Design of a nonlinear model for the propagation of COVID-19 and its efficient nonstandard computational implementation

Abstract

Highlights Mathematical considerations of a SEIQR model to describe the propagation of COVID-19 are proposed. We derive analytically the reproductive number and the equilibria with and without COVID-19. Necessary and sufficient conditions for the stability of the equilibria are mathematically established. An efficient nonstandard method to solve the continuous problem is proposed and analyzed. The numerical simulations confirm the analytical and numerical results derived in this work.

A time-delay COVID-19 propagation model considering supply chain transmission and hierarchical quarantine rate

“…In this paper, based on the model formulated in [ 25 ], we consider the influence of supply chain transmission, hierarchical quarantine rate and time delay, and then we develop a novel Susceptible–Expose–Infected–Quarantined–Recovered (SEIQR) COVID-19 propagation model with two delays. In the new model, we analyze the existence of a virus-free equilibrium and a virus-existence equilibrium.…”

“…Compared with the model in [ 25 ], we consider the situation that people may be infected by items in transmission. Besides, we assume that exposed individuals and infected individuals have different quarantine rates, and this measure makes our new model practical.…”

“…The quarantine strategy, which has been widely used in the prevention of various diseases [ 24 ], is considered to be one of the most effective virus prevention measures. So, Rafiq et al established a SEIQR model to describe the propagation of COVID-19 by taking the quarantine strategy into account, and they researched not only the equilibrium points and the reproduction number, but also the local and global asymptotic stability of the equilibria [ 25 ]: where , , , , express the number of susceptible individuals, exposed individuals, infected individuals, quarantine individuals and recovered individuals at time t , respectively. The meanings of the remaining parameters in system ( 1 ) can be found in [ 25 ].…”

“…In the process of model analysis in [ 25 ], Rafiq et al thought only exposed individuals would be quarantined, but in fact, infected individuals are more likely to be quarantined. And, since the exposed individuals may have no obvious symptoms of infection, the quarantine rate of exposed individuals is less than that of infected individuals.…”

“…The quarantine strategy, which has been widely used in the prevention of various diseases [24], is considered to be one of the most effective virus prevention measures. So, Rafiq et al established a SEIQR model to describe the propagation of COVID-19 by taking the quarantine strategy into account, and they researched not only the equilibrium points and the reproduction number, but also the local and global asymptotic stability of the equilibria [25]:…”