On the discrete model of West Nile-like epidemics. (English) Zbl 1062.92059
Ladde, G.S.(ed.) et al., Dynamic systems and applications. Volume 4. Proceedings of the 4th international conference, Morehouse College, Atlanta, GA, USA, May 21–24, 2003. Atlanta, GA: Dynamic Publishers (ISBN 1-890888-00-1/hbk). 358-366 (2004).
From the introduction: In recent years the West Nile virus has become a serious threat to public health in many countries in the world including USA. West Nile virus infection is a cause of encephalitis (inflammation of the brain) in human and horses, and leads to death of a number of people. The virus was first isolated in 1937 in the West Nile district of Uganda. In 1957, during the outbreak in Israel, the virus was a cause of severe meningoencephalitis (inflammation of the spinal cord) in elderly. In 1999 the virus appeared in United States.
A difference equation model that describes the evolution of the West Nile-like Encephalitis in New York City was recently introduced and analyzed by D. Thomas and B. Urena [Math. Comput. Modelling 34, No. 7–8, 771–781 (2001; Zbl 0999.92025)]. The model includes the effects of spraying, when it was done periodically – every other week. By applying the theory of asymptotically autonomous systems, they obtained sufficient conditions for the number of infected humans and birds to converge to \(0\).
In this paper our aim is to investigate the dynamics of a slightly modified Thomas-Urena model. In particular, we introduce the “spraying function”, that is not necessarily periodic and which can be used to study the effectiveness of various spraying strategies. We obtain some general results about the asymptotic behavior of the model. In Section 2 we give a detailed description of the modified model. In Section 3 we obtain some results about the asymptotic behavior of the model. Two open problems are formulated in Section 4.
For the entire collection see [Zbl 1054.34001].
A difference equation model that describes the evolution of the West Nile-like Encephalitis in New York City was recently introduced and analyzed by D. Thomas and B. Urena [Math. Comput. Modelling 34, No. 7–8, 771–781 (2001; Zbl 0999.92025)]. The model includes the effects of spraying, when it was done periodically – every other week. By applying the theory of asymptotically autonomous systems, they obtained sufficient conditions for the number of infected humans and birds to converge to \(0\).
In this paper our aim is to investigate the dynamics of a slightly modified Thomas-Urena model. In particular, we introduce the “spraying function”, that is not necessarily periodic and which can be used to study the effectiveness of various spraying strategies. We obtain some general results about the asymptotic behavior of the model. In Section 2 we give a detailed description of the modified model. In Section 3 we obtain some results about the asymptotic behavior of the model. Two open problems are formulated in Section 4.
For the entire collection see [Zbl 1054.34001].
