This article explores the global properties of a generalized \(SI_cIRS\) (susceptible-asymptomatically infected-symptomatically infected-recovered-susceptible) epidemic model, which takes into consideration the factors associated with government policies, public responses and social behavioural reactions. Essentially, this study centres on infectious diseases that can be propagated through asymptomatic carriers—individuals who are infected and contagious but do not exhibit any disease symptoms. Additionally, the analysis delves into the effects of environmental fluctuations on the dynamics of disease transmission. For the deterministic model, it has been observed that disease invasion occurs in the system when the basic reproduction number exceeds 1. On the other hand, if we raise the noise intensities in case of the stochastic model, the disease extinction happens quickly. Also, we have proved that the system undergoes transcritical bifurcation in the vicinity of the infection-free equilibrium. Also, two-parameter bifurcation provides the regions where stability of both the equilibrium points are analysed. This work, in particular, highlights the significance of nonlinear dynamic analyses on epidemic models. It also emphasizes the substantial impact that social behaviour and governmental action have on disease transmission by asymptomatically infected carriers and symptomatically infected individuals. The numerical data and simulations illustrate the critical role of government interventions in managing an epidemic, and the system tends to achieve an infection-free state more rapidly when the government takes early action during the onset of a disease outbreak.
