An application of the impulsive CSOH model for managing squirrels in the coconut farm

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 imp...

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Bibliographic Details
Published in:Advances in difference equations 2019-06, Vol.2019 (1), p.1-15, Article 248
Main Authors: Vajrapatkul, Adirek, Koonprasert, Sanoe, Sirisubtawee, Sekson
Format: Article
Language:English
Subjects:
Analysis
Coconut farm
Computer simulation
Difference and Functional Equations
Farms
Functional Analysis
Impulsive mathematical model
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Predator-prey simulation
Predators
Rodents
Samut Songkham
Squirrel management
Squirrels
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Summary: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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2161-x