Modelling Measles Reoccurrence in Vaccinated Infants

Abstract

Measles is a highly contagious viral disease caused by the morbillivirus, marked by symptoms including fever, cough, runny nose, conjunctivitis, and a characteristic widespread rash. In severe cases, especially among young children and pregnant women, it can lead to complications such as ear infections, pneumonia, encephalitis, and death. This study develops a six-compartment deterministic mathematical model, expressed as a system of ordinary differential equations, to investigate the transmission dynamics of measles in human populations. The model was demonstrated to be both mathematically and epidemiologically well-posed. The basic reproduction number (R₀) was derived, and the stability analysis of the disease-free equilibrium showed it to be locally and globally asymptotically stable when R₀ < 1, and unstable when R₀ > 1. Sensitivity analysis using normalized forward sensitivity indices revealed the impact of various parameters on R₀. Specifically, parameters with negative indices, such as the vaccination rate and treatment rate reduce R₀ when increased, while those with positive indices, such as the effective contact rate increase R₀ when increased. These findings underscore the importance of increasing vaccination coverage, enhancing treatment efforts, and isolating infected individuals to control and prevent measles outbreaks. The model provides a theoretical framework for designing effective public health strategies to minimize the disease burden in the population.