The beginning of a pandemic is a crucial stage for policymakers. Proper management at this stage can reduce overall health and economical damage. However, knowledge about the pandemic is insufficient. Thus, the use of complex and sophisticated models is challenging. In this study, we propose analytical and stochastic heat spread-based boundaries for the pandemic spread. These are compared with the stochastic Susceptible-Infected-Recovered (SIR) model taking place on an interaction graph. The proposed boundaries are not requiring accurate biological knowledge such as the SIR model does.