Analysis and control of an SEIR epidemic system with nonlinear transmission rate

Abstract

a b s t r a c tIn this paper, the dynamical behaviors of an SEIR epidemic system governed by differential and algebraic equations with seasonal forcing in transmission rate are studied. The cases of only one varying parameter, two varying parameters and three varying parameters are considered to analyze the dynamical behaviors of the system. For the case of one varying parameter, the periodic, chaotic and hyperchaotic dynamical behaviors are investigated via the bifurcation diagrams, Lyapunov exponent spectrum diagram and Poincare section. For the cases of two and three varying parameters, a Lyapunov diagram is applied. A tracking controller is designed to eliminate the hyperchaotic dynamical behavior of the system, such that the disease gradually disappears. In particular, the stability and bifurcation of the system for the case which is the degree of seasonality β 1 = 0 are considered. Then taking isolation control, the aim of elimination of the disease can be reached. Finally, numerical simulations are given to illustrate the validity of the proposed results.

Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity

“…In order to differentiate between the possibilities for the epidemic condition R 0 , the two cases of no epidemic (R 0 ≤ 1) and epidemic (R 0 > 1) were analyzed separately. For both the no epidemic and epidemic cases, the local stability of the DFE X DFE and EE X EE equilibrium points in (32) and (69) were evaluated using their corresponding eigenvalues λ i from their specific Jacobian matrix J X . The proportional population of the rescaled variables s, e, i, and r with total population n of unity was studied through the subsequent time-series with various initial conditions s(0), e(0), i(0) and r(0) over the course of a 90-day period.…”

“…As a way to merge the significant features of the foundational and more advanced SIR and SIRS models [13,14] along with the SEIR and SEIRS models [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], the focus of the work is to develop and implement an extension of the SEIRS model. Fundamentally, the new SEIRS model is now a more advanced generalization of the previous models and incorporates vital dynamics with unequal birth and death rates, vaccinations for both newborns and non-newborns, and temporary immunity for describing the spread of infectious diseases.…”

Dynamic Analysis of an SEIR Model with Distinct Incidence for Exposed and Infectives

“…The unique equilibrium P * of the system (2) is globally asymptotically stable in $\stackrel{\circ }{T}$, when b ≥ α , Δ > 1, R 01 > 1, and α < min⁡⁡{ σa , b , ε }. When q = a = γ = 0, (2) becomes the SEIR model without infectivity in latent and disease-caused death (see [8]). When q = 0, (2) becomes the SEIR model without infectious in latent (see [12]).…”

“…Li and Fang (see [7]) studied the global stability of an age-structured SEIR model with infectivity in latent period. Yi et al (see [8]) discussed the dynamical behaviors of an SEIR epidemic system with nonlinear transmission rate. Li and Zhou (see [9]) considered the global stability of an SEIR model with vertical transmission and saturating contact rate.…”

Sliding mode robust control of SEIR epidemic models

“…Control Theory has recently emerged as one of the proposed approaches to deal with the design of vaccination campaigns [1], [2]. Thus, different types of vaccination laws based on Control Theory have appeared in the literature during the last years such as the state-feedback control [2], feedback linearization [1], [3] and observer-based control [4].…”