Journal of Mathematical Biology

, Volume 73, Issue 2, pp 305–333 | Cite as

Optimal control for an age-structured model for the transmission of hepatitis B

  • Ramses Djidjou DemasseEmail author
  • Jean-Jules Tewa
  • Samuel Bowong
  • Yves Emvudu


One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention.


HBV Age structure Non-linear dynamical system  Stability Optimal control 

Mathematics Subject Classification

35Q92 49J20 35B35 92D30 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ramses Djidjou Demasse
    • 1
    • 4
    • 5
    • 6
    Email author
  • Jean-Jules Tewa
    • 2
    • 4
    • 5
    • 6
  • Samuel Bowong
    • 3
    • 4
    • 5
    • 6
  • Yves Emvudu
    • 1
  1. 1.Faculty of ScienceUniversity of Yaounde 1YaoundéCameroon
  2. 2.National Advanced School of EngineeringUniversity of Yaounde 1YaoundéCameroon
  3. 3.Faculty of ScienceUniversity of DoualaDoualaCameroon
  4. 4.UMI 209 IRD&UPMC UMMISCOBondyFrance
  5. 5.LIRIMA, Project Team GRIMCAPEYaoundéCameroon
  6. 6.The African Center of Excellence in Information and Communication Technologies (CETIC)University of Yaounde 1YaoundéCameroon

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