Investigating the Stability Analysis of a Mathematical Model for Awareness Initiatives on Registration of Persons in Kenya

Abstract

In this paper, we discuss stability analysis of a mathematical model of awareness initiatives in registration of persons in Kenya. Using Ordinary Differential Equations, a mathematical model to compare the efficacy of print media, electronic media and word-of-mouth media in disseminating registration information is developed. Positivity and boundedness of solutions is established to ensure that the model is mathematically meaningful. The Basic Reproduction number R₀ is derived using the Next Generation Matrix. We present both awareness free equilibrium and the maximum awareness equilibrium. Stability analysis of the model shows that Awareness free equilibrium is both locally and globally asymptotically stable when R₀ < 1 hence no spread of awareness and unstable when R₀ > 1 while MAE is locally asymptotically stable when R₀ > 1 indicating spread of information in the population.