The role of underreporting on the A-H1N1 2009 epidemic in Lima, Peru

Mathematical models can provide insight on how future epidemics may behave. Predictions and further public health strategies can be made more accurate when available, reliable data is used to estimate the model parameters. However, not all cases are reported, and this gap between the number of reported cases and the number of actual cases has not been studied in great detail. The aim of this work is to investigate how the level of underreporting under an epidemic outbreak is influenced by different isolation rates that contribute to the level of reporting, as isolated individuals are the only ones who are reported. To investigate this, we consider the case of the 2009 H1N1 influenza outbreak in Lima, Peru. A system of non-linear ODEs is constructed to eventually capture the dynamics of underreporting. Model parameters are estimated using data from the Peruvian Ministry of Health. These values, along with different values for isolation rates corresponding to stages of infectious classes are used to determine how the proportion of unreported cases varies. The final size relations for the total number of infected individuals and for the total number of reported cases are calculated. These size relations are used to obtain an expression for the level of underreporting. A sensitivity analysis is also conducted to determine which isolation rate most greatly affects the proportion of underreported cases.