Global stability of a multi-group SIS epidemic model with varying total population size

Kuniya, Toshikazu; Muroya, Yoshiaki

doi:10.1016/j.amc.2015.05.124

Cited by 18 publications

(16 citation statements)

References 32 publications

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“…The mathematical epidemiology models are based on the compartments such as Susceptible

, Exposed

, Infected

and Recovered

.The dispersal of population affects the dynamics of disease. The infectious disease brings misery and cause millions of death every year [4] . Significantly, recent example is COVID-19 [5] , [6] which has affected most of the countries.…”

Section: Introductionmentioning

confidence: 99%

Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model

Verma

Gupta

2021

Communications in Nonlinear Science and Numerical Simulation

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Connectivity and rates of movement have profound effect on the persistence and extinction of infectious diseases. The emerging disease spread rapidly, due to the movement of infectious persons to some other regions, which has been witnessed in case of novel coronavirus disease 2019 (COVID-19). So, the networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. Motivated by the recent empirical evidence on the dispersal of infected individuals among the patches, we present the epidemic model SEIR (Susceptible-Exposed-Infected-Recovered) in which the population is divided into patches which form a network and the patches are connected through mean-field diffusive coupling. The corresponding unstable epidemiology classes will be synchronized and achieve stable state when the patches are coupled. Apart from synchronization and stability, the coupled model enables a range of rhythmic processes such as birhythmicity and rhythmogenesis which have not been investigated in epidemiology. The stability of Disease Free Equilibrium (or Endemic Equilibrium) is attained through cessation of oscillation mechanism namely Oscillation Death (OD) and Amplitude Death (AD). Corresponding to identical and non-identical epidemiology classes of patches, the different steady states are obtained and its transition is taking place through Hopf and transcritical bifurcation.

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“…The mathematical epidemiology models are based on the compartments such as Susceptible

, Exposed

, Infected

and Recovered

Section: Introductionmentioning

confidence: 99%

Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model

Verma

Gupta

2021

Communications in Nonlinear Science and Numerical Simulation

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“…Reference [ 20 ] used a multi-group infectious disease model to describe the spread of viruses in epidemiology. Toshikazu Kuniya and Yoshiki Muroya [ 21 ] proposed a global dynamic model of a multi-population SIS epidemic model with threshold parameter changes and analyzed its dynamic behavior. The global stability of the multi-group SVIR epidemic model based on the recently developed Lyapunov function and graph theory was described in [ 22 ].…”

Section: Introductionmentioning

confidence: 99%

Qualitative analysis of a two-group SVIR epidemic model with random effect

Zhao

2021

Adv Differ Equ

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In this paper, we investigate the dynamical behavior of a two-group SVIR epidemic model with random effect. Firstly, the two-group SVIR epidemic model with random perturbation of natural death rate is established. The existence and uniqueness of positive solution are proved by using stopping time theory and the Lyapunov analysis method. Secondly, a property of the system solution is obtained by using the law of strong numbers and the continuous local martingale. Finally, a new combination of Lyapunov functions is applied. The solution of the model we obtained is oscillating around a steady state if the basic reproduction number is less than one, which is the disease-free equilibrium of the corresponding deterministic model. A numerical simulation is presented to verify our theoretical results.

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“…The SIS epidemic model is one of the most basic epidemic models, and assumes that recovered individuals become susceptible again immediately without immunity (see, e.g., Diekmann and Heesterbeek [8]). Many kinds of SIS epidemic models have been studied by researchers (see, e.g., [26,4,12,28,20,11,33,2,37,10,38,31,3,13,29,24,25]).…”

Section: Introductionmentioning

confidence: 99%

Global behavior of SIS epidemic models with age structure and spatial heterogeneity

Kuniya

Inaba

Yang

2018

Japan J. Indust. Appl. Math.

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In this study, we investigate two kinds of SIS epidemic models with an age structure and spatial heterogeneity. The first is the SIS epidemic model with age and patch structures, and the second is the SIS epidemic model with age structure and spatial diffusion. For both models, we prove that the global attractivity of each equilibrium is completely determined by the basic reproduction number R 0 ; that is, the disease-free equilibrium is globally attractive if R 0 < 1, whereas the endemic equilibrium uniquely exists and is globally attractive if R 0 > 1. In particular, we provide a theoretical justification for the basic reproduction number being the spectral radius of the next generation operator. This enables us to perform numerical simulations that verify our theoretical results, which is important from the viewpoint of applications.

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Global stability of a multi-group SIS epidemic model with varying total population size

Cited by 18 publications

References 32 publications

Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model

Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model

Qualitative analysis of a two-group SVIR epidemic model with random effect

Global behavior of SIS epidemic models with age structure and spatial heterogeneity

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