Modelling the effects of cutting off infected branches and replanting on fire-blight transmission using Filippov...

Fire blight is one of the most devastating plant diseases in the world. This paper proposes a Filippov fire-blight model incorporating cutting off infected branches and replanting susceptible trees. The Filippov-type model is formulated by considering that no control strategy is taken if the number of infected trees is less than an infected threshold level I_c; further, we cut off infected branches once the number of infected trees exceeds I_c; meanwhile, we replant trees if the number of susceptible trees is less than a susceptible threshold level S_c. The global dynamical behaviour of the Filippov system is investigated. It is shown that model solutions ultimately converge to the positive equilibrium that lies in the region above I_c, or below I_c, or on I=I_c, as we vary the susceptible and infected threshold values S_c and I_c. Our results indicate that proper combinations of the susceptible and infected threshold values based on the threshold policy can lead the number of infected trees to an acceptable level, when complete eradication is not economically desirable.