Analysis of a delayed epidemic model with pulse vaccination and saturation incidence

Gao, Shujing; Chen, Lansun; Nieto, Juan J.; Torres, Ángela

doi:10.1016/j.vaccine.2006.05.018

Cited by 259 publications

(135 citation statements)

References 36 publications

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“…If our model 1.6 does not have a limit cycle see Theorem 2.2 and Corollary 2.3 , its asymptotic behavior is determined by the stability of E 12 . When E 12 is stable, there is a region outside which positive semiorbits tend to E 0 as t tends to infinity and inside…”

Section: Discussionmentioning

confidence: 99%

A Viral Infection Model with a Nonlinear Infection Rate

Nieto

Torres

et al. 2009

Boundary Value Problems

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A viral infection model with a nonlinear infection rate is constructed based on empirical evidences. Qualitative analysis shows that there is a degenerate singular infection equilibrium. Furthermore, bifurcation of cusp-type with codimension two i.e., Bogdanov-Takens bifurcation is confirmed under appropriate conditions. As a result, the rich dynamical behaviors indicate that the model can display an Allee effect and fluctuation effect, which are important for making strategies for controlling the invasion of virus.

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Section: Discussionmentioning

confidence: 99%

A Viral Infection Model with a Nonlinear Infection Rate

Nieto

Torres

et al. 2009

Boundary Value Problems

Self Cite

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“…34 and has since been further developed, for example, in Refs. [35][36][37][38][39][40][41][42]. In contrast, state-dependent pulse vaccination strategies have been studied much less extensively (for example, Nie et al 43 proposed and analyzed such a control scheme for an SIR model).…”

Section: 13mentioning

confidence: 99%

Switching Vaccination Schemes for Vector-Borne Diseases With Seasonal Fluctuations

Liu

Stechlinski

2017

J. Biol. Syst.

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Theory is developed for an epidemic model of a seasonally-spreading vector-borne disease using a hybrid system framework. Applicable to diseases spread by mosquitoes (e.g., chikungunya and Zika virus via Aedes albopictus), seasonal variations in transmission are modeled using switching parameters to represent term-time forcing. The vector agent is assumed to exhibit a period of incubation upon infection, modeled using a distribution. Three hybrid control strategies are analyzed in detail: switching cohort immunization, pulse vaccination at pre-specified times, and state-dependent pulse vaccination. Methods from switched systems theory are used to derive threshold disease eradication conditions involving the model parameters; convergence of solutions to a disease-free set or periodic solution is shown. A comprehensive analysis is performed to compare and contrast the different control schemes.

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“…The SIS model is defined in that individuals start off susceptible, at some stage catch the disease, and after a short infectious period become susceptible again [2]. Therefore, some deterministic SIS epidemic models have been studied by many authors [3][4][5][6][7][8][9][10]. Recently, the authors of [11][12][13] investigated the epidemic model with double epidemic hypothesis which has two epidemic diseases caused by two different viruses.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

Liu

Meng

2017

Complexity

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We investigate the dynamics of a nonautonomous stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis. By constructing suitable stochastic Lyapunov functions and using Has'minskii theory, we prove that there exists at least one nontrivial positive periodic solution of the system. Moreover, the sufficient conditions for extinction of the disease are obtained by using the theory of nonautonomous stochastic differential equations. Finally, numerical simulations are utilized to illustrate our theoretical analysis.

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Analysis of a delayed epidemic model with pulse vaccination and saturation incidence

Cited by 259 publications

References 36 publications

A Viral Infection Model with a Nonlinear Infection Rate

A Viral Infection Model with a Nonlinear Infection Rate

Switching Vaccination Schemes for Vector-Borne Diseases With Seasonal Fluctuations

Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

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