Dynamics and Biocontrol: The Indirect Effects of a Predator Population on a Host-Vector Disease Model

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 . 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.