Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics

Abstract

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.

An optimal control model with cost effectiveness analysis of Maize streak virus disease in maize plant

“…In this study, a deterministic mathematical model with optimal control for the dynamics of MSV was formulated and analyzed to find the best strategy for controlling MSD in maize population. We derived and analyzed the necessary conditions for optimal control strategies using Pontryagin’s maximum principle ( Hugo et al., 2019 ; Alemneh, 2020 ). With the principle, we obtained the Hamiltonian, the adjoin variables, the characterization of the controls and the optimality system.…”

“…In order to achieve this, the following objective functional is considered: where t f is the final time, d 1 and d 2 are balancing constant coefficients of the infected maize and infected leafhopper respectively while w 1 , w 2 and w 3 are weight coefficients for each individual control measure. We choose a nonlinear cost on the controls based on the assumption that the cost takes nonlinear form ( Alemneh, 2020 ; Alemneh et al., 2020 ; Osman et al., 2020a ). The goal is to find the optimal control triple ( , ) such that: where the control set is measurable on [0, t f ], .…”

Mathematical Modelling and Analysis of Corruption of Morals amongst Adolescents with Control Measures in Kenya

“…e group accounts for one-third of the 44,789 new HIV adult infections in 2017. National AIDs and STIs Control Programme (NASCOP) 2018 [4] estimates show that 105,230 adolescents between 10-19 years were living with HIV; in addition, 184,700 young adults (15)(16)(17)(18)(19)(20)(21)(22)(23)(24) are also infected. Sadly, the data indicates that adolescents account for one in every 10 AIDS-related deaths.…”

“…It was also shown that the corruption endemic equilibrium is locally asymptotically stable provided that the basic reproduction number is greater than one. In [15], the author developed an epidemiology model for the corruption dynamics. Furthermore, he extended the model to include optimal control with combinations of two corruption preventive measures, namely, (i) campaigning about corruption through media and advertisement and (ii) exposing the corrupted individuals to jail and giving punishment.…”

“…Furthermore, he extended the model to include optimal control with combinations of two corruption preventive measures, namely, (i) campaigning about corruption through media and advertisement and (ii) exposing the corrupted individuals to jail and giving punishment. Tessema Alemneh [15] concluded that the combination of both strategies is effective in bringing down the exposed and corrupted population in the specified period of time.…”