Parameter estimation of influenza epidemic model

SEIRS and SVEIRS epidemic models are considered here to capture the main characteristic of transmission of influenza epidemic governed by a system of differential equations. All parameters estimations involved in these models are based on the influenza epidemic which occurred in Australia in 1919, often called Spanish flu data Sydney. Least squares method, which involves minimization of the sum of squared differences between the measurements and the model predictions is used to estimate the unknown parameters for both models. Graphical as well as numerical methods are used to validate these models. It is shown that our models reflect considerably the dynamical behavior of the influenza epidemic field data used. An important view of the disease dynamics including vaccine efficacy and level of vaccination is also drawn.