ARINO, Julien; DUCROT, Arnaud; ZONGO, Pascal

doi:10.1007/s00285-011-0418-4

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ARINO, Julien
Department of Mathematics

DUCROT, Arnaud
Institut de Mathématiques de Bordeaux [IMB]

ZONGO, Pascal
Laboratoire d'Analyse Numérique Informatique et Biomathématiques [LANIBIO]
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]

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Journal of Mathematical Biology. 2012-02, vol. 64, n° 3, p. 423-448

Springer

Résumé en anglais

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 R₀ 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.< Réduire

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Malaria

Reproduction number

Type reproduction number

Metapopulation

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

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