Malaysian Journal of Mathematical Sciences, June 2025, Vol. 19, No. 2
Global Stability and Sensitivity Analysis of SIAR Model with Influenza A (H1N1)
Sirijampa, A., Saksurakan, C., and Janreung, S.
Corresponding Email: aekabut.s@cit.kmutnb.ac.th
Received date: 23 March 2024
Accepted date: 19 August 2024
Abstract:
The SIAR model with symptomatic and asymptomatic individuals is introduced. The stability of equilibrium points are analyzed with the basic reproduction number ($R_0$). The Disease-Free Equilibrium (DFE) is globally stable when $R_{0}<1$, and the Endemic Equilibrium (EE) is locally asymptotically stable when $R_{0}>1$. For case $\alpha=0$, the global stability of EE is analyzed by using a geometric approach for the global stability. The Sensitivity Analysis (SA) of $R_0$ and EE with parameters of influenza A (H1N1) are presented. The most sensitive parameter for $R_{0}$ 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 $2016-2022$.
Keywords: basic reproduction number; global stability; sensitivity; SIAR model analysis
