On the dynamics of HIV-AIDS and cryptosporidiosis

  • K. O. Okosun
  • M. A. KhanEmail author
  • E. Bonyah
  • S. T. Ogunlade
Regular Article


This paper seeks to examine a mathematical model for cryptosporidiosis-HIV co-infection, in order to explore their synergistic relationship in the presence of prevention and treatment. Firstly, we investigate the sub-models and their steady states properties. They are found to be locally and globally stable. Thereafter, the steady states of the co-infected model waswere studied and itthey proved to exhibit backward bifurcation phenomena. Furthermore, we incorporate time-dependent controls in the model and apply Pontryagin’s maximum principle, so that we can determine the best optimal strategy to control the co-infected diseases. Finally, we present the numerical results, which show that the best strategy to control co-infection is to combine all the five controls at the same time.


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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • K. O. Okosun
    • 1
  • M. A. Khan
    • 2
    Email author
  • E. Bonyah
    • 1
    • 3
  • S. T. Ogunlade
    • 4
  1. 1.Department of MathematicsVaal University of TechnologyVanderbijlparkSouth Africa
  2. 2.Department of MathematicsCity University of Science and Information TechnologyKhyber PakhtunkhwaPakistan
  3. 3.Department of Mathematics and StatisticsKumasi Technical UniversityKumasiGhana
  4. 4.Department of Mathematical SciencesFederal University of TechnologyAkureNigeria

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