Modeling of infectious diseases with a low number of infections is a task that often arises since most real epidemics affect only a small fraction of the population. Agent-based methods simulate individuals and their behavior. When the model is simulated, the epidemic automatically arises without being explicitly defined. Surprisingly, it is not easy to produce such epidemics with small infection numbers. Instead, it needs model improvements to accomplish that task. In this paper, we show different extensions, addressing the person’s behavior, the pathogen’s behavior and the environmental impacts. It turns out that the discussed improvements have different consequences. Hence, they need to be used deliberately to overcome modeling issues of a specific epidemic in an appropriate and valid way. Even more, these improvements address the underlying behavior of epidemics and hence have the ability to provide a deeper insight into the real spreading process of a disease.