A mathematical analysis of Pine Wilt disease with variable population size and optimal control strategies

The present paper describes the dynamics of the Pine Wilt disease with variable population size. The basic mathematical results for the model are presented. The stability analysis of both the disease-free and endemic cases are presented whenever R0 lesser or greater than one, respectively. Further, an optimal control problem is formulated and the necessarily involved results are presented. Moreover, the numerical simulation of the optimal control problem with suggested control strategies for the possible eliminations of the infection in the pine trees population is presented.