Compartmental modelling in epidemic diseases: a comparison between SIR model with constant and time-dependent parameters

PAPER • OPEN ACCESS Compartmental modelling in epidemic diseases: a comparison between SIR model with constant and time-dependent parameters To cite this article: Arun Kumar Sikder et al 2023 Inverse Problems 39 035005 You may also like -Exploring the spatiotemporal distribution of measles in China and predicting the level of measles risk in each province Wang Tan, Rencong Nie, Qianqian Yang et al. -Study on epidemic dynamics model with time delay to eliminate measles in China Yiming Li -Mathematics model of measles and rubella with vaccination D Amelia and H Tasman View the article online for updates and enhancements. Inverse Problems 39 (2023) 035005 (15pp) https://doi.org/10.1088/1361-6420/acb4e7 Compartmental modelling in epidemic diseases: a comparison between SIR model with constant and time-dependent parameters Arun Kumar Sikder, Md Biplob Hossain and Md Hamidul Islam∗ Department of Applied Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh E-mail: hamidul.islam@ru.ac.bd Received 25 August 2022; revised 10 January 2023 Accepted for publication 20 January 2023 Published 8 February 2023 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.