# Spatio-Temporal Epidemic Spread

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This Demonstration shows the spatio-temporal propagation of an epidemic that starts in the center of a square that contains a homogeneous population. The triangle at the bottom shows the ratio between susceptible, infected, and recovered individuals. Depending on the ratios between the contact rate , the recovery rate , and the mobility of the individuals , the disease either propagates through the space or fades away. For a given instant in time, the 3D plot illustrates the proportion of infected individuals as a function of and .

Contributed by: Jan Baetens (July 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This model is a spatial extension of the well-established SIR-type epidemiological models that account for the dispersal rate , contact rate , recovery rate , and the mobility of the individuals . As such, it provides far more realistic simulations of *in natura* disease outbreaks than the classical epidemiological models that have become well established since the work of Kermack and McKendrick (1927). The model equations are given by:

Snapshots 1–4 show the spatio-temporal evolution of the proportion of infected individuals for a parameter setting that allows the epidemic wave to propagate across the region.

References

[1] W. O. Kermack and A. G. McKendrick, "A Contribution to the Mathematical Theory of Epidemics," *Proceedings of the Royal Society London A, *115(772), 1927 pp. 700–721. dx.doi.org/doi:10.1098/rspa.1927.0118.

[2] J. D. Murray, *Mathematical Biology II: Spatial Models and Biomedical Applications*, 3rd ed., Berlin: Springer, 2003.

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