Epidemic in Networks
Looking for some of the best papers or thesis to go through.
While some of the references below are dated, they should provide you with a good place to start and traditional well established model from which you can start looking for improvements and variations in more recent publications.
Wieland, S., Aquino, T., & Nunes, A. (2012). The structure of coevolving infection networks. EPL (Europhysics Letters), 97(1), 18003.
Kenah, E., & Robins, J. M. (2007). Second look at the spread of epidemics on networks. Physical Review E, 76(3), 036113.
Tao, Z., Zhongqian, F., & Binghong, W. (2006). Epidemic dynamics on complex networks. Progress in Natural Science, 16(5), 452-457.
Saramäki, J., & Kaski, K. (2005). Modelling development of epidemics with dynamic small-world networks. Journal of Theoretical Biology, 234(3), 413-421.
Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM review, 42(4), 599-653.
Korobeinikov, A. (2004). Global properties of basic virus dynamics models. Bulletin of Mathematical Biology, 66(4), 879-883.
Day, T., & Proulx, S. R. (2004). A general theory for the evolutionary dynamics of virulence. The American Naturalist, 163(4), E40-E63.
May, R. M., & Lloyd, A. L. (2001). Infection dynamics on scale-free networks. Physical Review E, 64(6), 066112.
The final size distribution described in 'A Framework for Epidemic Models', J. Biol. Syst. 12 (2003) pp. 337-405 should be worthwhile.
The spread of TB/HIV in human networks...
http://orgnet.com/contagion.html
Follow links to original papers with the CDC at bottom of article.
1. SIR Model: This is a classic epidemiological model that divides the population into three groups: susceptible (S), infected (I), and recovered (R). It assumes that every individual in the population is either susceptible or infected, and that the infection spreads through direct contact between susceptible and infected individuals.
2. SEIR Model: This model adds an exposed (E) compartment to the SIR model. It assumes that individuals who have been infected but are not yet infectious move into the exposed compartment before moving into the infectious compartment.
3. Network-Based Models: These models consider the network structure of the population, where individuals are represented as nodes in the network and the edges represent social or physical contacts between individuals. The most popular of these models are the Susceptible-Infected-Removed (SIR) model on a network, the Metapopulation Model, and the Stochastic Epidemic Model.
4. Agent-Based Models: These models simulate the behavior of individuals within a population and allow for more detailed analysis of the spread of infection over time. They are particularly useful for studying complex social and behavioral interactions that may impact the spread of disease.
5. Compartmental Models: These models divide the population into compartments based on their disease status, and track the flow of individuals between these compartments over time. Examples of compartmental models include the Susceptible-Exposed-Infectious-Recovered (SEIR) model and the Susceptible-Infectious-Recovered (SIR) model.
Overall, the choice of model depends on the specific context and research question. Each model has its strengths and limitations, and the appropriate model should be chosen based on the available data, the size and structure of the population, and the research question being addressed.
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