Epidemic Spread and Transmission Network Dynamics

Infectious diseases show complex patterns of spread in their host populations that can range from short and peaked epidemics to persistent, endemic scenarios. Epidemic dynamics are determined by a disease's course and infectious profile that can pass through different stages, here represented by infected individuals in initial and latent stages and . Furthermore, there is mutual influence between the dynamic transmission network of infectious contacts and epidemic spread. This Demonstration simultaneously studies the temporal evolution of epidemic prevalence and transmission network dynamics in terms of the average number of contacts among healthy (susceptible) and infected individuals (, and , ).

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This Demonstration is an implementation of the epidemic model introduced in [1, 2]: Healthy individuals are susceptible to infection from initially and latently infected individuals and . Once infected, individuals progress from an initial stage to a latent stage before dying at rates and , therefore representing a simplified model for an HIV infection. Individuals are connected through a network of potentially infectious contacts in which the distribution in the number of concurrent contacts per individual can be parameterized. Further complexity is added to the dynamics of the transmission network by allowing for demographic change (through birth and death at rates and ) and switching of contacts at a rate .
The model is sketched in the following figure, a detailed presentation can be found in [1]. Note that the model with and corresponds to the classical SIR model with representing the number of recovered individuals ( if demographic change is neglected).
References
[1] C. Kamp, "Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics," PLoS Computational Biology, 6(11), 2010 e1000984. doi:10.1371/journal.pcbi.1000984
[2] C. Kamp, "Demographic and Behavioural Change during Epidemics," Procedia Computer Science, 1(1), 2010 pp. 2247–2253. doi:10.1016/j.procs.2010.04.252

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