Complex dynamics of epidemic models on adaptive networks

Zhang, Xiaoguang; Shan, Chunhua; Jin, Zhen; Zhu, Huaiping

doi:10.1016/j.jde.2018.07.054

Cited by 44 publications

(21 citation statements)

References 27 publications

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“…Most of approaches attributed the oscillation to a sinusoidal time dependence of parameters of the model. Oscillations in SIR models have also been discussed by evolving networks 4 and asynchronous probabilistic cellular automaton 5 . Recently, Greer et al 6 proposed a simple dynamical model with timevarying births and deaths to explain sustained periodicity of epidemics like smallpox.…”

Section: Introductionmentioning

confidence: 99%

Self-organized wavy infection curve of COVID-19

Odagaki

2021

Sci Rep

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Exploiting the SIQR model for COVID-19, I show that the wavy infection curve in Japan is the result of fluctuation of policy on isolation measure imposed by the government and obeyed by citizens. Assuming the infection coefficient be a two-valued function of the number of daily confirmed new cases, I show that when the removal rate of infected individuals is between these two values, the wavy infection curve is self-organized. On the basis of the infection curve, I classify the outbreak of COVID-19 into five types and show that these differences can be related to the relative magnitude of the transmission coefficient and the quarantine rate of infected individuals.

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Section: Introductionmentioning

confidence: 99%

Self-organized wavy infection curve of COVID-19

Odagaki

2021

Sci Rep

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“…These results mean that the structure of the contact network is crucial in investigating and characterizing transmission of epidemics. So, many researchers studied the spread of epidemics such as foot-and-mouth disease, SARS, dengue, A/H1N1, and AIDS [ 12 – 16 ] on complex networks and analyzed the threshold of outbreaks and stability of equilibriums [ 17 – 21 ], which can seize the epidemic dynamics and further devise control measures. However, few studies have cautioned on the importance of the contact structures in understanding measles spread.…”

Section: Introductionmentioning

confidence: 99%

Measles dynamics on network models with optimal control strategies

2021

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To investigate the influences of heterogeneity and waning immunity on measles transmission, we formulate a network model with periodic transmission rate, and theoretically examine the threshold dynamics. We numerically find that the waning of immunity can lead to an increase in the basic reproduction number $R_{0}$ R 0 and the density of infected individuals. Moreover, there exists a critical level for average degree above which $R_{0}$ R 0 increases quicker in the scale-free network than in the random network. To design the effective control strategies for the subpopulations with different activities, we examine the optimal control problem of the heterogeneous model. Numerical studies suggest us no matter what the network is, we should implement control measures as soon as possible once the outbreak takes off, and particularly, the subpopulation with high connectivity should require high intensity of interventions. However, with delayed initiation of controls, relatively strong control measures should be given to groups with medium degrees. Furthermore, the allocation of costs (or resources) should coincide with their contact patterns.

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“…This process needs a contact between them. Recently, it is found that the best pattern of contact is contact in the networks, 8‐15 and study epidemic model on networks has been a hot issue in mathematic biology 16‐23 . The other question is who is the infector 24 ?…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a mathematical model of disease spreading on networks with symptomatic and asymptomatic infectors

Zhang

Liu

Hou

2020

Math Methods in App Sciences

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We establish an SEIaIdRS model to present the dynamics of epidemic on networks. Following the method of the next generation matrix, we derive the explicit formulas of the basic reproduction number R0. It shows that the asymptomatic infector plays an important role in disease spreading. By theoretical analysis, we find that the disease‐free equilibrium E0 is globally asymptotically stable if R0 ≤ 1; and the endemic equilibrium E+ is globally asymptotically stable if R0 > 1. At last, numerical simulations also show that the role that the asymptomatic infector plays in disease spreading on networks cannot be neglected.

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Complex dynamics of epidemic models on adaptive networks

Cited by 44 publications

References 27 publications

Self-organized wavy infection curve of COVID-19

Self-organized wavy infection curve of COVID-19

Measles dynamics on network models with optimal control strategies

Dynamical analysis of a mathematical model of disease spreading on networks with symptomatic and asymptomatic infectors

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