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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

A model for the transmission of malaria

Pages: 479 - 496, Volume 11, Issue 2, March 2009      doi:10.3934/dcdsb.2009.11.479

 
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Hui Wan - Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China (email)
Jing-An Cui - Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China (email)

Abstract: 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, Partial Immunity, Reproduction number, Stability, Backward bifurcation
Mathematics Subject Classification:  Primary: 92D30; Secondary: 34C60, 34C23

Received: October 2007;      Revised: June 2008;      Available Online: December 2008.