The dynamics of emerging epidemics are complex to understand and difficult to model. Moreover, data for rare conditions (over time and space) often include excess zeros which may result in inefficient inference and ineffective prediction for such processes. This is a common issue in modeling rare or emerging diseases or diseases that are not common in specific areas, specific time periods, or those conditions that are hard to detect. Here, we provide a hierarchical Bayesian modeling approach to effectively model the dynamics of disease spread based on zero-modified modeling approaches. To this end, we incorporate a physical-statistical modeling approach to model the dynamics of disease spread using zero-modifies models. The flexibility of the proposed approach allows us to model the dynamics of disease spread for rare conditions that are on the rise (over time and/or space). To demonstrate our work, we provide a case study of modeling the spread of Lyme disease based on confirmed cases of the disease in the United States.