A deterministic model of measles with imperfect vaccination and quarantine intervention

Abstract

A modified SVIQR (Susceptible-Vaccinated-Infected-Quarantine-Recovered) deterministic model for measles infection will be discussed in this article. An intervention of two times vaccination (one of them is imperfect to protect measles infection) is implemented along with the quarantine intervention in a purpose to controlling the spread of measles among human population. A measles-free and measles endemic equilibrium, for a complete and a simplified model, established analytically. A basic-reproduction number (R 0) as the endemic indicator is performed using the next-generation matrix approach. We find that the disease-free equilibrium is locally stable if R 0 < 1 and the endemic equilibrium of measles is achieved when R 0 > 1. Some numerical simulation regarding the sensitivities of R 0 and simulation for the autonomous model is given to give a better interpretation for the analytical results.