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.

在这项研究中，我们利用数学建模检查了松树的枯萎病。该模型基于韩国 2010-2019 年期间传染性松树的参数化。该模型在初期进行了开发，其近似结果与获得的数据几乎吻合。我们使用次世代矩阵的方法来计算基本再生数。借助这个数字，人们可以了解这种疾病如何在人群中分散或控制。平衡点，一个包含所有疾病类别，另一个是没有疾病类别，已经设置。利用李雅普诺夫泛函理论，研究了平衡点的稳定性。已进行敏感性分析以观察参数对松枯病传播及其流行的相对重要性。为了控制疾病的传播，我们制定了一个最优控制问题。用于控制这种疾病的策略是根据估计参数对基本繁殖数的显着影响的结果而制定的。最后，对数值结果再次提出问题，并且认识到数值结果和解析结果是相互一致的。 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 已经组成了估计参数对基本再生数的显着影响的后果。最后，对数值结果再次提出问题，并且认识到数值结果和解析结果是相互一致的。 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 已经组成了估计参数对基本再生数的显着影响的后果。最后，对数值结果再次提出问题，并且认识到数值结果和解析结果是相互一致的。 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?