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Global Stability Analysis of HIV+ Model

  • Farouk Tijjani Saad
  • Tamer SanlidagEmail author
  • Evren Hincal
  • Murat Sayan
  • Isa Abdullahi Baba
  • Bilgen Kaymakamzade
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 896)

Abstract

We developed and studied a mathematical model of HIV+. Two equilibriums points were found, disease free and endemic equilibrium, and basic reproduction ratio \( R_{0} \) was also calculated by the use of next generation matrix. Global stability analysis of the equilibria was carried out by the use of Lyapunov function, and it was shown that the stability of the equilibria depends on the magnitude of the basic reproduction ratio. When \( R_{0} < 1 \), the disease free equilibrium is globally asymptotically stable, and disease dies out. On the other hand if \( R_{0} \ge 1 \), the endemic equilibrium is globally asymptotically stable and epidemics occurs. Reported cases of 13646 HIV-1 positive were obtained in the year 2016 from Ministry of Health, Turkey (MOH). This data is used to present the numerical simulations, which supports the analytic result. \( R_{0} \) was found to be 1.98998, which is bigger than 1, this shows the threat posed by HIV in Turkey.

Keywords

HIV AIDS Mathematical model Global stability Basic reproduction ratio Turkey 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Farouk Tijjani Saad
    • 1
  • Tamer Sanlidag
    • 2
    • 4
    Email author
  • Evren Hincal
    • 1
  • Murat Sayan
    • 3
    • 4
  • Isa Abdullahi Baba
    • 1
  • Bilgen Kaymakamzade
    • 1
  1. 1.Department of MathematicsNear East UniversityNicosiaCyprus
  2. 2.Faculty of Medicine, Department of Medical MicrobiologyCelal Bayar UniversityManisaTurkey
  3. 3.Faculty of Medicine, Clinical Laboratory, PCR UnitKocaeli UniversityKocaeliTurkey
  4. 4.Research Center of Experimental Health SciencesNear East UniversityNicosiaCyprus

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