Dynamics Analysis and Vaccination-Based Sliding Mode Control of a More Generalized SEIR Epidemic Model

Abstract

In this paper, based on the latest discovery of epidemiology, a more general SEIR epidemic model is firstly proposed and its main properties such as positivity and boundedness have been analyzed and proven. Meanwhile, a method is proposed to solve basic reproduction number. In addition, a vaccinationbased sliding mode control strategy is designed to guarantee that the proportion of infected subpopulation in the total population converge to the desired signal. Finally, by using computer simulation, the positivity and boundedness of the epidemic model and some control strategies are verified and evaluated, respectively.

On a Discrete SEIR Epidemic Model with Two-Doses Delayed Feedback Vaccination Control on the Susceptible

“…Then, Property (i) follows from (A8) combined with −1 < a − (ρ 1 + ρ 2 )K < 1, which jointly ensure that the unforced difference Equation (A1) has the property that {x k } ∞ k=0 → 0 for any finite x 0 by defining f : R 0+ → R 0+ by f (y) = sup θ∈(0,2π) (ρ 2 (cos(θd 2 ) − 1) + ρ 1 (cos(θ(d 1 + d 2 )) − 1)) 2 + (ρ 2 sin(θd 2 ) + ρ 1 sin(θ(d 1 + d 2 ))) 2 1 + (a − (ρ 1 + ρ 2 )y) 2 − 2(a − (ρ 1 + ρ 2 )y)cosθ (A9)…”

“…Thus, an output feedback approach is adopted in this work and discussed in the sequel. However, control theory has developed many analytical tools that allows one to face this problem by using other approaches such as state feedback and feedback linearization [ 2 ], output-controllability [ 19 ], optimal control [ 21 ], impulsive control [ 22 ], sliding mode [ 23 ] and lockdown and quarantine [ 18 , 28 ], to cite just a few.…”

“…In that way, the basic reproduction number and its physical and biological insight are discussed in [ 1 ] which is related to pertussis and measles descriptions. In addition, feedback vaccination laws have been developed using techniques such as sliding-mode control or linear or impulsive feedback vaccination [ 2 , 3 ]. The transient evolution of epidemic diseases is also an important issue for properly describing the day-to-day time-transmission levels and the appropriate eventual interventions to perform since the stability properties are more related to the stationary states, typically the disease-free and the endemic ones.…”

Vaccination control of an epidemic model with time delay and its application to COVID-19

“…When there exist various effective vaccines, appropriate vaccination strategy is needed to improve the efficacy of vaccination [ 27 – 29 ]. Since the epidemic models are nonlinear, many nonlinear control methods are used to design appropriate vaccination strategy [ 30 – 36 ]. For example, in [ 30 ], the authors considered an SEIR epidemic model and proposed a vaccination strategy based on feedback linearization techniques.…”

“…The impulsive vaccination strategy was also studied for other cases, such as SIR epidemic model [ 33 ] and SEIR epidemic model with time delay [ 34 ]. The sliding mode control has been used to design vaccination strategy for SEIR epidemic model [ 36 ]. Although there are many vaccination strategies for various epidemic models, they cannot be directly used for proposed epidemic model with time delay.…”