Global Stability and Sensitivity Analysis of SIAR Model with Influenza A (H1N1)

The SIAR model with symptomatic and asymptomatic individuals is introduced. The stability of equilibrium points are analyzed with the basic reproduction number (R0). The Disease-Free Equilibrium (DFE) is globally stable when R0 < 1, and the Endemic Equilibrium (EE) is locally asymptotically stable when R0 > 1. For case α = 0, the global stability of EE is analyzed by using a geometric approach for the global stability. The Sensitivity Analysis (SA) of R0 and EE with parameters of influenza A (H1N1) are presented. The most sensitive parameter for R0 is the transmission rate to symptomatic infected individuals. The sensitivity of EE shows that the recovery rate of symptomatic and asymptomatic individuals have an effect on reducing patients when the recovery rate are increased. Therefore, controlling the spread of disease and reducing the treatment time can reduce the number of infected individuals. Simulations results by using numerical method are used to confirm the stability of the model. Further, this model is applied to predict the trend of influenza A cases of (H1N1) in Thailand during 2016 − 2022.