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A metapopulation model for malaria with transmission-blocking partial immunity in hosts. (English) Zbl 1236.92036
Summary: 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.

##### MSC:
 92C60 Medical epidemiology 34C60 Qualitative investigation and simulation of ordinary differential equation models 92D30 Epidemiology 37N25 Dynamical systems in biology
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