Journal of Mathematical Biology

, Volume 77, Issue 4, pp 857–933 | Cite as

Mathematical modeling of climate change and malaria transmission dynamics: a historical review

  • Steffen E. EikenberryEmail author
  • Abba B. Gumel


Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the Plasmodium malaria parasite and Anopheles mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature Anopheles habitats are also strongly dependent upon rainfall and local hydrodynamics. A wide variety of process-based (or mechanistic) mathematical models have thus been proposed for the complex, highly nonlinear weather-driven Anopheles lifecycle and malaria transmission dynamics, but have reached somewhat disparate conclusions as to optimum temperatures for transmission, and the possible effect of increasing temperatures upon (potential) malaria distribution, with some projecting a large increase in the area at risk for malaria, but others predicting primarily a shift in the disease’s geographic range. More generally, both global and local environmental changes drove the initial emergence of P. falciparum as a major human pathogen in tropical Africa some 10,000 years ago, and the disease has a long and deep history through the present. It is the goal of this paper to review major aspects of malaria biology, methods for formalizing these into mathematical forms, uncertainties and controversies in proper modeling methodology, and to provide a timeline of some major modeling efforts from the classical works of Sir Ronald Ross and George Macdonald through recent climate-focused modeling studies. Finally, we attempt to place such mathematical work within a broader historical context for the “million-murdering Death” of malaria.


Malaria Climate change Ross–Macdonald Thermal-response 

Mathematics Subject Classification

01-02 92-02 92B05 



This work is supported, in part, by the Global Security Initiative of Arizona State University. One of the authors (ABG) is grateful to National Institute for Mathematical and Biological Synthesis (NIMBioS) for funding the Working Group on Climate Change and Vector-borne Diseases (VBDs). NIMBioS is an Institute sponsored by the National Science Foundation, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville. The authors are grateful to the two anonymous reviewers for their very constructive comments, which have significantly enhanced the clarity of the paper. Author SEE is also grateful to Lindsey Van Sambeek for her assistance with Fig. 3.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Global Security InitiativeArizona State UniversityTempeUSA
  2. 2.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA
  3. 3.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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