Mathematical analysis of pulse vaccination in controlling the dynamics of measles transmission

Although the incidence of measles has been significantly reduced through vaccination, it remains an important public health problem. In this paper, a measles model with pulse vaccination is formulated to investigate the influential pulse vaccination on the period of time for the extinction of the disease. The threshold value of the formulated model, called the control reproduction number and denoted by $R^{\ast }$, is derived. It is found that the disease-free periodic solution of the model exists and is globally attractivity whenever $R^{\ast }<1$ in the sense that measles is eliminated. If $R^{\ast }>1$, the positive solution of the model exists and is permanent which indicates the disease persists in the community. Theoretical conditions for disease eradication under various constraints are given. The effect of pulse vaccination is explored using data from Thailand. The results obtained can guide policymakers in deciding on the optimal scheduling in order to achieve the strategic plan of measles elimination by vaccination.