American Institute of Mathematical Sciences

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March  2009, 11(2): 479-496. doi: 10.3934/dcdsb.2009.11.479

A model for the transmission of malaria

Hui Wan 1, and  Jing-An Cui 1,

1. 

Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China

Received  October 2007 Revised  June 2008 Published  December 2008

In this paper, a new transmission model of human malaria in a partially immune population is formulated. We establish the basic reproduction number $\tilde{R}_0$ 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 $\tilde{R}_0 < 1$ 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.
Keywords: Malaria, Reproduction number, Partial Immunity, Stability, Backward bifurcation.
Mathematics Subject Classification: Primary: 92D30; Secondary: 34C60, 34C23.
Citation: Hui Wan, Jing-An Cui. A model for the transmission of malaria. Discrete and Continuous Dynamical Systems - B, 2009, 11 (2) : 479-496. doi: 10.3934/dcdsb.2009.11.479
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