A stochastic SIS epidemic model with saturating contact rate

Lan, Guijie; Huang, Youlin; Wei, Chunjin; Zhang, Shuwen

doi:10.1016/j.physa.2019.121504

Cited by 12 publications

(12 citation statements)

References 45 publications

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“…In this paper, we consider a deterministic SIS epidemic model with saturating contact rate proposed and analyzed in a recent work (Lan et al 2019). The model is given by the following system of ODEs:…”

Section: Introductionmentioning

confidence: 99%

“…• β = βb, where β is the probability per unit time of transmitting the infection between two individuals taking part in a contact. The derivation of the function h(N ) in particular and contact rate functions in general was introduced and explained in Lan et al (2019). For simplicity in notations, we replace β with β again.…”

Section: Introductionmentioning

confidence: 99%

“…All the parameters in the model (1) are positive. We refer the readers to Lan et al (2019) for the details of the model (1).…”

Section: Introductionmentioning

confidence: 99%

“…In Lan et al (2019), the asymptotic stability of equilibria of the model (1) was established based on the Lyapunov stability theory for ODEs. It was proved that the disease-free equilibrium is global asymptotically stable if the basic reproduction number is less than unity, whereas, if the basic reproduction number is greater than unity, then the model admits a unique endemic equilibrium, which is locally asymptotically stable.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics and numerical approximations for a fractional-order SIS epidemic model with saturating contact rate

2020

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The aim of this paper is to propose and analyze a fractional-order SIS epidemic model with saturating contact rate that is a generalization of a recognized deterministic SIS epidemic model. First, we investigate positivity, boundedness, and asymptotic stability of the proposed fractional-order model. Secondly, we construct positivity-preserving nonstandard finite difference (NSFD) schemes for the model using the Mickens' methodology. We prove theoretically and confirm by numerical simulations that the proposed NSFD schemes are unconditionally positive. Consequently, we obtain NSFD schemes preserving not only the positivity but also essential dynamical properties of the fractional-order model for all finite step sizes. Meanwhile, standard schemes fail to correctly reflect the essential properties of the continuous model for a given finite step size, and therefore, they can generate numerical approximations which are completely different from the solutions of the continuous model. Finally, a set of numerical simulations are performed to support and confirm the validity of theoretical results as well as advantages and superiority of the constructed NSFD schemes. The results indicate that there is a good agreement between the numerical simulations and the theoretical results and the NSFD schemes are appropriate and effective to solve the fractional-order model.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…All the parameters in the model (1) are positive. We refer the readers to Lan et al (2019) for the details of the model (1).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics and numerical approximations for a fractional-order SIS epidemic model with saturating contact rate

2020

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“…Lv et al [11] showed that solutions to a stochastic Lotka-Volterra model having degenerate diffusion coefficients are almost surely confined in a compact set. A stochastic epidemic model having a saturated contact rate has been studied with an SDE possessing degenerate drift and diffusion coefficients [9]. Grandits et al [6] analysed the value of information in epidemiological dynamics using a system of SDEs having degenerate coefficients combined with a dynamic programming principle.…”

Section: Introductionmentioning

confidence: 99%

On a non-standard two-species stochastic competing system and a related degenerate parabolic equation

Yoshioka

2020

Preprint

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We propose and analyse a new stochastic competing two-species population dynamics model. Competing algae population dynamics in river environment, important engineering problems, motivate this model. It is a system of stochastic differential equations (SDEs) and has a characteristic that the two populations are competing with each other through the environmental capacities. Unique existence of the uniformly bounded strong solution is proven and an attractor is identified. The Kolmogorov backward equation associated with the population dynamics is formulated and its unique solvability in a Banach space with a weighted norm is discussed. Our mathematical analysis results can be effectively utilized for a base-stone of modelling, analysis, and control of the competing population dynamics.

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Bifurcation analysis of a respiratory disease model about air pollution direct and indirect effects

Shi

Ding

2022

Math Methods in App Sciences

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In this paper, a class of respiratory disease model is established by taking into account simultaneously two situations that susceptible individuals directly got sick by inhaling air pollutants and indirectly fallen ill from infection by patients with respiratory diseases. The sufficient conditions for equilibria existence of the system and locally asymptotically stability of endemic equilibria are obtained. The existence of saddle‐node bifurcation is derived by using the Sotomayor theorem. The stability of periodic solution of Hopf bifurcation is determined by calculating the first Lyapunov number. The direct conversion rate and indirect infection rate in the system are selected as bifurcation parameters; the existence of Bogdanov–Takens bifurcation of codimension 2 of the system is proved by calculating the universal unfolding near the cusp. This research shows that direct and indirect ways of getting sick have a significant influence on dynamical behaviors of the respiratory disease system.

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A stochastic SIS epidemic model with saturating contact rate

Cited by 12 publications

References 45 publications

Dynamics and numerical approximations for a fractional-order SIS epidemic model with saturating contact rate

Dynamics and numerical approximations for a fractional-order SIS epidemic model with saturating contact rate

On a non-standard two-species stochastic competing system and a related degenerate parabolic equation

Bifurcation analysis of a respiratory disease model about air pollution direct and indirect effects

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