A Theoretical Model of Corruption Using Modified Lotka Volterra Model: A Perspective of Interactions between  Staff and Students

Mercy Kawira; Cyrus Gitonga Ngari; Stephen Karanja

doi:10.9734/jamcs/2020/v35i730299

Research Article Open access CC BY 4.0

A Theoretical Model of Corruption Using Modified Lotka Volterra Model: A Perspective of Interactions between Staff and Students

Mercy Kawira, Cyrus Gitonga Ngari, Stephen Karanja

Journal of Advances in Mathematics and Computer Science · pp. 12–25 · Published 8 Sep 2020

10.9734/jamcs/2020/v35i730299

Abstract

Corruption is the misuse of power or resources for private gain. This undermines economic development, political stability, and government legitimacy, the society fabric, allocation of resources to sectors crucial for development, and encourages and perpetuates other illegal opportunities. Despite Mathematical modeling being a powerful tool in describing real life phenomena it still remains unexploited in the fight of corruption menace. This study uses Lotka Volterra, predator-prey equations to develop a model to describe corruption in institutions of higher learning, use the developed model to determine its equilibria, determine the condition for stability of the equilibria and finally carry out the simulation. The corrupt students and staff act as predators while their non-corrupt counterparts act as prey in the paper. Theory of ordinary differential equations was used to determine steady states and their stability. Mathematica was used for algebraic analysis and Matlab was used for numerical analysis and simulation. Analytical result suggested multiple steady state however numerical result confirmed that the model has four steady states. Numerical bifurcation analysis suggests the possibility of backward of corrupt staff when is about 39. Numerical simulation points to an increasing trend on corrupt staff and decrease trend on corrupt student. This study concludes that more focus should be put to staff than students in curbing the spread of corruption. Future study should strive to fit this model in real data.

Corruption predator-prey steady states stability

References (3)

1 A modified predator–prey model for the interaction of police and gangs [DOI]
2 A System-Social Approach to the Modeling of Corruption. [DOI]
3 Modelling Corruption in a Cobb-Douglas Production Function Framework [DOI]

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Mercy Kawira, Cyrus Gitonga Ngari, Stephen Karanja (2020). A Theoretical Model of Corruption Using Modified Lotka Volterra Model: A Perspective of Interactions between Staff and Students. Journal of Advances in Mathematics and Computer Science , 12–25. https://doi.org/10.9734/jamcs/2020/v35i730299

Affiliations

Mercy Kawira — Department of Mathematics, School of Pure and Applied Science, Meru University of Science and Technology, P.O. Box 972-60200, Meru, Kenya.
Cyrus Gitonga Ngari — Department of Mathematics, Computing and Information Technology, School of Pure and Applied Science, University of Embu, P.O. Box 6-60100, Embu, Kenya.
Stephen Karanja — Department of Mathematics, Computing and Information Technology, School of Pure and Applied Science, University of Embu, P.O. Box 6-60100, Embu, Kenya.

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