Biological Control of Vector-Borne Viral  Diseases in Solanaceous Vegetable Plants:  Mathematical Modeling Approach

Timothy A. Shamaki; Olaide A. Adesanya; Samuel Musa

doi:10.4314/cajost.v3i1.64

Authors

Timothy A. Shamaki Department of Mathematics, USCOEGA – Yobe State, Nigeria
Olaide A. Adesanya
Samuel Musa

DOI:

https://doi.org/10.4314/cajost.v3i1.64

Keywords:

Biological Control, Disease Free Equilibrium, Disease Endemic Equilibrium, Basic Reproduction Number, Local Stability, Global Stability

Abstract

A mathematical model for the biological control of Vector-Borne Virus Diseases
(VBVDs) in solanaceous vegetable plants is examined. The study adopts
linearization method. Disease-free equilibrium and endemic disease equilibrium
states have been established. The basic reproduction number for the control of
VBVDs is obtained. Analytically, the local and global stability of disease-free
equilibrium and disease endemic equilibrium were established. The numerical
simulation carried out on the model have proven that ladybug beetles can be
used as biological control agents in tackling viruses being transmitted by aphids,
thrips and whiteflies in solanaceous vegetable plants.