Analysis of an influenza A (H1N1) epidemic model with vaccination

A nonlinear mathematical model for the spread of influenza A (H1N1) infectious diseases including the role of vaccination is proposed and analyzed. It is assumed that the susceptibles become infected by direct contact with infectives and exposed population. We take under consideration that only a susceptible person can be vaccinated and that the vaccine is not 100% efficient. The model is analyzed using stability theory of differential equations and numerical simulation. We have found a threshold condition, in terms of vaccination reproduction number [Formula: see text] which is, if less than one, the disease dies out provided the vaccine efficacy is high enough, and otherwise the infection is maintained in the population. It is also shown that the spread of an infectious disease increases as the infective rate increases.