Afrika Matematika

, Volume 25, Issue 4, pp 1095–1112 | Cite as

Assessing the impact of temperature on malaria transmission dynamics

  • E. T. Ngarakana-Gwasira
  • C. P. Bhunu
  • E. Mashonjowa
Article
First Online:
Received:
Accepted:

Abstract

A mathematical model to assess the impact of temperature on malaria transmission dynamics is explored and analysed. Threshold quantities of the model are determined and analysed. The model is shown to exhibit backward bifurcation. Analysis of the reproduction number suggests that increase in temperature to about \(32~{}^{\circ }\mathrm{C}\) has the potential to increase the epidemic. The burden of the disease increases with increase in temperature with an optimal temperature window of 30–\(32~{}^{\circ }\mathrm{C}\) for malaria transmission. However as temperatures approach \(40~{}^{\circ }\mathrm{C}\), infected human and mosquito populations decline to asymptotically low levels.

Keywords

Mathematical model Reproduction number Malaria 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

The authors thank the editor and anonymous reviewers for the critical comments and suggestions which resulted in much improvement of the manuscript.

References

  1. 1.
    World Malaria Report 2011 World Health Organisation, Geneva, p 278Google Scholar
  2. 2.
    Intergovernmental Panel on Climate Change, 2007 Working Group III Fourth Assessment Report, IPCC. http://www.ipcc.ch/publicationsanddata/publicationsanddatareports.shtml
  3. 3.
    Li, J.: Malaria model with stage-structured mosquitoes. Math. Biosci. Eng. 8(3), 753–768 (2011)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Abebe, A., Abebel, G., Tsegaye, W., Golassa, L.: Climatic variables and malaria transmission dynamics in Jimma town. South West Ethiopia, Parasites Vectors 4(30), 1–11 (2011)Google Scholar
  5. 5.
    Alonso, D, Bouma, M.J., Pascual, M.: Epidemic malaria and warmer temperatures in recent decades in an East African highland. Proc. R. Soc. B (2010)Google Scholar
  6. 6.
    Craig, M.H., Snow, R.W., le Sueur, D.: A climate-based distribution model of malaria transmission in sub-Saharan Africa. Parasitol. Today 15, 105–111 (1999)CrossRefGoogle Scholar
  7. 7.
    Hoshen, M.B., Morse, A.P.: A model structure for estimating malaria risk. In: Environmental Change and Malaria Risk Global and Local Implications, pp. 41–50. Springer, Dordrecht (2005)Google Scholar
  8. 8.
    Martens, W.J.M., Jetten, T.H., Focks, D.A.: Sensitivity of malaria, schistosomiasis and dengue to global warming. Clim. Change 35, 145–156 (1997)CrossRefGoogle Scholar
  9. 9.
    Parham, P.E., Michael, E.: Modeling the Effects of weather and climate change on malaria transmission. Environ. Health Perspect. 118(5), 620–626 (2010)CrossRefGoogle Scholar
  10. 10.
    Paaijmans, K.P., Cator, L.J., Thomas, M.B.: Temperature-dependent pre-bloodmeal period and temperature-driven asynchrony between parasite development and mosquito biting rate reduce malaria transmission intensity. PLOS one. 8(1), e55777 (2013)CrossRefGoogle Scholar
  11. 11.
    Rubel, F., Brugger, K., Hantel, M., Chvala-Mannsberger, S., Bakonyi, T., Weissenbo, H., Nowotny, N.: Explaining Usutu virus dynamics in Austria: Model development and calibration. Preventive Veterinary Medicine 85, 166186 (2008)Google Scholar
  12. 12.
    Martens, P., Niessen, L.W., Rotmans, J., et al.: Potential impact of global climate change on malaria risk. Environ. Health Perspect. 103(5), 458–464 (1995)CrossRefGoogle Scholar
  13. 13.
    McDonald, G.: The epidemiology and control of malaria. Oxford University Press, London (1957)Google Scholar
  14. 14.
    Chiyaka, C., Tchuenche, J.M., Garira, W., Dube, S.: A mathematical analysis of the effects of control strategies on the transmission dynamics of malaria. Appl. Math. Comput. (2007)Google Scholar
  15. 15.
    Kbenesh, B., Yanzhao, C., Hee-Dae, K.: Optimal control of vector-borne diseases: treatment and prevention. Discr. Contin. Dyn. Syst. Ser. B 11(3), 1–11 (2009)Google Scholar
  16. 16.
    Diekmann, O., Heestterbeek, J.A.P., Metz, J.A.P.: On the computation of the basic reproduction ratio \(R_0\) in models for infectious diseases in heterogenous populations. J. Math. Biol. 28, 365–382 (1990)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    van den Drissche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for the compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2005)CrossRefGoogle Scholar
  18. 18.
    McMichael, A.J.: Haines, pp. 78–86. Sloof, Kovats, Climate Change and Human Health, World Health Organization (1996)Google Scholar
  19. 19.
    Shetty, P.: Climate Change and Insect-borne Disease: Facts and Figures–SciDev.Net. http://www.scidev.net/en/south-east-asia/features/climate-change-and-insect-borne-disease-facts-and-1.html
  20. 20.
    Remais, J., Akullian, A., Ding, L., Seto, E.: Analytical methods for quantifying environmental connectivity for the control and surveillance of infectious disease spread. J. R. Soc. Interface. 7(49), 1181–93 (2010)CrossRefGoogle Scholar
  21. 21.
    Castillo-Chavez, C., Song, B.: Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1, 361404 (2004)MathSciNetGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • E. T. Ngarakana-Gwasira
    • 1
  • C. P. Bhunu
    • 1
  • E. Mashonjowa
    • 2
  1. 1.Department of MathematicsUniversity of ZimbabweHarareZimbabwe
  2. 2.Department of PhysicsUniversity of ZimbabweHarareZimbabwe

Personalised recommendations