Abstract
In this paper, we have inquired pine wilt disease (PWD) governed by a mathematical model to access its dynamics. By using next generation matrix method, we worked out for basic reproduction number R∘, which apprises us about the disease dissemination or control in the community. Two kinds of equilibria, disease absent and disease present, have been established. Stability of both equilibria has been discussed. Lypunove functional theory and graph theoretic approach are used for disease free and endemic equilibrium, respectively. The parameters, expressed in the model, captured the growth in case onsets and the estimated results are almost compatible with the studied actual reported cases. By using the estimated parameters, we found the sensitivity indices of the basic reproduction number through the calculation of ratio of relative change in the parameter to the relative change in R∘. Influence of the parameters on the number of infectious pines and bark beetles has also been observed by the variation of parameters. Keeping in mind those vital factors, calculated through sensitivity analysis, that can help to overcome the disease, an effective control strategy has been designed and optimal control problem has been formulated. To get in sight the comparison of analytical results with numerical ones, the problem has been reconsidered, and it has been seen that numerical results, obtained by using estimated parameters, express effectiveness of the applied controls to reduce pine wilt infection.