Stability Analysis of Mathematical Model of Meningococcal Meningitis Disease Between Two Regions Using (Scir)ina-(Si)ksa Compartment

Abstract

Mathematical research about Meningococcal meningitis disease usually focused in one region, however the spread of this disease also can be caused by residents who visiting epidemic region. So, the purposes of this study are (1) to establish a mathematical model of Meningococcal meningitis disease between two regions, particularly Indonesia and Saudi Arabia, (2) to analyze the stability of each equilibrium points, (3) and to explain the model simulation of Meningococcal meningitis with the effect of vaccination on populations from Indonesia. The disease-free equilibrium point is locally asymptotically stable when the reproduction number is less than one and unstable when the reproduction number is more than one. In addition to the stability of the locally asymptotically stable endemic equilibrium point when the reproduction number is more than one. Based on the model simulation, if the level of vaccination is higher, then the infected class on populations from Indonesia and Inffected class from Saudi Arabia will decrease tend to zero. The vaccination program can be used to control the transmission of Meningococcal meningitis disease. It also can be useful to monitor the efficiency of vaccination program in the country.