Global analysis of an SIR epidemic model with infection age and saturated incidence

Chen, Yuming; Zou, Shaofen; Yang, Junyuan

doi:10.1016/j.nonrwa.2015.11.001

Cited by 54 publications

(21 citation statements)

References 25 publications

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“…The Kermack-McKendrick system and its generalizations were widely investigated. We mention a very short list of works [15][16][17]. We also notice the applications of such type of systems in health, networks, informatics, economics, and finance (see, for example, [18] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Stability and Energy-Casimir Mapping for Integrable Deformations of the Kermack-McKendrick System

Lăzureanu

Petrişor

2018

Advances in Mathematical Physics

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Integrable deformations of a Hamilton-Poisson system can be obtained altering its constants of motion. These deformations are integrable systems that can have various dynamical properties. In this paper, we give integrable deformations of the KermackMcKendrick model for epidemics, and we analyze a particular integrable deformation. More precisely, we point out two Poisson structures that lead to infinitely many Hamilton-Poisson realizations of the considered system. Furthermore, we study the stability of the equilibrium points, we give the image of the energy-Casimir mapping, and we point out some of its properties.

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Section: Introductionmentioning

confidence: 99%

Stability and Energy-Casimir Mapping for Integrable Deformations of the Kermack-McKendrick System

Lăzureanu

Petrişor

2018

Advances in Mathematical Physics

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“…For instance, the susceptibility of a susceptible can depend on the physical age. Epidemic models with continuous age structures (generally described by partial differential equations in theoretical models) have been extensively studied in recent years (see, for example, previous studies [13][14][15][16][17][18][19][20][21][22][23][24] ). Among those on vector-borne diseases with age structures, 14,17,[20][21][22] Vargas-De-León et al 22 proposed 2 age-structured models for the transmission of a vector-borne infectious disease.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an age‐structured host‐vector model for malaria transmission

Wang

Chen

Liu

2018

Math Methods in App Sciences

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In this paper, we propose a host‐vector model for malaria transmission by incorporating infection age in the infected host population and nonlinear incidence for transmission from infectious vectors to susceptible hosts. One novelty of the model is that the recovered hosts only have temporary immunity and another is that successfully recovered infected hosts may become susceptible immediately. Firstly, the existence and local stability of equilibria is studied. Secondly, rigorous mathematical analyses on technical materials and necessary arguments, including asymptotic smoothness and uniform persistence of the system, are given. Thirdly, by applying the fluctuation lemma and the approach of Lyapunov functionals, the threshold dynamics of the model for a special case were established. Roughly speaking, the disease‐free equilibrium is globally asymptotically stable when the basic reproduction number is less than one and otherwise the endemic equilibrium is globally asymptotically stable when no reinfection occurs. It is shown that the infection age and nonlinear incidence not only impact on the basic reproduction number but also could affect the values of the endemic steady state. Numerical simulations were performed to support the theoretical results.

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“…Therefore, epidemic models with infection age have been extensively studied in the literature. To name a few, see [3,4,22,25,28,32], where the incidence is bilinear in most of the models. Recently, epidemic models with infection age and nonlinear incidence have been extensively studied (see, for instance, [4,25,28]).…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical results for an age-structured SIVS model with a general nonlinear incidence rate

Yang

Chen

2018

Journal of Biological Dynamics

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In this paper, we propose an SIVS epidemic model with continuous age structures in both infected and vaccinated classes and with a general nonlinear incidence. Firstly, we provide some basic properties of the system including the existence, uniqueness and positivity of solutions. Furthermore, we show that the solution semiflow is asymptotic smooth. Secondly, we calculate the basic reproduction number R 0 by employing the classical renewal process, which determines whether the disease persists or not. In the main part, we investigate the global stability of the equilibria by the approach of Lyanpunov functionals. Some numerical simulations are conducted to illustrate the theoretical results and to show the effect of the transmission rate and immunity waning rate on the disease prevalence.

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Global analysis of an SIR epidemic model with infection age and saturated incidence

Cited by 54 publications

References 25 publications

Stability and Energy-Casimir Mapping for Integrable Deformations of the Kermack-McKendrick System

Stability and Energy-Casimir Mapping for Integrable Deformations of the Kermack-McKendrick System

Dynamics of an age‐structured host‐vector model for malaria transmission

Theoretical and numerical results for an age-structured SIVS model with a general nonlinear incidence rate

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