Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-08-01
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations.
The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method.
The conditions for local and global asymptotic stability of corruption-free and endemic equilibria are established.
From the analysis using center manifold theory, the model exhibits forward bifurcation.
Then, the model was extended by reformulating it as an optimal control problem, with the use of two time-dependent controls to assess the impact of corruption on human population, namely, campaigning about corruption through media and advertisement and exposing corrupted individuals to jail and giving punishment.
By using Pontryagin’s maximum principle, necessary conditions for the optimal control of the transmission of corruption were derived.
From the numerical simulation, it was found that the integrated control strategy must be taken to fight against corruption.
American Psychological Association (APA)
Alemneh, Haileyesus Tessema. 2020. Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics. Journal of Applied Mathematics،Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1174533
Modern Language Association (MLA)
Alemneh, Haileyesus Tessema. Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics. Journal of Applied Mathematics No. 2020 (2020), pp.1-13.
https://search.emarefa.net/detail/BIM-1174533
American Medical Association (AMA)
Alemneh, Haileyesus Tessema. Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics. Journal of Applied Mathematics. 2020. Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1174533
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174533