Dynamics and control of COVID-19 pandemic with nonlinear incidence rates
- PDF / 712,856 Bytes
- 14 Pages / 547.087 x 737.008 pts Page_size
- 48 Downloads / 158 Views
ORIGINAL PAPER
Dynamics and control of COVID-19 pandemic with nonlinear incidence rates G. Rohith
· K. B. Devika
Received: 21 April 2020 / Accepted: 17 June 2020 © Springer Nature B.V. 2020
Abstract World Health Organization (WHO) has declared COVID-19 a pandemic on March 11, 2020. As of May 23, 2020, according to WHO, there are 213 countries, areas or territories with COVID-19 positive cases. To effectively address this situation, it is imperative to have a clear understanding of the COVID-19 transmission dynamics and to concoct efficient control measures to mitigate/contain the spread. In this work, the COVID-19 dynamics is modelled using susceptible–exposed–infectious–removed model with a nonlinear incidence rate. In order to control the transmission, the coefficient of nonlinear incidence function is adopted as the Governmental control input. To adequately understand the COVID-19 dynamics, bifurcation analysis is performed and the effect of varying reproduction number on the COVID-19 transmission is studied. The inadequacy of an open-loop approach in controlling the disease spread is validated via numerical simulations and a robust closed-loop control methodology using sliding mode control is also presented. The proposed SMC strategy could bring the basic reproduction number closer to 1 from an initial value of 2.5, thus limiting the exposed and infected individuals to a controllable threshold value. The model and the proposed G. Rohith (B)· K. B. Devika Department of Engineering Design, IIT Madras, Chennai 600036, India e-mail: [email protected] K. B. Devika e-mail: [email protected]
control strategy are then compared with real-time data in order to verify its efficacy. Keywords COVID-19 · SEIR model · Nonlinear incidence rate · Bifurcation analysis · Sliding mode control · Model-based control
1 Introduction COVID-19, a novel coronavirus, caused an outbreak of atypical pneumonia first in Wuhan, Hubei province, China, in December 2019 and then rapidly spread out to the whole world. As per World Health Organization (WHO), as of May 23, 2020, globally, there are 5,105,881 confirmed cases and 333,446 deaths [1]. The whole world is in a lockdown scenario, having widespread socio-economic-political impacts. In this context, a study on the dynamics and possible control strategies could be of great interest to the research community and society as a whole. Compared with statistics methods, mathematical modelling based on dynamical equations has received relatively less attention, though they can provide more detailed mechanism for the epidemic dynamics. The study of dynamics of epidemics started from 1760 by modelling smallpox dynamics, and since then, it has become an important tool in understanding the transmission and control of infectious diseases [2]. A watershed moment in the mathematical modelling and analysis of epidemic dynamics was the introduction of
123
G. Rohith, K. B. Devika
susceptible–infectious–removed (SIR) compartmental modelling approach to study the plague dynamics in India [3]. Since
Data Loading...
