Models for Malaria

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


Malaria is one of the most important diseases transmitted by vectors. The vectors for many vector-transmitted diseases are mosquitoes or other insects which tend to be more common in warmer climates. One influence of climate change in coming years may be to extend the regions where mosquitoes can thrive and thus to cause the spread of vector-transmitted diseases geographically.


  1. 1.
    Aron, J.L. (1982) Dynamics of acquired immunity boosted by exposure to infection, Math. Biosc. 64: 249–259.CrossRefGoogle Scholar
  2. 2.
    Aron, J.L. (1988) Mathematical modeling of immunity to malaria (1988) Math. Biosc. 90: 385–396.zbMATHGoogle Scholar
  3. 3.
    Aron, J.L. & R.M. May (1982) The population dynamics of malaria, in Population Dynamics of Infectious Diseases, R.M. Anderson, ed. Chapman and Hall, London, pp. 139–179.CrossRefGoogle Scholar
  4. 4.
    Chitnis, N., J.M.Cushing, & J.M. Hyman (2006) Bifurcation analysis of a mathematical model for malaria transmission, SIAM J. App. Math. 67: 24–45.zbMATHGoogle Scholar
  5. 5.
    Feng, Z., D.L. Smith, E.F. McKenzie & S.A. Levin (2004) Coupling ecology and evolution: malaria and the S-gene across time scales, Math. Biosc. 189: 1–19,MathSciNetCrossRefGoogle Scholar
  6. 6.
    Feng, Z., Y. Yi, & H. Zhu (2004) Fast and slow dynamics of malaria and the S-gene frequency, Journal of Dynamics and Differential Equations, 16: 869–896.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Karlin, S. & H.M. Taylor (1975) A First Course in Stochastic Processes, 2nd ed., Academic Press, New York.zbMATHGoogle Scholar
  8. 8.
    MacDonald, G. (1950) The analysis of infection rates in diseases in which superinfection occurs, Tropical Diseases Bull. 47: 907–915.Google Scholar
  9. 9.
    MacDonald, G. (1952) The analysis of equilibrium in malaria, Tropical diseases Bull. 49: 813–828.Google Scholar
  10. 10.
    MacDonald, G. (1957) The Epidemiology and Control of Malaria, Oxford University Press, London.Google Scholar
  11. 11.
    Ross, R. (1911) The Prevention of Malaria, 2nd ed., (with Addendum), John Murray, London.Google Scholar
  12. 12.
    Shim, E., Z. Feng, C. Castillo-Chavez (2012) Differential impact of sickle cell trait on symptomatic and asymptomatic malaria, Math. Biosc. & Eng., 9: 877–898.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Teboh-Ewungkem, M.I., G.A. Ngwa & C.N. Ngonghala (2013) Models and proposals for malaria: A review Math. Pop. Studies 20: 57–81.CrossRefGoogle Scholar
  14. 14.
    Vafa M., M. Troye-Blomberg, J. Anchang, A. Garcia & F. Migot-Nabias (2008) Multiplicity of Plasmodium falciparum infection in asymptomatic children in Senegal: relation to transmission, age and erythrocyte variants, Malaria J. 7: 17.CrossRefGoogle Scholar
  15. 15.
    Williams T.N. (2006) Human red blood cell polymorphisms and malaria, Curr. Opin. Microbiol. 9: 388–394.CrossRefGoogle Scholar

Copyright information

© 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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