A model for the transmission of malaria

Hui Wan; Jing-An Cui

doi:10.3934/dcdsb.2009.11.479

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2009, Volume 11, Issue 2: 479-496. Doi: 10.3934/dcdsb.2009.11.479

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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

Received: September 30, 2007

Revised: May 31, 2008

Published: August 2009

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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.

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Mathematics Subject Classification: Primary: 92D30; Secondary: 34C60, 34C23.

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