Stage-structure model for the dynamics of whitefly transmitted plant viral disease: an optimal control approach

In this article, a mathematical model is formulated to study the dynamics of whitefly transmitted viral diseases in plants. Here, the aim is to capture the effect of whitefly’s age-stages on the disease dynamics. The existence of the equilibria, basic reproductive number (R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_0$$\end{document}), and stability have been studied through qualitative analysis. It is found that the onset of oscillations may occur through Hopf bifurcation in the system. Forward bifurcation is also observed at R0=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_0=1$$\end{document}. Finally, optimal control theory has been applied for the cost-effectiveness of disease management.