Abstract
In this paper, a new transmission model of human malaria in apartially immune population is formulated. We establish the basicreproduction number $\tilde{R}_0$ for the model. The existence andlocal stability of the equilibria are studied. Our results suggestthat, if the disease-induced death rate is large enough, there maybe endemic equilibrium when $\tilde{R}_0 < 1$ and the modelundergoes a backward bifurcation and saddle-node bifurcation, whichimplies that bringing the basic reproduction number below 1 is notenough to eradicate malaria. Explicit subthreshold conditions interms of parameters are obtained beyond the basic reproductionnumber which provides further guidelines for accessing control ofthe spread of malaria.
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