Modeling the Dynamics of Banana Weevil, Cosmopolites Sordidus (Germar), by Trapping with Holling Type II Response Function

Eliab Horub Kweyunga, Julius Tumwiine, Eldad B. Karamura

Abstract


A harvested logistic growth model that incorporates trapping of the adult banana weevils is formulated and solved both analytically and numerically. Key in the analysis of the model is the derivation of the critical trapping rate, that is, the threshold above which extinction of the banana weevils is a possibility. The existence of the saddle-node bifurcation is investigated. It is established that the stability of the equilibria is dependent on the relative sizes of the intrinsic growth rate and the carrying capacity. It is also found out that when the trapping rate exceeds the critical value, the model displays chaotic behavior and the trapping of the adult banana weevils in isolation can only provide short term relief. Thus a management package that targets all developmental stages of the banana weevils would be more effective. Numerical simulations are performed and agree with the analytical results.


Keywords


Asymptotic stability; Banana weevil; Holling type 2 functional response; Logistic growth model; Pseudostem traps; Saddle node bifurcation

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v12i3.1387

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