Mumbai Epidemic Simulator

Version 1.1.1. Earlier versions: 1.1, 1.0.
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, placed where the 2011 Census counted people in Mumbai, Thane, Navi Mumbai and Mira-Bhayandar. People roam near home, many travel to a job centre each working day, 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)

1. Each person moves around an anchor: home, or their workplace between 9 am and 6 pm if they commute. The offset from the anchor is a mean-reverting random walk; steps into the sea are refused.
2. Infected travellers arrive at stations and the airport as a Poisson stream, each infecting the nearest susceptible person there.
3. 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.
4. A contact with a susceptible person infects them with the infected person's infectivity.
5. 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.
• Commuting: gravity model with exponential distance decay, P(job centre j) ∝ w_j·e^−d/β. Wilson, A. G. (1971). A family of spatial interaction models. Environment and Planning A 3, 1–32.
• Placing people: each 100 m land cell gets its ward's census population, split between slum and other cells by the slum share, and people are drawn in proportion.
• Random numbers: Mulberry32 seeded generator, so runs are reproducible.

Limits

Populations are from 2011 and are spread evenly within each ward apart from slum clusters. The Thane outline is hand-drawn and approximate, because no open boundary was found. Job centres and their sizes are illustrative, not measured, and real travel such as the local trains is not modelled route by route. Contact radius and roaming distance are illustrative.

Data

Population: Census of India 2011, Primary Census Abstract, by BMC ward, collated in Mumbai-Population-Map; city totals for Thane, Navi Mumbai and Mira-Bhayandar from the same census. Ward, Navi Mumbai, Mira-Bhayandar and slum cluster boundaries: DataMeet Municipal Spatial Data, CC BY-SA 2.5 India.

Map tiles © OpenStreetMap contributors. 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.