Basic reproduction number for the SIR epidemic in degree correlated networks

Yi, Wang; Ma, Junling; Cao, Jinde

doi:10.1016/j.physd.2022.133183

Cited by 12 publications

(4 citation statements)

References 39 publications

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“…After that, A definition of the basic reproduction number R 0 will be introduced. It is presented for a general compartmental disease transmission model based on a system of time depending ordinary differential equations [23]. It means that if is R 0 < 1, the DFE is locally asymptotically stable; while if R 0 > 1, then the equilibrium is unstable, and the disease is going to break out [24].…”

Section: Methods Theorymentioning

confidence: 99%

Analysis of dynamic transmission of HPV with reproduction numbers R₀

2023

J. Phys.: Conf. Ser.

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In this paper, we discuss the patterns of the transmission of how the Human papillomavirus (HPV) spreads in the public. We analyze the behaviors of infectious disease in SIR, SEIR, and Multistrian models. In terms of this disease, HPV has many subtypes, some are high-risk, and some are low-risk. Unfortunately, many people in some areas are not aware of it. That will always cause many delays for the disease and aggravations. The harm caused by HPV is different for different groups of people, people will take various measures to handle the situation according to the severity. We divided them into 3 cases. That is case1-negative for people who may have caught HPV; case 2-negative people who may have caught HPV, but excluding exposures; case 3-negative for people who is sure to catch HPV. After that, by computing the disease-free equilibrium (DFE) to get the value for calculating reproduction number R 0 to estimate the stability for every case. Then the way of getting the derivatives and partitioned matrix and computing reproduction number with the measure of the Jacobian matrix were used for deciding the response for the epidemic eventually.

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Section: Methods Theorymentioning

confidence: 99%

Analysis of dynamic transmission of HPV with reproduction numbers R₀

2023

J. Phys.: Conf. Ser.

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“…Thus, the equilibrium point of a disease-free is 𝑬 𝟎 = ( 𝜶 𝜸 , 𝟎, 𝟎, 𝟎). Than, we can define the basic reproduction number 𝑹 𝟎 [21] and [4] that characterises the ability of the spreads of congestion epidemic. Using the Next Generation Matrix (NGM) method [22] with 𝑲 = 𝑻𝑼 −𝟏 , we derive the 𝑹 𝟎 by choosing new infection vector and transmission vector respectively as follows,…”

Section: Stability Analysismentioning

confidence: 99%

Traffic Congestion Analysis Using Sir Epidemic Model

Rafsanjani,

Herdiana,

Tjahjana

et al. 2023

BAREKENG: J. Math. & App.

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In this work, we propose a mathematical model to represent traffic congestion in the street under some consideration. A congestion problem in a city highway becomes a critical issue since congestion at one point affected congestion propagation on the other points. We focus on the propagation of traffic propagation by adopting the concept of disease spread using the SIR model. We consider that the disease in traffic problems is congestion. Meanwhile, vehicles that enter the highway are susceptible to congestion. In contrast, vehicles free from traffic jams represent individuals free from disease. The SIR model can explain the spread of congestion by looking at the congestion variable as an infected variable. We discuss and analyze the existence and stability of the equilibrium points. The local stability equilibrium point is verified using the Routh-Hurwitz criteria. At the same time, the global stability is analyzed using Lyapunov function. The numerical simulation is provided in the last section to validate the discussion results.

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“…A large number of valuable research results have been obtained based on the degree correlation properties of networks [10][11][12][13][14]. In this section, by describing the degree correlation of complex networks and combining the composition characteristics of conflict networks, they are classified into assortative, disassortative and neutral conflict networks.…”

Section: Degree Correlation Of the Networkmentioning

confidence: 99%

“…Conflict networks have characteristics that are generally found in complex networks, and therefore can be characterized by means of complex networks.Newman et al [9] first proposed in 2002 that there is a certain degree matching pattern between complex network nodes, and using this pattern can better understand and analyze the characteristics of complex networks. In the field of aviation, there are fewer studies based on network degree correlation, but there are a large number of studies in other fields that are worthy of reference: Kai Mao [10] used the degree correlation property to classify complex networks into three types and explored the stability and robustness of complex networks using variable gradient analysis; Wang et al [11] analyzed the variation of the basic regeneration number R-0 of SIR epidemics in degree correlation networks. mou et al [12] provided theoretical references for port planning and national bulk trade strategies by analyzing trade networks with different degree correlation characteristics; Lu et al [13] identified key nodes in complex networks by constructing similarity coefficients; Zhao Na et al [14] classified the dependent networks into heterogeneous, homogeneous and random dependent ways according to the degree value of nodes and then analyzed the network robustness.…”

Section: Introductionmentioning

confidence: 99%

Robustness Analysis of Flight Conflict Networks Based on Degree Correlation

Wen

Lin

et al. 2022

IEEE Access

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Analyzing the composition and robustness of flight conflicts is beneficial to find the vulnerable sources of conflicts and dissipate flight conflicts, and effectively improve the safety and operational efficiency of air traffic. Therefore, this paper proposes a flight conflict network robustness evaluation method based on degree correlation. Firstly, a flight conflict network is constructed by using the velocity obstacle method, and it is classified into three types of assortative, disassortative and neutral conflict networks according to the degree correlation of the network. Several common robustness metrics in complex networks are explored, and a comprehensive robustness metric is proposed. The relationship between degree correlation and robustness of conflict networks under different node removal methods is analyzed by simulation experiments. The results show that the false alarm rate of the flight conflict network is decreased by 37.5% compared with the traditional state network. The degree correlation of the flight conflict network is closely related to the robustness. The assortative and disassortative conflict networks demonstrate stronger vulnerability with degree and betweenness removal, respectively, and the stronger the correlation the more obvious the vulnerability. The robustness of the neutral conflict network does not differ significantly under the two removal methods. Compared with random deletion, target removal can significantly decrease the network robustness.INDEX TERMS Flight conflict; air traffic; complex networks; degree correlation; robustness

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Basic reproduction number for the SIR epidemic in degree correlated networks

Cited by 12 publications

References 39 publications

Analysis of dynamic transmission of HPV with reproduction numbers R₀

Analysis of dynamic transmission of HPV with reproduction numbers R₀

Traffic Congestion Analysis Using Sir Epidemic Model

Robustness Analysis of Flight Conflict Networks Based on Degree Correlation

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Basic reproduction number for the SIR epidemic in degree correlated networks

Cited by 12 publications

References 39 publications

Analysis of dynamic transmission of HPV with reproduction numbers R0

Analysis of dynamic transmission of HPV with reproduction numbers R0

Traffic Congestion Analysis Using Sir Epidemic Model

Robustness Analysis of Flight Conflict Networks Based on Degree Correlation

Contact Info

Product

Resources

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Analysis of dynamic transmission of HPV with reproduction numbers R₀

Analysis of dynamic transmission of HPV with reproduction numbers R₀