Mathematical modelling of measles disease with double dose vaccination

Abstract

This article presents a mathematical model for measles disease incorporating double dose vaccination strategies as control measures. The model, developed using a system of differential equations, aims to understand the dynamics of measles transmission and the impact of vaccination interventions. The basic reproduction number, (R₀), is obtained using the next-generation operator, providing insights into the disease's transmission potential. Analysis of the model revealed that the disease-free equilibrium is locally and asymptotically stable when R₀ < 1 and unstable otherwise. Numerical simulations revealed a progressive reduction of susceptible individuals to zero over time, indicative of successful disease control. Sensitivity analysis identified the contact rate of infection  as positively influential on disease transmission, emphasizing the importance of reducing this parameter. Conversely, the vaccination rate  exhibited a negative sensitivity index, emphasizing the critical role of enhancing vaccination efforts in disease prevention. These findings highlight the effectiveness of vaccination campaigns and targeted interventions in controlling measles outbreaks. Recommendations include intensifying vaccination programs, promoting awareness, and adapting control measures to local contexts to sustain disease control efforts and prepare for future challenges. This study contributes to the evidence base for informed public health policies aimed at reducing measles transmission and improving population health outcomes.