Dynamics and Biocontrol: The Indirect Effects of a Predator Population on a Host-Vector Disease Model. (27th January 2014)

• Record Type: Journal Article
• Authors: Zhou, Fengyan; Yao, Hongxing
• Other Names: Xiao Yanni Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-01-27
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/252718
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : A model of the interactions among a host population, an insect-vector population, which transmits virus from hosts to hosts, and a vector predator population is proposed based on virus-host, host-vector, and prey (vector)-enemy theories. The model is investigated to explore the indirect effect of natural enemies on host-virus dynamics by reducing the vector densities, which shows the basic reproduction numbers R 01 (without predators) and R 02 (with predators) that provide threshold conditions on determining the uniform persistence and extinction of the disease in a host population. When the model is absent from predator, the disease is persistent if R 01 > 1 ; in such a case, by introducing predators of a vector, then the insect-transmitted disease will be controlled if R 02 < 1 . From the point of biological control, these results show that an additional predator population of the vector may suppress the spread of vector-borne diseases. In addition, there exist limit cycles with persistence of the disease or without disease in presence of predators. Finally, numerical simulations are conducted to support analytical results.