Threshold Dynamics of an $$\mathbf {SEIS}$$ Epidemic Model with Nonlinear Incidence Rates

Naim, Mouhcine; Lahmidi, Fouad; Namir, Abdelwahed

doi:10.1007/s12591-021-00581-9

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…A SEIR type age-structured model with migration and nonlinear incidence rates was studied in [32]. While models where asymptomatic people transmit the disease and consider non-linear incidence rates but do not consider immigration have been studied in [7,8,21].…”

Section: Introductionmentioning

confidence: 99%

Mathematical model of a SCIR epidemic system with migration and nonlinear incidence function

Gómez¹,

Mondragón²,

Rubio³

2023

J. Math. Computer Sci.

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In this paper, we proposed a generalization for a model that considers Susceptible, Infected, Carrier, and Recovered by introducing a general incidence rate and considering migration in all its populations. This model has the characteristic that carriers and infected can transmit the disease, besides it has not a disease-free equilibrium point and no basic reproductive number. The focus of this study is to show a generalized model and the conditions required to analyze the equilibrium point stability. Using an appropriate Lyapunov function and with suitable conditions on the functions involved in the general incidence, we showed that the disease equilibrium point is globally asymptotically stable. Also, we presented numerical simulations of two applications to illustrate the results obtained from the analytical part.

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Section: Introductionmentioning

confidence: 99%

Mathematical model of a SCIR epidemic system with migration and nonlinear incidence function

Gómez¹,

Mondragón²,

Rubio³

2023

J. Math. Computer Sci.

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“…Some mathematical models have been developed in order to understand the disease transmission about the SEIS epidemic model. Naim et al [7,8] discussed the two signi cant equilibrium points and obtained the conditions of asymptotic behavior. Huo et al [9] obtained the basic reproduction number about the SEIS epidemic model.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behavior of the SEIS Infectious Disease Model with White Noise Disturbance

Song

Han

2022

Journal of Mathematics

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Mathematical model plays an important role in understanding the disease dynamics and designing strategies to control the spread of infectious diseases. In this paper, we consider a deterministic SEIS model with a saturation incidence rate and its stochastic version. To begin with, we propose the deterministic SEIS epidemic model with a saturation incidence rate and obtain a basic reproduction number R 0 . Our investigation shows that the deterministic model has two kinds of equilibria points, that is, disease-free equilibrium E 0 and endemic equilibrium E ∗ . The conditions of asymptotic behaviors are determined by the two threshold parameters R 0 and R 0 c . When R 0 < 1 , the disease-free equilibrium E 0 is locally asymptotically stable, and it is unstable when R 0 > 1 . E ∗ is locally asymptotically stable when R 0 c > R 0 > 1 . In addition, we show that the stochastic system exists a unique positive global solution. Conditions d > σ ˇ 2 / 2 and R 0 s < 1 are used to show extinction of the disease in the exponent. Finally, SEIS with a stochastic version has stationary distribution and the ergodicity holds when R 0 ∗ > 1 by constructing appropriate Lyapunov function. Our theoretical finding is supported by numerical simulations. The aim of our analysis is to assist the policy-maker in prevention and control of disease for maximum effectiveness.

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Assessing the effect of migration and immigration rates on the transmission dynamics of infectious diseases

Gómez,

Mondragón,

Bernate

2023

J. Appl. Math. Comput.

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Threshold Dynamics of an $$\mathbf {SEIS}$$ Epidemic Model with Nonlinear Incidence Rates

Cited by 3 publications

References 25 publications

Mathematical model of a SCIR epidemic system with migration and nonlinear incidence function

Mathematical model of a SCIR epidemic system with migration and nonlinear incidence function

Dynamical Behavior of the SEIS Infectious Disease Model with White Noise Disturbance

Assessing the effect of migration and immigration rates on the transmission dynamics of infectious diseases

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