Modeling the Spread of Measles with the Role of Vaccination and Treatment

Abstract

Protection of children from vaccine-preventable diseases, such as measles, is among primary goal for health workers. Since vaccination and treatment has turned out to be the most effective method against childhood diseases, developing a framework that would predict an optimal vaccine coverage level needed to control the spread of these diseases is important and essential, with inclusion of treatment to those who have contracted the disease but not yet infectious. In this project, the use of a population with variable size to provide this framework was adopted. It majorly relied on a compartmental model expressed by a set of ordinary and partial differential equations based on the dynamics of measles infections. The numerical and qualitative analyses of the model were performed and different state variables were determined. Qualitative results show that the model has the disease-free equilibrium which is locally asymptotically stable when a certain threshold quantity is less than one and unstable when the quantity is more than one. Simulation of different epidemiological classes revealed that most of the individuals undergoing treatment join the recovered class.