Modelling the Trend of HIV Transmission and Treatment in Kenya

  • E. O. OmondiEmail author
  • R. W. Mbogo
  • L. S. Luboobi
Original Paper


HIV infection remains a major contributor to disease burden and a global leading cause of death. Although progress is being made to control HIV infections, Kenya still remains one of the high HIV burden countries in Sub-Sahara Africa. A deterministic model was proposed to describe the trend of HIV infection in Kenya and suggest some control strategies. The basic reproduction number, \(\mathcal {R}_0\), is derived and global asymptotic stability analysis of the disease-free equilibrium carried out. We proved that HIV infections will be contained if the reproduction number is kept below one. Routine data from national survey is used to assess the variation of the new HIV infections in Kenya. Based on this data, least squares method was used to estimate the unknown parameters. The HIV incidence shows of an infection at an endemic state implying of ceaseless problem. Furthermore, improvement in immunological status of the HIV patients on ART due to attrition, may lead to decline in HIV infection and be beneficial to the disease control. The findings suggested that treatment with ART greatly aids the decline in HIV infections hence strengthening its intensity will effectively contribute to the disease control.


HIV transmission Reproduction number Least squares curve fitting Simulations 



The authors acknowledge, with thanks, the support of Institute of Mathematical Sciences, Strathmore University for the production of this manuscript. Authors are also very grateful to the referees and the editor for the constructive and valuable comments and recommendations and for making us pay attention to certain references.

Author Contributions

All authors worked together to produce the results and read and approved the final manuscript.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature India Private Limited 2018

Authors and Affiliations

  1. 1.Institute of Mathematical SciencesStrathmore UniversityNairobiKenya

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