, IloiloPhilippines
  2. 2.Natural Sciences and Mathematics DivisionUniversity of the Philippines Visayas, Cebu CollegeLahug, Cebu CityPhilippines
  3. 3.Institute of MathematicsUniversity of the PhilippinesDiliman, Quezon CityPhilippines

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