A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process

Wang, Weiming; Cai, Yongli; Ding, Zuqin; Gui, Zhanji

doi:10.1016/j.physa.2018.06.099

Cited by 113 publications

(53 citation statements)

References 28 publications

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“…Ho et al [7] and Perelson et al [22] considered two different ordinary differential equations (ODEs) to describe the interaction of susceptible cell, infected cell and free virus. Since then, a lot of mathematical models of HIV infection or other infectious disease have been extensively investigated by incorporating various factors [2,3,5,[8][9][10]13,27,29,30,32,34,35,37]. These models include ODEs, DDEs (delay differential equations) and PDEs (partial differential equations).…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation of an age-structured HIV infection model with logistic target-cell growth

Guo

Huo

Hong

2019

Journal of Biological Dynamics

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In this paper, we investigate an age-structured HIV infection model with logistic growth for target cell. We rewrite the model as an abstract non-densely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analysing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state. Furthermore, by using Hopf bifurcation theorem in Liu et al., we show that Hopf bifurcation occurs at the positive steady state when bifurcating parameter crosses some critical values. Finally, we perform some numerical simulations to illustrate our results.

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Section: Introductionmentioning

confidence: 99%

Hopf bifurcation of an age-structured HIV infection model with logistic target-cell growth

Guo

Huo

Hong

2019

Journal of Biological Dynamics

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“…Following [22,25], the choice for the following parameters remains unaltered: (19) and the initial value is I 0 = 10. In this case, R 0 = 2.143 > 1, and the deterministic model (6) has an unstable disease-free equilibrium E 0 = 0 and a unique globally stable endemic equilibrium E * = 34.4494.…”

Section: Numerical Results Via Disease Dynamicsmentioning

confidence: 99%

“…5(a)). Simple calculations show that the skewness (i.e., the measure of the asymmetry of the probability distribution of a real-valued random variable about its mean) in Other parameters are taken as (19) In order to understand the effect of the intensity of noise σ on the skewness of the distribution of I(t), we show the four probability density functions with σ = 0.01, 0.05, 0.1, and 0.15 in Fig. 6.…”

Section: Stochastic Endemic Dynamicsmentioning

confidence: 99%

“…It is now widely believed that environmental variations have a critical influence on the spread of the disease [1][2][3][4], and stochastic noise plays an indispensable role in the transmission of diseases, especially in a small population. Therefore, it seems more practical to consider stochastic epidemic models [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Global threshold dynamics of a stochastic epidemic model incorporating media coverage

et al. 2018

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In this paper, we investigate the global threshold dynamics of a stochastic SIS epidemic model incorporating media coverage. We give the basic reproduction number R s 0 and establish a global threshold theorem by Feller's test: if R s 0 ≤ 1, the disease will die out a.s.; if R s 0 > 1, the disease will persist a.s. In the case of R s 0 > 1, we prove the existence, uniqueness, and global asymptotic stability of the invariant density of the Fokker-Planck equations associated with the stochastic model. Via numerical simulations, we find that the average extinction time decreases with the increase of noise intensity σ , and also find that the increasing σ will be beneficial to control the disease spread. Thus, in order to control the spread of the disease, we must increase the intensity of noise σ .

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“…The last decade has witnessed the extensive researches for dynamics of complex networks (CNs) since CNs can characterize a quantity of real systems, such as biological and artificial neural networks, complex ecosystems, epidemic models, and coupled oscillators on lattices . One of the major topics drawing considerable concerns is synchronization of CNs.…”

Section: Introductionmentioning

confidence: 99%

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

2019

Math Methods in App Sciences

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This paper concentrates on the global synchronization of the fractional‐order multi‐linked complex network (FMCN) via periodically intermittent control. It should be stressed that periodically intermittent control is employed to the FMCN for the first time. Moreover, the network is defined on digraphs with different weights, and two situations on topological structure of the network are discussed, including each digraph being strongly connected, and the biggest one being strongly connected. Based on Lyapunov method and graph theory, some synchronization criteria are obtained under two situations. And, the obtained synchronization criteria have a close relationship with the order of fractional‐order derivative, coupling strength, control gain, control rate, and control period. Besides, for practicability, theoretical results are applied to studying the synchronization of fractional‐order multi‐linked chaotic systems, and some sufficient conditions are provided. For a special case, fractional‐order multi‐linked Lorenz chaotic systems, numerical simulations are given to indicate the feasibility of theoretical results and the effectiveness of control strategy.

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A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process

Cited by 113 publications

References 28 publications

Hopf bifurcation of an age-structured HIV infection model with logistic target-cell growth

Hopf bifurcation of an age-structured HIV infection model with logistic target-cell growth

Global threshold dynamics of a stochastic epidemic model incorporating media coverage

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

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