We propose a generalization of the adaptive N-Intertwined Mean-Field Approximation (aNIMFA) model studied in Achterberg and Sensi [Nonlinear Dyn. 111, 12657-12670 (2023)] to a heterogeneous network of communities. In particular, the multigroup aNIMFA model describes the impact of both local and global disease awareness on the spread of a disease in a network. We obtain results on the existence and stability of the equilibria of the system, in terms of the basic reproduction number R 0 . Assuming individuals have no reason to decrease their contacts in the absence of disease, we show that the basic reproduction number R 0 is equivalent to the basic reproduction number of the NIMFA model on static networks. Based on numerical simulations, we demonstrate that with just two communities periodic behavior can occur, which contrasts the case with only a single community, in which periodicity was ruled out analytically. We also find that breaking connections between communities is more fruitful compared to breaking connections within communities to reduce the disease outbreak on dense networks, but both strategies are viable in networks with fewer links. Finally, we emphasize that our method of modeling adaptivity is not limited to Susceptible-Infected-Susceptible models, but has huge potential to be applied in other compartmental models in epidemiology.

We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission patterns of the disease. We provide a global stability analysis for the model. We determine the value of the basic reproduction number R₀ and prove that the disease-free equilibrium is globally asymptotically stable if R₀<1. If R₀>1, the disease free equilibrium is unstable and a unique endemic equilibrium exists. We investigate the global stability of the endemic equilibrium for some variations of the original model under study and answer an open problem proposed in Ansumali et al. (2020). In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when R₀=1. We provide a thorough numerical exploration of our model to illustrate our analytical results.