 
Summary: J. Math. Biol.
DOI 10.1007/s0028501104184 Mathematical Biology
A metapopulation model for malaria
with transmissionblocking partial immunity in hosts
Julien Arino · Arnaud Ducrot · Pascal Zongo
Received: 21 September 2009 / Revised: 4 February 2011
© SpringerVerlag 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 nonendemic areas and the interaction between
rural and urban areas are given.
Keywords Malaria · Reproduction number · Type reproduction number ·
Metapopulation
Mathematics Subject Classification (2000) 92B05 · 92D30
J. Arino (B)
