  We investigate a mathematical model in crop pest management, considering
plant biomass, pest, and the effect of farming awareness. The pest population
is divided into two compartments: susceptible pest and infected pest. We assume
that the growth rate of self-aware people is proportional to the density of
healthy pests present in the crop field. Impacts of awareness is modeled via a
saturated term. It is further assumed that self-aware people will adopt
biological control methods, namely integrated pest management. Susceptible
pests are detrimental to crops and, moreover, there may be some time delay in
measuring the healthy pests in the crop field. A time delay may also take place
while becoming aware of the control strategies or taking necessary steps to
control the pest attack. In agreement, we develop our model incorporating two
time delays into the system. The existence and the stability criteria of the
equilibria are obtained in terms of the basic reproduction number and time
delays. Stability switches occur through Hopf-bifurcation when time delays
cross critical values. Optimal control theory has been applied for the
cost-effectiveness of the delayed system. Numerical simulations illustrate the
obtained analytical results.
