Identifiability Analysis of the Human H1N1 Influenza Virus
Influenza is a significant source of morbidity and mortality both worldwide and also in the United States. In the U.S., the Center for Disease Control (CDC) estimates over 490,000 hospitalizations and 34,000 deaths during the 2018-2019 influenza season . The objective of this research is to determine the epidemiologically important parameters of the H1N1 influenza virus such as the infection and recovery rates using mathematical modeling. Publicly available influenza incidence data from the CDC webpage was used to validate the mathematical model. The spread of the H1N1 influenza virus is modeled using the Susceptible-Infected- Recovered (SIR) compartmental model. To account for vaccination and treatment of the virus, SIVR and SITR models are considered. The models were run on the computer software MATLAB to compare the predictions of the model to the CDC data. To ensure the model’s precision, the parameters were manipulated so that the model predictions could mirror the data. It was found that the 2018 2019 season H1N1 influenza infection rate is 0.2567 per day and the recovery rate is 0.1774 per day. Finally, the identifiability of the models was analyzed through Monte Carlo Simulations, which were performed on MATLAB. The results show that the average relative errors of all the model parameters remained lower than the measurement errors. Thus, these results validate the identifiability of the epidemiological models considered in this study and the reliability of the parameter estimates.