Mathematical Modelling and Analysis of Measles Control Using Vaccination and Treatment: Children Under Ten Years in Kwale and Kilifi Countries, Kenya

Abstract

Measles is a communicable disease that mainly spreads through body contact, posing a serious public health challenge, especially in low-resource settings. Kwale and Kilifi counties continue to record high measles outbreaks despite the availability of vaccines. Emphasising the need for a deeper insight into the factors that drive the spread of measles and its control strategies, the study developed a compartmental model with treatment and vaccination strategies to analyse measles transmission. The next-generation matrix technique was applied to determine the basic reproduction number. The equilibrium stability was analysed using the Jacobian matrix, eigenvalue analysis, and Lyapunov function. The normalised forward sensitivity index method was used to identify key drivers of measles transmission. The simulations were performed in MATLAB to evaluate the effectiveness of vaccination and treatment on measles transmission. Monte Carlo results indicate strong model parameter estimates and a good model fit. The model ensured the positivity and boundedness for a feasible population dynamic. The results demonstrate that the reproduction numbers of Kilifi and Kwale counties are 1.212 and 1.517, respectively, which signify the persistence of the disease. The equilibrium of the disease-free state is unstable with a stable endemic state. The susceptible population, infection, treatment, and death rates are the parameters that influence measles transmission. The findings emphasise the need for strengthening both vaccination and treatment as control measures to eliminate measles and reduce its burden in the population of children in high-risk regions.