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

Main Article Content

Mercy Kawira
Cyrus Gitonga Ngari
Stephen Karanja

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.

Keywords:
Corruption, predator-prey, steady states, stability

Article Details

How to Cite
Kawira, M., Ngari, C. G., & Karanja, S. (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, 35(7), 12-25. https://doi.org/10.9734/jamcs/2020/v35i730299
Section
Original Research Article

References

Development d.o. Why corruption matters: understanding causes, effects and how to address them. Uk: ukaid from british people; 2015.

M. Chene. Community policing as a tool against corruption, Transparency International. 2012;2.

Kenya RO. The constitution of Kenya: republic of Kenya; 2010.

TI (Transparency International).Corruption Perceptions Index results; 2014.
Available:http://www.transparency.org/cpi2014/results [Google Scholar]; 2014.

Afrobarometer Kenyans decry incessant corruption but reluctant to report incidents. Nairobi safari club: Afrobarometer: (2015).

Murray J. Mathematical Biology: An Introduction, Third Edition. Washington: Springer. (2002)

Nika, M. synthedemic modeling and prediction of internet – based spreading phenomena. London: imperial college London department of computing; 2015.

Jonathan P, et al. A Dynamic Analysis of Schelling’s Binary Corruption Model: A Competitive Equilibrium Approach. Vienna: Operation Research and Control system, Institute of Mathematical Methods in Economics, Vienna University of Technology; 2011.

Sirajo, A. Stability Analysis of the Transmission Dynamics and Control of Corruption. The Pacific Journal of Science and Technology; 2014.

Salem, H. Epidemic corruption: a bio-economic homology; 2013.

Brianzoni S., Coppier R. and Michetti E. Complex Dynamics in a Growth Model with Corruption in Public Procurement. Hindawi Publishing Corporation; 2011;27.
DOI:10.1155/2011/862396

Sooknanan J, Bhatt B, Comissiong DMG. A modified predator–prey model for the interaction of police and gangs. R. Soc; 2016.
DOI: dx.doi.org/10.1098/rsos.160083

Farida M, Ahmadi-Esfahani F. Modelling Corruption in a Cobb-Douglas Production Function Framework. AARES 51st Annual Conference (p. 21). Queenstown NZ: University of Sydney; 2007.

Nathan O. M. and Jackob K. O. Stability Analysis in a Mathematical Model of Corruption in Kenya. Asian Research Journal of Mathematics. 2019;1-15.
DOI: 10.9734/ARJOM/2019/v15i430164

Mikhailov AP, Gorbatikov EA, Kornilina ED. A System-Social Approach to the Modeling of Corruption. Mediterranean Journal of Social Sciences; 2013.
DOI: 10.5901/mjss.2013.v4n9p332

Nekovee M, Pinto J. Modeling the impact of organization structure and whistle-blowers on intra-organizational corruption contagion. Physica. 2019;339-449.

Waykar SR. Mathematical Modelling: A study of Corruption in the society. International Journal of Scientific & Engineering Research. 2013;1-16.

Bot TD. On Vital Role of Mathematics for Inculcating Good Behaviors/Values towards Curbing Corrupt Tendencies among Nigeria Students. Journal of Educational Policy and Entrepreneurial Research (JEPER). 2015;44-52.