Derivation of the economic value of R0 for macroparasitic diseases and application to sea lice in salmon

Macroparasites, such as ticks, lice, and helminths, are a concern in livestock and aquaculture production, and can be controlled by genetic improvement of the host population. Genetic improvement should aim at reducing the rate at which parasites spread across the farmed population. This rate is determined by the basic reproduction ratio, i.e. R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}, which is the appropriate breeding goal trait. This study aims at providing a method to derive the economic value of R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document}. Costs of a disease are the sum of production losses and expenditures on disease control. Genetic improvement of R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document} lowers the loss-expenditure frontier. Its economic effect depends on whether the management strategy is optimized or not. The economic value may be derived either from the reduction in losses with constant expenditures or from the reduction in expenditures with constant losses. When R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document} [less than or equai to] 1, the economic value of a further reduction is zero because there is no risk of a major epidemic. When R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{0}$$\end{document} > 1 and management is optimized, the economic value increases with decreasing values of R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{a