Dynamics and control of COVID-19 pandemic with nonlinear incidence rates

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

Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic

“…It will be worthy to notice that the dynamics of SEIR COVID-19 epidemic model with two bilinear incidence functions was tackled in [ 35 ], and the authors introduce seasonality and stochasticity in order to describe the infection rate parameters. Taking into account non-monotone incidence function, the technique of sliding mode control was used to study an SEIR epidemic model describing COVID-19 disease [ 36 ]. The COVID-19 SEIR epidemiological model with Crowley–Martin incidence rate was studied [ 37 ], and the authors study the effect of different parameters on the disease spread.…”

An Augmented SEIR Model with Protective and Hospital Quarantine Dynamics for the Control of COVID-19 Spread

“…Considering the latent state that exists for COVID-19 disease, model including an additional compartment called exposed state, called Susceptible-Exposed-Infectious-Removed (SEIR) model [4] is usually used to model COVID-19 dynamics. Literature suggest widespread use of SEIR model to study the early dynamics of COVID-19 outbreak [5][6][7][8][9][10]. Effectiveness of various mitigation strategies are also studied.…”

Understanding COVID-19 nonlinear multi-scale dynamic spreading in Italy

“…Data from Italy, the UK, and the USA were shown to fit well the model. A wealth of different compartmental models were recently proposed to understand the influence of asymptomatic individuals and the effects of control measures on the evolution of the disease [ 18 ], SEIR models combined with particle swarm optimization algorithm for parameter optimization [ 19 , 20 ], a SAIR model in the context of social networks [ 21 ], a SEIRD model with classical and fractional-order derivatives based on data in Italy to show that the fractional-order model has less RMS error than the classical one [ 22 ].…”