Click the map to infect people there
Epidemic curve
dashed = mean-field SIR · faint = 10 seeds
Spatial structure Compute now
Semivariogram of “ever infected” (1) vs not (0) by distance. Below the dashed sill = nearby people share infection status, so the epidemic is clustered.
Mumbai Epidemic Simulator
v1.0 · Developed by Somdeep Kundu , a PhD student of IIT Bombay working on Agriculture and Rural Water Management using Earth Observation and bottom-up ground data.
Each dot is one simulated person living on the real land of Mumbai, Thane and Navi Mumbai. People wander, meet others, catch the disease, recover, and may lose immunity. It is a teaching and exploration tool, not a forecast of any real disease.
How one step works (0.1 day)
Each person takes a random-walk step. Steps that would land in the sea are refused and the person turns back.
Each infected person makes a Poisson-distributed number of contacts (mean = contacts per day × 0.1). In spatial mode each contact is a random person within the contact radius, found with a grid (cell list); in well-mixed mode it is anyone.
A contact with a susceptible person infects them with the infected person's infectivity.
Each infected person recovers with probability 0.1 / illness duration; recovered people lose immunity with probability 0.1 / waning days.
Methods and references
SIR compartments: Kermack, W. O. & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A 115, 700–721.Final-size relation z = 1 − e−R0·z , used as a check of the well-mixed mode (same source).Monte Carlo method: Metropolis, N. & Ulam, S. (1949). The Monte Carlo method. J. Am. Stat. Assoc. 44, 335–341.Poisson sampling: Knuth, D. E. (1997). The Art of Computer Programming , Vol. 2, 3rd ed.Mean-field model: Euler's method for the SIR ordinary differential equations.Semivariogram: Matheron, G. (1963). Principles of geostatistics. Economic Geology 58, 1246–1266. Here applied to a 0/1 indicator (indicator variogram).Moran's I: Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika 37, 17–23.Random numbers: Mulberry32 seeded generator, so runs are reproducible.
Limits
People are placed by a simple rule, not by census population density. Movement is a random walk, not real travel such as local trains. Contact radius and speed are illustrative. With few people over a large area, the spatial mode spreads slower than the well-mixed model.
Data
Map tiles © OpenStreetMap contributors, © CARTO . Land outline from OpenStreetMap and DataMeet, as used in the Mumbai Durga Pujo Map . Code under the MIT licence.
Ideas or bugs? Write to somdeepkundu@gmail.com , or on LinkedIn or Instagram .