A reaction-diffusion malaria model with incubation period in the vector population

Yijun Lou, Xiao Qiang Zhao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

267 Citations (Scopus)


Malaria is one of the most important parasitic infections in humans and more than two billion people are at risk every year. To understand how the spatial heterogeneity and extrinsic incubation period (EIP) of the parasite within the mosquito affect the dynamics of malaria epidemiology, we propose a nonlocal and time-delayed reaction-diffusion model. We then define the basic reproduction ratio R0 and show that R0 serves as a threshold parameter that predicts whether malaria will spread. Furthermore, a sufficient condition is obtained to guarantee that the disease will stabilize at a positive steady state eventually in the case where all the parameters are spatially independent. Numerically, we show that the use of the spatially averaged system may highly underestimate the malaria risk. The spatially heterogeneous framework in this paper can be used to design the spatial allocation of control resources.
Original languageEnglish
Pages (from-to)543-568
Number of pages26
JournalJournal of Mathematical Biology
Issue number4
Publication statusPublished - 1 Apr 2011
Externally publishedYes


  • Basic reproduction ratio
  • Global attractivity
  • Incubation period
  • Malaria transmission
  • Spatial heterogeneity
  • Threshold dynamics

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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