Modelling and stability analysis of the dynamics of measles with application to Ethiopian data

Abstract

Measles, a highly contagious airborne disease, remains endemic in many developing countries with low vaccination coverage. In this paper, we present a deterministic mathematical compartmental model to analyze the dynamics of measles. We establish global stability conditions for both disease-free and endemic equilibria using the Lyapunov functional stability method. By using arbitrary parameters, we find that the proposed model exhibits forward bifurcation. To simulate the solution of the model for the forward problem, we perform numerical integration using MATLAB software. Moreover, we calibrate the model with real data from Ethiopia and estimate the parameters along with a 95 percent confidence interval (CI) by formulating an inverse problem. It is noteworthy that our model fits well with the actual data from Ethiopia. The estimated basic reproduction number (R0) is determined to be R0=1.3973, demonstrating the endemic status of the disease. Additionally, our local sensitivity analysis indicates that reducing the transmission rate and increasing vaccination coverage can effectively minimize R0.

Keywords

• Measles
• Basic reproduction number
• Global stability
• Vaccination
• Forward bifurcation
• Model calibration