Understanding theoretically the impact of reporting of disease cases in epidemiology

In conducting preliminary analysis during an epidemic, data on reported disease cases offer key information in guiding the direction to the in-depth analysis. Models for growth and transmission dynamics are heavily dependent on preliminary analysis results. When a particular disease case is reported more than once or alternatively is never reported or detected in the population, then in such a situation, there is a possibility of existence of multiple reporting or under reporting in the population. In this work, a theoretical approach for studying reporting error in epidemiology is explored. The upper bound for the error that arises due to multiple reporting is higher than that which arises due to under reporting. Numerical examples are provided to support the arguments. This paper mainly treats reporting error as deterministic and one can explore a stochastic model for the same.