Measles Transmission Model with Vaccination and Hospitalization Treatments

Abstract

Measles (Rubeola) as one of notifiable diseases gets serious concern worldwide since it was first found in ninth century. The implementation of vaccines for controlling measles transmission since 1963 up to nowadays requires various studies regarding the effectiveness of the vaccines. Studies in the area of mathematical modeling of measles virus transmission has been done by many authors. This study intended to propose a model of measles virus transmission that also considered hospitalization as a complementary treatment for vaccination implementation program. The model is an SIHR model that divided the population into Susceptibles (S), Infectives (I), Hospitalized (H), and Recovered (R). The analysis started with determining the the equilibria and their stability based on the value of Basic Reproduction Ratio (R0). The analitical results were implemented to recorded data of measles of Jakarta, Indonesia in 2017 for numerical simulation. The simulation result said that hospitalization for measles patients in Jakarta escalates the effectiveness of vaccination program being implemented in the city. This can be considered by the city policy makers for giving more concern on hospitalizing measles-infected patients.

Keywords

• measles
• hospitalized
• vaccination
• equilibrium
• basic reproduction ratio