Stability Analysis for the Disease Free Equilibrium of a Discrete Malaria Model with Two Delays
A discrete-time model is established to show the transmission of malaria between humans and mosquitoes with the incubation periods of parasites within both human and mosquito concerned. It is proved that the disease free equilibrium of the model is globally asymptotically stable when the basic reproduction number is less than 1 by constructing appropriate Lyapunov functions.
KeywordsMalaria transmission Discrete time model Time delay Global stability Lyapunov function
Unable to display preview. Download preview PDF.
- 2.Wu, C.Q., Jiang, Z.Y.: A Delayed Discrete Model and Control for Malaria Transmission. In: Proceedings of 4th International Conference on Bioinformatics and Biomedical Engineering. IEEE press, NewYork (2010)Google Scholar
- 3.World Health Organization, World Malaria Report (2008), http://malaria.who.int/wmr2008
- 5.Ross, R.: The Prevention of Malaria, 2nd edn. Murray, Lodon (1911)Google Scholar
- 6.Macdonald, G.: The Epidemiology and Control of Malaria. Oxford University Press, London (1957)Google Scholar
- 10.Wu, Z.Y., Zhou, Y.C.: Advances in Mathematical Biology. Science Press of China, Beijing (2006) (in Chinese)Google Scholar
- 11.Wang, L., Wang, M.Q.: Ordinary Difference Equations. Xinjiang University Press, Urumqi (1991) (in Chinese)Google Scholar