Journal of Mathematical Biology

, Volume 64, Issue 3, pp 423–448

A metapopulation model for malaria with transmission-blocking partial immunity in hosts



A metapopulation malaria model is proposed using SI and SIRS models for the vectors and hosts, respectively. Recovered hosts are partially immune to the disease and while they cannot directly become infectious again, they can still transmit the parasite to vectors. The basic reproduction number \({\mathcal{R}_0}\) is shown to govern the local stability of the disease free equilibrium but not the global behavior of the system because of the potential occurrence of a backward bifurcation. Using type reproduction numbers, we identify the reservoirs of infection and evaluate the effect of control measures. Applications to the spread to non-endemic areas and the interaction between rural and urban areas are given.


Malaria Reproduction number Type reproduction number Metapopulation 

Mathematics Subject Classification (2000)

92B05 92D30 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada
  2. 2.IMB UMR CNRS 5251 & INRIA Bordeaux Sud Ouest AnubisUniversité de BordeauxBordeauxFrance
  3. 3.Laboratoire d’Analyse Numérique d’Informatique et de Biomathématique & INRIA Bordeaux Sud Ouest AnubisUniversité de Bordeaux & Université de OuagadougouBordeauxFrance

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