Mathematical analysis of an influenza epidemic model, formulation of different controlling strategies using optimal control and estimation of basic reproduction number

In this article, a deterministic model is formulated to perform a thorough investigation of the transmission dynamics of influenza. In particular, our model takes into account the effects of medication as well as hospitalization. An in-depth stability analysis of the model is performed, and it is subsequently shown that the model is locally, as well as globally asymptotically stable, when R₀ > 1. It is also shown that there exists a unique endemic equilibrium whenever R₀ > 1. After estimating the effective contact rate, we estimate the basic reproduction number, using both an ordinary least squares and generalized least squares methodology. We also estimated confidence intervals for the effective contact rate using parametric bootstrapping. Furthermore, we perform uncertainty and sensitivity analysis to recognize the impact of crucial model parameters on R₀. In addition, using ideas from the optimal control theory, optimal medication and hospitalization strategies are proposed to eliminate the disease.