Modelling, Analysis, and Simulation of Measles Disease Transmission Dynamics

Abstract

Measles is one of the top communicable diseases, which is still responsible for 2.6 million deaths every year. Due to this reason, the paper focuses on measles transmission dynamics concerning the impact of indirect contact rate (transmitted from the host of the virus to the healthy individual) and improving the SEVIR model into the SVIRP model. From the model, we 6rst estimated the disease-free equilibrium, calculated the e9ective reproduction number (REff ), and established the stability analysis. ,e Castillo– Chavez stability criterion is used to demonstrate the global stability of the disease-free equilibrium point, while the linearization method is used to justify its local stability analysis and gives a result REff < 1. ,e stability analysis of endemic equilibrium point is explained by de6ning a Lyapunov function, and its global stability exists when REff > 1. To identify the e9ect of parameters on the transmission dynamics, we performed sensitivity index and numerical simulation. From the result, we obtained that the indirect contact rate has the highest impact in maximizing the transmission dynamics of measles. Also, we found that working on prevention and treatment strategies brings a signi6cant contribution in reducing the disease e9ect in the community