Abstract
In this work, we formulate the mathematical model that incorporates two equations to represent the ultimate goal and controlling strategy to the traditional prey-predator model so that we can investigate the interaction between preys and predators. The model is shortly called the CSOH model. The impulsive practice is added into the model for squirrel control purposes. In particular, we are interested in pulsing the squirrel hunters into the system for every fixed period to control squirrels at the level allowing farmers to have sufficient amount of coconuts so that they can continue their business. We establish the conditions for the squirrel-free periodic solution exists and is globally stable. The numerical simulations reveal that squirrels in the coconut farm could be entirely eradicated by the pulsing strategy. However, the disappearance of squirrels on the farm is not an ecological desire because all species should be allowed to coexist in the system. Consequently, we recommend that the number of squirrel hunters pulsed into the coconut farm should be properly set by considering the time of intervention, expenditure, ecological reasons, and emotional sensitivity of village members.
Highlights
Plant producers have recognized the issue of plant protection from pests for a long time
The various practices to prevent pests have been modified according to the situations in which the plant producers have encountered. We may classify those practices into two main categories, i.e., the human-made and the natural practices. The former refers to any intervention invented by humans, e.g., chemicals, cages, and guns, while the latter refers to mechanisms that occur naturally to strengthen the ecological balance
By means of the natural mechanisms, they are useful in maintaining the ecological balance, they may not be effective because the natural control usually takes a longer time than human interventions
Summary
Plant producers have recognized the issue of plant protection from pests for a long time. In 2010, Tang et al [5] formulated the IPM model with a different pulsing time of the chemical and natural enemy and showed the periodic solution under a specific threshold. The first one represents the coconut yield indicating the ultimate result and the other one is the squirrel hunter presenting a group of people who have been used in the squirrel control strategy This hunter equation shows a new kind of predators who can improve their predation skills which are not generally presented in the traditional prey-predator model. With the initial condition (C(0+), S(0+), O(0+), H(0+)) = (C0, S0, O0, H0) = X0, where C(t), S(t), O(t), and H(t) are the number of coconut yields, squirrels, barn owls, and squirrel hunters at time t, respectively.
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