Disease-induced mortality may have a crucial impact on disease dynamics. In addition, different mixing functions between groups also play an essential role in disease transmission. Thus, we develop a multigroup Susceptible-Infectious-Removed-Susceptible (SIRS) model with disease-induced mortality and structured mixing. Particularly, we deduce the basic reproduction number \(\mathcal{R}_0\) and investigate the dynamic behaviour of the model by employing the Lyapunov function method and the monotone iterative approach, respectively. If \(\mathcal{R}_0 < 1\) , we prove that the disease-free equilibrium is globally asymptotically stable; whereas if \(\mathcal{R}_0 > 1\) and a sufficient condition is satisfied, we prove that the endemic equilibrium is globally asymptotically stable by two different approaches, without considering disease-induced mortality. Next, we consider three types of mixing functions between two groups: restricted mixing, proportional mixing and preferred mixing. Moreover, we set different preferred mixing proportions to study the impact of three different mixing functions on the spread of diseases by numerical simulations. Our findings indicate that when two sub-populations differ significantly in size, the inter-group mixing function has a substantial impact on both the temporal dynamics and the magnitude of susceptible and infectious individuals. In contrast, when the sub-populations are of similar size, the inter-group mixing function has little effect on the evolution of all epidemic compartments. Furthermore, differences in the inter-group mixing function directly influence the peak time of the epidemic.
