Mathematical modelling and analysis of Kidnapping dynamics

Abstract

The problem of kidnapping as a social menace to a society is increasing in some African countries such as Nigeria. We therefore proposed a new deterministic mathematical model for the dynamics of Kidnapping in a community. This menace is considered like a two strains communicable disease with kidnapping propagation mission by kidnappers as one strain and adoption mission for kidnapped victims as the other strain to assess the impact of super-infection. The model exhibits four equilibrium points each of which is unique and asymptotically stable both locally and globally under certain conditions. We obtain the kidnapping propagation number where is the propagation number associated with strain . Another important threshold parameters associated with respective strains 1 and 2 are and . Indeed, we show that at most one strain invades the population if one of these parameters is less than unity. while the two strains coexist at endemic state when both and are greater than unity. The global stability results of the model equilibria are established by numerical simulations. This simulations results indicate that the super-infection destabilizes the coexistence equilibrium.