Abstract
We will discuss some adaptations of the standard epidemic models to incorporate various kinds of restrictions on the interaction between susceptible and infected individuals and study the effect of such restrictions on the prognosis of an epidemic. In one case, we study the effect of avoiding known infected neighbors on the persistence of a recurring infection process. In another case, we develop a flexible mathematical framework for pool-testing and badging protocol in the context of controlling contagious epidemics and tackling the far-reaching associated challenges, including understanding and evaluating individual and collective risks of returning prior infected individuals to normal society and other economic and social arrangements and interventions to protect against disease.