Abstract
In this study, we examined the wilt ailment, of pines, by utilizing mathematical modelling. The model is based on the parametrization of infectious pine trees in Korea for the period of 2010-2019. The model has taken the development in the beginning, and the approximated findings are nearly agreeable with the obtained data. We have used the method of next-generation matrix to work out for the basic reproduction number. With the help of this number, one can know about the disease that how it can be dispersed or can be controlled in the population. Equilibrium points, one contains all the disease classes and other is without disease classes, have been set up. By making use of Lyapunov functional theory, stability of equilibrium points has been examined. Sensitivity analysis has been performed to observe the relative significance of parameters to pine wilt malady transmission and its prevalence. To control the dissemination of disease, we formulated an optimal control problem. Strategies, which are used to control this disease, have been composed on the consequences of significant effects of estimated parameters on the basic reproduction number. Lastly, problem has been taken again for numerical results, and it is recognized that both the results, numerical and analytical, are in consensus with each other.