# Further Readings

###### tags: `articles`

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*[Influence Maximization on Social Graphs: A Survey](https://ieeexplore.ieee.org/abstract/document/8295265?casa_token=moKM-fd_YTIAAAAA:hCCfEXCqmZKVQgIrnMDK3faCQ2UXXD3Teh68-uWnRio8W8EslRuoE7BH1QCsxusSQWSUM8TKnw)*

- Models
- time-unaware
1. Independent Cascade Model
2. Linear Threshold Model
3. Triggering Model
- time-aware

- Theorem
- Computing the influence function $f(S)$ is **#P-hard** under Independent Cascade Model
- Complexity of the Greedy algorithm is $O(knf^*)$, where $f^*$ is the time of computing the influence function

- Algorithms
1. Simulation-based approach
2. Proxy-based approach
3. sketch-based approach


[EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5931789/)
1. Deterministic compartmental models(DCM): based on systems of differential equations
2. Stochastic individual contact models(ICM): Similar with Indepedent Cascade Model
3. Network models: generalization of the ICM


Summary

Plots



[MODELLING INFECTIOUS DISEASE IN DYNAMIC NETWORKS CONSIDERING VACCINE.](https://www.sysrevpharm.org/articles/modelling-infectious-disease-in-dynamic-networks-considering-vaccine.pdf)

1. In addition to *SIR*, *V* compartment which represent vaccinated is added.

[Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy](https://www.nature.com/articles/s41591-020-0883-7)

1. Showing us how to construct the systems of the differential equations in detail
2. Compare the model and the real data



[Heterogeneity matters: Contact structure and individual variation shape epidemic dynamics](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0250050)

Translate COVID-19 ODE model to stochastic model

1. Stochastic COVID-19 Simulation

2. Analyze modeling COVID-19 under DCM and ICM

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### [A Time-Dependent SIR Model for COVID-19 With Undetectable Infected Persons](https://ieeexplore-ieee-org.ezproxy.lib.nctu.edu.tw/abstract/document/9200529?casa_token=aePjKmvtAHwAAAAA:N1k67eImhTrFQlyfs4rJHm12WwZFT9PArx17aPYxmlofUWxibmsnaAOa0ZMZfBMsBAdJMaxN2Q)
- Propose a time-dependent SIR model
- Analyze the impact of the undetectable infections
- To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network.

[Page](https://hackmd.io/@O4ihgx_1Qh2kbnKJjRZAIA/ryCKVW-1Y)

### [A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2](https://science-sciencemag-org.ezproxy.lib.nctu.edu.tw/content/369/6505/846.abstract)
[Supplementary Materials](https://science-sciencemag-org.ezproxy.lib.nctu.edu.tw/content/sci/suppl/2020/06/22/science.abc6810.DC1/abc6810-Britton-SM.pdf)
- Heterogeneity affects herd immunity a lot.
- The classical herd immunity level $h_C = 1 – 1/R_0$
- $(1-h_c)R_0=1 \Rightarrow h_C = 1 – 1/R_0$
- Thus, if a fraction $v$ is vaccinated (immunity fraction: $E$) and vaccinees are selected uniformly in the community, then the new reproduction number is $R_v = (1 –Ev)R_0$
- From this, the critical vaccination coverage $v_c = E^{-1}(1 –1/R_0)$.
- 2 additional features
- Different age cohorts
- Social activity level
- 

### [A Simulation of a COVID-19 Epidemic Based on a Deterministic SEIR Model](https://www.frontiersin.org/articles/10.3389/fpubh.2020.00230/full)
- Implement an SEIR model to compute the infected population and the number of casualties of this epidemic.(Italy)

[Page](https://hackmd.io/@O4ihgx_1Qh2kbnKJjRZAIA/rkWuPNzyY)

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- [_Dynamic-Sensitive centrality of nodes in temporal networks_](https://www.nature.com/articles/srep41454)
- Measuring the **centrality** of nodes is an essential part of analysing networked systems
- _Classic definition of centrality: degree, betweenness, closeness_
- Classic works looked at analysing static networks but rarely highlighted the **dynamics**
- TDC (temporal Dynamic-Sensitive centrality) is more accurate than static versions of centrality
- [_Theories for Influencer Identification in Complex Networks_](https://link.springer.com/chapter/10.1007/978-3-319-77332-2_8)
- The successful identification of **influencers** should have profound implications in various real-world spreading dynamics
- Summarizing the centrality-based approach in finding single influencers
- Locating multiple influencers from a collective point of view
- [_Superspreaders and superblockers based community evolution tracking in dynamic social networks_](https://www.sciencedirect.com/science/article/pii/S0950705119306264?casa_token=rLcZQYT-00YAAAAA:PxSX7iFz12xHH9HgGvxzvtPvdSNPjlk2iUILDMtzRd2Vz6auzAjJVFO30W8gm7zXiE10uOEocg)
- Propose a two-stage method to increase the accuracy of tracking the community evolution:
1. Error accumulation sensitive **(EAS)** incremental community detection
2. Superspreaders and superblockers **(SAS)** based community evolution tracking

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*[Hethcote HW (2000). "The mathematics of infectious diseases". Society for Industrial and Applied Mathematics. 42: 599–653](https://epubs.siam.org/doi/abs/10.1137/s0036144500371907?casa_token=CCF_qc2t66YAAAAA:V95boIjGcv5xwyPuwHEpGuCdJKRDYlxPybX-pBAVtY5xHcJcy--ZwIKH4RVJMoMuOad9MMUGZTff)*

- SIR model
- MSEIR model
- differential equation
- [Introduction](https://hackmd.io/UCuq_6ugS96t6lH0h1ivuA)

*[J Kleinberg (2007). "Cascading Behavior in Networks: Algorithmic and Economic Issues"](http://perso.ens-lyon.fr/christophe.crespelle/enseignements/GGT/inutilise/cascades.pdf)*

- the source of this chapter

*[IZ Kiss, JC Miller, PL Simon (2017) "Mathematics of epidemics on networks"](https://link.springer.com/content/pdf/10.1007/978-3-319-50806-1.pdf)*

- covering a wide range of SIR and SIS model networks

*[MEJ Newman (2002) "Spread of epidemic disease on networks" Phys. Rev. E 66, 016128](https://journals.aps.org/pre/abstract/10.1103/PhysRevE.66.016128)*

- detailed discussion of SIR model network
- [Introduction](https://hackmd.io/ld59w9lqRUeHDb5v55d0vg)

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papers with keyword on vaccination etc. that cite this survey paper.

Search papers that cite this surevy paper (or other important papers) that include the terms like vaccination, COVID-19, simulation, network characteristics, etc.