Human behavior is a key determinant of epidemic outcomes. During health crises, variations in people’s responses to control measures, often driven by different levels of risk perception, lead to variability in epidemic parameters such as infectiousness and susceptibility. We introduce a model within the Susceptible-Infected-Removed (SIR) class that accounts for these heterogeneities. We find that there is a region in the space of parameters just above the epidemic threshold, where trajectories showing an initial decline in the number of Infected can suddenly reverse and give rise to widespread transmission. Such heterogeneity can lead to an underestimation of transmission potential and delayed recognition of epidemic resurgence, thereby severely compromising efforts for a timely response. We examine this phenomenon in the mean-field scenario and then simulate the dynamics on homogeneous and heterogeneous contact networks, confirming that this phenomenology persists beyond mean field. Our model also encompasses cases where the heterogeneity originates from biological or other factors.