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J. Math. Biol. DOI 10.1007/s00285-011-0418-4 Mathematical Biology

Summary: J. Math. Biol.
DOI 10.1007/s00285-011-0418-4 Mathematical Biology
A metapopulation model for malaria
with transmission-blocking partial immunity in hosts
Julien Arino Arnaud Ducrot Pascal Zongo
Received: 21 September 2009 / Revised: 4 February 2011
Springer-Verlag 2011
Abstract 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 reproduc-
tion 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.
Keywords Malaria Reproduction number Type reproduction number
Mathematics Subject Classification (2000) 92B05 92D30
J. Arino (B)


Source: Arino, Julien - Department of Mathematics, University of Manitoba


Collections: Mathematics