Local Stability of Influenza Virus with Vaccination

Influenza virus is an infectious disease. This caused by influenza virus. The symptoms consist of high fever, runny nose, sore throat, muscle and joint pain. In this paper, we construct the mathematical model for the transmission of influenza virus.We separate the human into 2 groups such as group of persons who obtain the vaccination and group of persons who do not obtain the vaccination. Each group, we separated the persons intothe susceptible, exposed, infectious, quarantined and recovered groups. We analyzed the equilibrium point and find the local stability of them by using standard dynamical modeling method. The basic reproduction number of this mathematical model is found. We obtain the condition for the disease fee steady state and endemic disease state will be local stability. Numerical results of the model are shown.