Stability Analysis in a Mathematical Model of Corruption in Kenya

Abstract

The term corruption refers to the process that involves the abuse of a public trust or office for some private benet. Corruption becomes a threat to national development and growth especially when there is no political will to fight it. Prevention and disengagement initiatives are part of EACC strategies used to fight corruption. Prevention strategies aim to stop or discourage citizens from engaging in corruption. Disengagement strategies attempt to reform corrupt individuals and to reclaim the stolen resources back to the public kitty. We describe prevention and disengagement strategies mathematically using an epidemiological compartment model. The prevention and disengagement strategies are modeled using model parameters. The population at risk of adopting corrupt ideology was divided into three compartments: S(t) is the susceptible class, C(t) is the Corrupted class, and M(t) is the corrupt political/sympathersizer class. The model exhibits a threshold dynamics characterised by the basic reproduction number R0. When R0 < 1 the system has a unique equilibrium point that is asymptotically stable. For R0 > 1, the system has additional equilibrium point known as endemic, which is globally asymptotically stable. These results are established by applying lyapunov functions and the LaSalles invariance principle. Based on our model we assess strategies to counter corruption vice.