Transmission dynamics and sensitivity analysis of pine wilt disease with asymptomatic carriers via fractal-fractional differential operator of Mittag-Leffler kernel

Pine wilt disease is caused by nematodes transmitted by pine sawyer beetles and is fatal for several pine species. The trees might be destroyed within a few months after being attacked, leads to major ecological and financial losses. In this article, we presented a model of pine wilt disease in the trees considering the interaction between nematodes, transmitting beetles with both asymptomatic and symptomatic pine trees. The disease dynamics is first displayed through a schematic diagram which is then transformed to non-linear coupled integer order ODEs through the law of mass action. The positivity, boundedness and equilibrium points has been analyzed and basic reproduction number is calculated through the next generation technique. Sensitivity analysis is also done for the most sensitive parameters which is also displayed through different figures and tables. The solution of the considered nonlinear fractal-fractal model has been obtained through numerical method via MATLAB software. Some numerical results have been obtained and it has been observed that the fractional model give us the more general results by considering different non-integer orders and the integer order results can be easily recovered. It is also noticed that reducing the interaction among the infected beetles and susceptible trees by killing the main source of the infection i.e., killing beetles can reduce the infection drastically, which are briefly discussed and conclusion has been drawn on the basis of the obtained results.