Local stability analysis of an influenza virus transmission model case study: Tondano health center in pekalongan city

Abstract

Influenza Virus is an infectious disease caused by the Orthomyxoviridae virus. This paper discussed mathematical modeling that explains the model of the influenza virus transmission with SEIR model, where S is susceptible, E is exposed, I is infected, and R is recovered. Basic reproduction numbers (R 0) are used to analyze the stability of the model. When R 0 less than 1 the virus free equilibrium is stable asymptotically local, while when R 0 greater than 1 the endemic equilibrium is stable asymptotically local. From the numerical simulation results based on data from Pekalongan, Indonesia, it's found that reproduction number is equal to 0,03492209390.This indicates that the virus free equilibrium is locally asymptotically stable and the endemic equilibrium is not locally asymptotically stable, so that there is no virus transmission in Pekalongan.