Dynamic models of pest propagation and pest control

This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution behaviours of pest aggregates are investigated by the rate equation approach based on the mean-field theory. For a system with a self-birth rate kernel I(k)=Ik and a fragmentation rate kernel L(i,j)=L, we find that the total number M^A_0(t) and the total mass of the pest aggregates M^A_1(t) both increase exponentially with time if L\neq0. Furthermore, we introduce two catalysis-driven monomer death mechanisms for the former pest propagation model to study the evolution behaviours of pest aggregates under pesticide and natural enemy controlled pest propagation. In the pesticide controlled model with a catalyzed monomer death rate kernel J_1(k)=J_1k, it is found that only when I