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Abstract and Applied Analysis
Volume 2014, Article ID 289349, 9 pages
Research Article

Stability of a Mathematical Model of Malaria Transmission with Relapse

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 6 December 2013; Accepted 10 January 2014; Published 27 February 2014

Academic Editor: Weiming Wang

Copyright © 2014 Hai-Feng Huo and Guang-Ming Qiu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A more realistic mathematical model of malaria is introduced, in which we not only consider the recovered humans return to the susceptible class, but also consider the recovered humans return to the infectious class. The basic reproduction number is calculated by next generation matrix method. It is shown that the disease-free equilibrium is globally asymptotically stable if , and the system is uniformly persistence if . Some numerical simulations are also given to explain our analytical results. Our results show that to control and eradicate the malaria, it is very necessary for the government to decrease the relapse rate and increase the recovery rate.