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A model for the transmission of malaria. (English) Zbl 1153.92028
Summary: A new transmission model of human malaria in a partially immune population is formulated. We establish the basic reproduction number \(\widetilde{R}_0\) for the model. The existence and local stability of the equilibria are studied. Our results suggest that, if the disease-induced death rate is large enough, there may be endemic equilibrium when \(\widetilde{R}_0 < 1\) and the model undergoes a backward bifurcation and saddle-node bifurcation, which implies that bringing the basic reproduction number below 1 is not enough to eradicate malaria. Explicit subthreshold conditions in terms of parameters are obtained beyond the basic reproduction number which provides further guidelines for accessing control of the spread of malaria.

92D30 Epidemiology
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D05 Asymptotic properties of solutions to ordinary differential equations
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