Uncertainty and sensitivity analysis of the basic reproduction number of a vaccinated epidemic model of influenza

The basic reproduction number and the point of endemic equilibrium are two very important factors in any deterministic compartmental epidemic model as the basic reproduction number and the point of endemic equilibrium represent the nature of disease transmission and disease prevalence respectively. In this article the sensitivity analysis based on mathematical as well as statistical techniques has been performed to determine the importance of the epidemic model parameters. It is observed that 6 out of the 11 input parameters play a prominent role in determining the magnitude of the basic reproduction number. It is shown that the basic reproduction number is the most sensitive to the transmission rate of disease. It is also shown that control of transmission rate and recovery rate of the clinically ill are crucial to stop the spreading of influenza epidemics.