Sensitivity Analysis for the Mathematical Modeling of Measles Disease Incorporating Temporary Passive Immunity

Abstract

Measles is an airborne disease which spreads easily through the coughs and sneezes of those infected. Measles antibodies are transferred from mothers who have been vaccinated against measles or have been previously infected with measles to their newborn children. These antibodies are transferred in low amounts and usually last six months or less. In this paper a mathematical model of measles disease was formulated incorporating temporary passive immunity. There exist two equilibria in the model; Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The Disease Free Equilibrium (DFE) state was analyzed for local and global stability. The Basic Reproduction Number 0R was computed and used to carried out the sensitivity analysis with some parameters of the mode. The analysis shows that as contact rate  increases the 0 R increases and as the vaccination rate v increases the 0R decreases. Sensitive parameters with the 0R were presented graphically. The disease will die out of the population if the attention is given to high level immunization.