Local Stability Analysis of Modeling the Effect of Double Dose Vaccination of Measles Disease Dynamics in Zamfara State and Nigeria

Abstract

Measles is one of communicable diseases caused by the measles virus. In this research paper, we proposed and established a model for Measles disease dynamics, we incorporated the Treatment rate of both Exposed and Infected individuals, Enlightenment Rate and Effectiveness of Drug usage. We analyzed and shown the dynamics of the model system is in the region  and the model equations is considered epidemiologically and mathematically well posed with the invariant region method. The non-negativity solutions was presented and we found that the system is positive and remain in . The equilibrium states were obtained and we present the effective reproduction number of the model system. Analysis of the reproduction number was obtained. The Local stability analysis of the model equation was obtained and we found that the model is locally asymptotically stable if .