Simple Compartmental Models for Disease Transmission

  • Fred Brauer
  • Carlos Castillo-Chavez
  • Zhilan Feng
Part of the Texts in Applied Mathematics book series (TAM, volume 69)


Communicable diseases that are endemic (always present in a population ) cause many deaths). For example, in 2011 tuberculosis caused an estimated 1,400,000 deaths and HIV/AIDS caused an estimated 1,200,000 deaths worldwide. According to the World Health Organization there were 627,000 deaths caused by malaria, but other estimates put the number of malaria deaths at 1,2000,000. Measles, which is easily treated in the developed world, caused 160,000 deaths in 2011, but in 1980 there were 2,600,000 measles deaths. The striking reduction in measles deaths is due to the availability of a measles vaccine. Other diseases such as typhus, cholera, schistosomiasis, and sleeping sickness are endemic in many parts of the world. The effects of high disease mortality on mean life span and of disease debilitation and mortality on the economy in afflicted countries are considerable. Most of these disease deaths are in less developed countries, especially in Africa, where endemic diseases are a huge barrier to development.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Fred Brauer
    • 1
  • Carlos Castillo-Chavez
    • 2
  • Zhilan Feng
    • 3
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Mathematical and Computational Modeling Center (MCMSC), Department of Mathematics and StatisticsArizona State UniversityTempeUSA
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA

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