Compartmental modelling in epidemic diseases: a comparison between SIR model with constant and time-dependent parameters. (1st March 2023) - Sikder, Arun Kumar; Hossain, Md Biplob; Islam, Md Hamidul
Abstract: The compartmental modelling is one of the most widely used techniques in investigating the dynamics of infectious diseases. This modelling technique usually treats model parameters as constant. However, the parameters associated with infectious diseases randomly change following the changes in the conditions of disease transmission. As a result, the estimated parameters are often found over or under-determined by direct problems when some conditions change and the forecasting using direct problems often goes wrong. In this study, we estimate the model parameters over different time intervals by means of the inverse problem method and then solve the forward problem using these estimated parameters to compare them with the real epidemic data. We apply the method to estimate the parameters corresponding to Nipah virus, Measles and COVID-19 in the context of Bangladesh. The results suggest that the method helps to gain improved insights into epidemic scenarios corresponding to smaller time intervals. The results of the direct problem are found to fall apart fairly quickly from the real epidemic data as the length of the interval used in the inverse problem method increased.