Analysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate

Zhou, Xueyong; Cui, Jinǵan

doi:10.1007/s11071-010-9826-z

Cited by 46 publications

(36 citation statements)

References 27 publications

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“…Note that if R * 1 < 1, then a < 0 and a > 0 if R * 1 > 1. Hence, we have the following theorem, which is similar to the result established in [27]: …”

Section: ) Is the Is The Liberalization Matrix Of The System (312) Asupporting

confidence: 72%

“…As similar as in [27], we will establish that R 0 = 1 is a bifurcation point, in fact, across R 0 = 1 the adopter free equilibrium changes its stability properties. In the following we consider system (2.1)-(2.3) and investigate the nature of the bifurcation involving the adopter-free equilibrium E 0 for R 0 = 1.…”

Section: Steady State Basic Influence Number and Stabilitysupporting

confidence: 58%

See 1 more Smart Citation

The impact of media on a new product innovation diffusion: a mathematical model

Dhar¹,

Tyagi²,

Sinha³

2014

B Soc Paran Mat

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In this paper, we proposed a three compartment model consisting of non-adopter, adopter and frustrated classes of population to discuss the influence of media coverage in spreading and controlling of adopter of a particular product in a region. The model exhibits two equilibria:(i) a adopter-free and (ii) unique interior equilibrium. Stability analysis of the model shows that the adopter-free equilibrium is always locally asymptotically stable if the influence number of adopter (R 0 ), which depends on parameters of the system is less than unity. Otherwise if R 0 > 1, a unique interior equilibrium exists, it is locally asymptotically stable under some set of conditions. Further analytically and numerically it is observed that the region for backward bifurcation of adopter population increases with the decrease of the valid contact rate before media alert. Finally, numerically experimentation are presented to establish the effect of different media alert rate on adopter and non adopter population.

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“…Note that if R * 1 < 1, then a < 0 and a > 0 if R * 1 > 1. Hence, we have the following theorem, which is similar to the result established in [27]: …”

Section: ) Is the Is The Liberalization Matrix Of The System (312) Asupporting

confidence: 72%

Section: Steady State Basic Influence Number and Stabilitysupporting

confidence: 58%

The impact of media on a new product innovation diffusion: a mathematical model

Dhar¹,

Tyagi²,

Sinha³

2014

B Soc Paran Mat

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show abstract

“…Epidemic models admit only a globally asymptotically stable disease free equilibrium if R 0 \1 (Zhou and Cui 2011;Van den Driessche and Watmough 2002;Diekmann and Heesterbeek 2000). There are several measures for the eradication of infectious diseases via chemical method.…”

Section: Introductionmentioning

confidence: 99%

Effects of additional food in a susceptible-exposed-infected prey–predator model

Sahoo

Poria

2016

Model. Earth Syst. Environ.

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In this paper, we propose a susceptible-exposedinfected prey-predator model supplying additional food to predator. We discuss the existence and the local stability conditions of both the disease free and endemic equilibrium points. Basic reproduction number is determined. The impact of additional food on infected prey population is discussed. Numerical simulation results establish that there exists a critical infection rate above which disease present in the system in absence of additional food. However, in such case supply of suitable additional food can make the system disease free. We compute the disease free regions in various parametric planes. Effects of variation of latent period is presented. Season dependent infection rate is also introduce in the system and the role of additional food is discussed. The main goal of this study is to show the nontrivial consequences of providing additional food for controlling infection in a diseased predator-prey system. This study is aimed to introduce a new non-chemical method for controlling disease of prey population.

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“…Media plays a very important role to communicate awareness in public for the use of nonpharmaceutical interventions (NPIs) to control the epidemics. Many researchers studied the epidemic models in controlling the epidemics [Hui & Zhu, 2007;Cañada & Zertiti, 1994;Bansal & Meyers, 2012;Liu et al, 2013;Gao et al, 2013;Tharakaraman et al, 2013;Chao et al, 2012;Safi & Gumel, 2013;Zhou & Cui, 2011;Hu et al, 2012Hu et al, , 2014Alexander & Moghadas, 2005;Kaddar et al, 2010;Zhang et al, 2009;Samsuzzoha et al, 2013;He et al, 2013;Sun et al, 2011;Liu et al, 2007;Tchuenche et al, 2011;Liu & Cui, 2008;Cui et al, 2008a;Cui et al, 2008b;Funk et al, 2009]. Recently, the dynamics of some communicable diseases have been studied by various scientists Buscarino et al, 2014;Meloni et al, 2011;Poletto et al, 2014;Bajardi et al, 2011].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation in Disease Dynamics with Latent Period of Infection and Media Awareness

Singh

Dhar

Bhatti³

2016

Int. J. Bifurcation Chaos

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In the present study, an SIS epidemic model with a latent period of infection and media awareness as control strategy is proposed. The asymptotic stability of the model is studied for both disease-free equilibrium and endemic equilibrium states with respect to the basic reproduction number R 0 . It is observed that the coefficient of media awareness m does not affect R 0 , but significantly affects the level of endemic equilibrium. Further, the specific conditions for the existence of Hopf bifurcation have been obtained for the endemic equilibrium state. We also performed the sensitivity analysis of the basic reproduction number and state variables at endemic steady state with respect to the model parameter and identified the respective sensitive parameters. Numerical simulations have been presented in support of our analytic findings.

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Analysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate

Cited by 46 publications

References 27 publications

The impact of media on a new product innovation diffusion: a mathematical model

The impact of media on a new product innovation diffusion: a mathematical model

Effects of additional food in a susceptible-exposed-infected prey–predator model

Bifurcation in Disease Dynamics with Latent Period of Infection and Media Awareness

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