Spread and control of influenza in two groups: A model

Influenza, or the flu, is a common respiratory disease caused by influenza virus. The flu spreads easily from person to person through coughing, sneezing and hands touching your eyes, mouth or nose. In order to study the spread of influenza an economic status based structured model has been proposed and analyzed in this paper. In the proposed model the total underling populations is divided into two subpopulations, consisting of persons having higher and lower economic status. For the control of the disease it has been assumed in the model that susceptibles of both the subpopulations are vaccinated at a constant rate. Linear and non-linear stability analyses of the model have been carried out. From the analysis we have derived the control reproductive number Rc which involves vaccination rate and vaccine efficacy. We have also found from the stability analysis that the disease free equilibrium point is locally asymptotically stable for Rc < 1 and unstable for Rc > 1. Further, we have proved that a unique endemic equilibrium point will exist when Rc > 1. Thus, we have concluded from the analysis of the model that the disease will either die out or will remain endemic depending on the value of control reproductive number.