A Mathematical Model on the Dynamics of Poverty and Prostitution in Nigeria

Abstract

In this paper, we propose a compartmental mathematical model that tracks the dynamic of poverty and prostitution in Nigeria. Our model incorporates an infected compartment that allows for a non-violent approach of government interventions. The stability of the system is analyzed for the existence of the prostitution free equilibrium. We established that there exist a prostitution free equilibrium point that is locally asymptotically stable when the reproduction number  and unstable when . Result in this paper shows that high rate of government interventions will reduce to the barest minimum the number of members in both poverty and prostitution class.

Keywords: Mathematical model, Poverty, Prostitution, Stability Analysis, Reproduction number