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 eorts 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 eectiveness 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