Stability analysis and optimal control of production-limiting disease in farm with two vaccines

Abstract

<p style='text-indent:20px;'>The transmission of production-limiting disease in farm, such as Neosporosis and Johne's disease, has brought a huge loss worldwide due to reproductive failure. This paper aims to provide a modeling framework for controlling the disease and investigating the spread dynamics of <i>Neospora caninum</i>-infected dairy as a case study. In particular, a dynamic model for production-limiting disease transmission in the farm is proposed. It incorporates the vertical and horizontal transmission routes and two vaccines. The threshold parameter, basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula>, is derived and qualitatively used to explore the stability of the equilibria. Global stability of the disease-free and endemic equilibria is investigated using the comparison theorem or geometric approach. On the case study of <i>Neospora caninum</i>-infected dairy in Switzerland, sensitivity analysis of all involved parameters with respect to the basic reproduction number <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> has been performed. Through Pontryagin's maximum principle, the optimal control problem is discussed to determine the optimal vaccination coverage rate while minimizing the number of infected individuals and control cost at the same time. Moreover, numerical simulations are performed to support the analytical findings. The present study provides useful information on the understanding of production-limiting disease prevention on a farm.</p>