African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Full Length Research Paper

Transmission dynamics of infectious diseases by immigrants in a vaccinated and temporary immune protected population

Helikumi Mlyashimbi1, Estomih S. Massawe1* and Daniel Makinde2
  1Mathematics Department, University of Dar es Salaam, P. O. Box 35062, Dar es Salaam, Tanzania. 2Faculty of Engineering, Cape-Peninsula University of Technology, P. O. Box 1906, Bellville 7535, South Africa.
Email: [email protected]

  •  Accepted: 10 December 2010
  •  Published: 28 February 2011



In this paper, a mathematical model of infectious diseases by immigrants in a vaccinated and temporary immune protected population has been investigated. The model incorporates the assumption that immigrant individuals enter in the respective population with an immunity received from either vaccination or recover from the disease. The stability of the system has been analyzed for the existence of the disease-free and endemic equilibrium points, and it has been shown that the disease free equilibrium point is asymptotically stable when an effective reproduction number is less than unity and unstable when an effective reproduction number is greater than unity. From the analysis of the model, it is shown that vaccination coverage is greater than the vaccination; otherwise the disease will persist within the community. It is also shown that the increase of immigrants in a population tends to lower the first dose-vaccination coverage, hence the disease become endemic in the population. Numerical simulations of the model showed that in the absence of the immigrants, the disease can be eradicated in a population with a single-dose vaccination only.


Key words: Immune protection, infectious diseases, infections by immigrants, disease transmission, recovered individuals, vaccinated population.