Fractional order SEIQRD epidemic model of Covid-19: A case study of Italy

PLOS ONE RESEARCH ARTICLE Fractional order SEIQRD epidemic model of Covid-19: A case study of Italy Subrata Paul1, Animesh Mahata ID2*, Supriya Mukherjee ID3, Prakash Chandra Mali4, Banamali Roy ID5 1 Department of Mathematics, Arambagh Government Polytechnic, Arambagh, West Bengal, India, 2 Mahadevnagar High School, Maheshtala, Kolkata, West Bengal, India, 3 Department of Mathematics, Gurudas College, Narkeldanga, Kolkata, West Bengal, India, 4 Department of Mathematics, Jadavpur University, Kolkata, India, 5 Department of Mathematics, Bangabasi Evening College, Kolkata, West Bengal, India a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Paul S, Mahata A, Mukherjee S, Mali PC, Roy B (2023) Fractional order SEIQRD epidemic model of Covid-19: A case study of Italy. PLoS ONE 18(3): e0278880. https://doi.org/10.1371/ journal.pone.0278880 Editor: Pablo Martin Rodriguez, Federal University of Pernambuco: Universidade Federal de Pernambuco, BRAZIL Received: June 12, 2022 Accepted: November 26, 2022 Published: March 6, 2023 Peer Review History: PLOS recognizes the benefits of transparency in the peer review process; therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. The editorial history of this article is available here: https://doi.org/10.1371/journal.pone.0278880 Copyright: © 2023 Paul et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: Data may be accessed by any researcher at https://www. worldometers.info/coronavirus/. * Abstract The fractional order SEIQRD compartmental model of COVID-19 is explored in this manuscript with six different categories in the Caputo approach. A few findings for the new model’s existence and uniqueness criterion, as well as non-negativity and boundedness of the solution, have been established. When RCovid19<1 at infection-free equilibrium, we prove that the system is locally asymptotically stable. We also observed that RCovid 19<1, the system is globally asymptotically stable in the absence of disease. The main objective of this study is to investigate the COVID-19 transmission dynamics in Italy, in which the first case of Coronavirus infection 2019 (COVID-19) was identified on January 31st in 2020. We used the fractional order SEIQRD compartmental model in a fractional order framework to account for the uncertainty caused by the lack of information regarding the Coronavirus (COVID-19). The Routh-Hurwitz consistency criteria and La-Salle invariant principle are used to analyze the dynamics of the equilibrium. In addition, the fractional-order Taylor’s approach is utilized to approximate the solution to the proposed model. The model’s validity is demonstrated by comparing real-world data with simulation outcomes. This study considered the consequences of wearing face masks, and it was discovered that consistent use of face masks can help reduce the propagation of the COVID-19 disease. 1. Introduction The world is still addressing the Coronavirus illness 2019 (COVID-19), which is caused by the new Coronavirus SARSCoV-2, a highly aggressive virus that attacks the individual respiratory system. The hospitalized individuals’ ailments were linked to the marine and moist animal industries in Wuhan, Hubei Province, China [1]. COVID-19 spreads from person to person by touching contaminated surfaces and inhalation of infected persons’ respiratory droplets [2]. Those who have been infected with COVID-19 have reported high fever, persistent cough, and exhaustion. Nonetheless, depending on the immune system, COVID-19 symptoms and consequences differ from person to person. People with a strong immune response seem to be more PLOS ONE | https://doi.org/10.1371/journal.pone.0278880 March 6, 2023 1 / 19 PLOS ONE Funding: The author(s) received no specific funding for this work. Competing interests: The authors have declared that no competing interests exist. Fractional order SEIQRD epidemic model of Covid-19 likely to get mild—to—moderate illnesses as well as recover avoid going to the hospital. Various investigations, however, have identified other symptoms such as neurological illnesses and gastroenteritis of different severity [3, 4]. With so many waves of infection, the illness caused numerous deaths in many countries. COVID-19 outbreaks have occurred in Italy, with the population suffering the effects of the consequences. The number of confirmed incidence and mortality in every phase has been published, and there appears to be an increasing incidence. On February 21, 2020, the first Italian victim of COVID-19, a 38-year-old male hospitalized at Codogno Hospital in Lodi, was diagnosed. On the 12th of February, 2022, it has infected over 424,636,034 people over the world, resulting in 5903,485 deaths and 349,857,774 recoveries [5]. According to reports, the mortality rate in waves 1 and 2 was 1%. Many social programmers and events have been discontinued or extended as a result of the epidemic. The T-20 cricket world cup will be hosted in Australia in 2020, while the Summer Olympics, which were scheduled to be held in Tokyo, have been postponed. The Indian Premier League, one of the most popular cricket events, has been relocated from India to the United Arab Emirates. Its importance has been demonstrated by the construction of mathematical models in the fields of epidemiology and physics. The Coronavirus infection has been examined by several researchers from various perspectives. While biologists and mathematicians working on the systems of the COVID-19 disease analyzed and constructed mathematical systems based on real-world cases from various countries, and offered information on the infection’s peak and clearance. In this context [4, 5], are some mathematical models that have been developed for this disease. The information from Italy is taken into account, and a mathematical model for the COVID-19 disease is developed, with its study reported in [6, 7]. Examines the number of genuine instances from the Mexican population using a mathematical model [8]. Proposes a fractional SEIR model utilizing the wavelet approach. The authors investigated the influence of social distance and other factors that might be regarded important for the reduction of COVID-19 infection in [9]. The authors used a mathematical modeling technique to evaluate genuine infected patients from Saudi Arabia and generated results on disease eradication in the nation [10, 11], Describes a comparative study of Coronavirus infection dynamics. In [12, 13] suggests some additional relevant work on COVID-19 modeling and associated illness outcomes. In [14], Paul et al. analyzed the scenario analysis of COVID-19 pandemic using SEIR epidemic model. (...truncated)