Open Access. © 2021 Swati Tyagi et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License. Nonauton. Dyn. Syst. 2021; 8:75–86 Research Article Open Access Swati Tyagi, Shaifu Gupta, Syed Abbas*, Krishna Pada Das, and Baazaoui Riadh Analysis of infectious disease transmission and prediction through SEIQR epidemic model https://doi.org/10.1515/msds-2020-0126 Received November 3, 2020; accepted March 25, 2021 Abstract: In literature, various mathematical models have been developed to have a better insight into the transmission dynamics and control the spread of infectious diseases. Aiming to explore more about various aspects of infectious diseases, in this work, we propose conceptual mathematical model through a SEIQR (Susceptible-Exposed-Infected-Quarantined-Recovered) mathematical model and its control measurement. We establish the positivity and boundedness of the solutions. We also compute the basic reproduction num- ber and investigate the stability of equilibria for its epidemiological relevance. To validate the model and estimate the parameters to predict the disease spread, we consider the special case for COVID-19 to study the real cases of infected cases from [2] for Russia and India. For better insight, in addition to mathematical model, a history based LSTM model is trained to learn temporal patterns in COVID-19 time series and predict future trends. In the end, the future predictions from mathematical model and the LSTM based model are compared to generate reliable results. Keywords: Infectious disease; Mathematical model; Stability analysis; Long Short Term Memory networks (LSTM); Parameter estimation MSC: 00A71; 92B20; 34D20  Introduction In history, various pandemics and epidemics have emerged out several times, which have demolished human- ity, sometimes resulting into end of civilizations and tremendous change in the course of history. Mathemati- cal modelling plays an important role in understanding the complexities of such infectious diseases and their control. The initial models of infectious diseases primarily focused on the theoretical disease research. More recently, there have been eorts to broaden the eld still further by incorporating many aspects of complex- ity of natural systems. Provided this rich history in development of fundamental theory, the applied aspect of the questions being asked, and the extensive data collected on many disease systems, the eld of infec- tious disease modelling represents one of the richest areas of research at the interface of pure theory and data. Mathematical modelling can be used to study the mechanisms underlying observed epidemiological patterns, assessing the eectiveness of control strategies, and predicting epidemiological trends. The investigation of dynamics of infectious disease transmission can be reached from various frameworks, such as relatively sim- ple curve tting techniques to standard SIR, SEIR etc. compartmental models to complex stochastic models using simulations. To model the outbreaks of infectious diseases, there are two major components, namely; Swati Tyagi: Department of Mathematics, Amity University, Punjab, 140306, India Shaifu Gupta: Department of Computer Science & Engineering, Indian Institute of Technology Jammu, Jammu, Jammu and Kashmir, 181221, India *Corresponding Author: Syed Abbas: School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, 175005, H.P., India, E-mail: sabbas.iitk@gmail.com; abbas@iitmandi.ac.in Krishna Pada Das: Mahadevananda Mahavidyalaya Monirampore, P.O.-Barrackpore, Kolkata 700120, India Baazaoui Riadh: College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Saudi Arabia