Epidemic simulation

Step 0 Tap a person or “Random case” to start; tap more people later to add cases

Vaccinated
Not vaccinated
Infected
Convalescent
Deceased

Population:

Vaccine coverage:

Speed:

Advanced settings

Contagiousness Chance that one meeting with an infected person passes the illness on, before immunity is considered.

Population density Chance, each step, that an infected person meets each of their 8 neighbours. Low = remote area, high = crowded.

Illness duration Steps a person stays infectious before the outcome (recover, die, or stay ill) is decided.

Mortality Chance of dying when the illness ends. Vaccinated people divide this by the "other benefits" factor.

Chance of longer illness Chance that, instead of recovering, a person stays infectious for another round.

Vaccinated immunity Chance that a vaccinated person shrugs off an exposure. 0.97 ≈ measles vaccine, 0.5 ≈ a leaky vaccine.

Unvaccinated immunity Chance that an unvaccinated person shrugs off an exposure (prior immunity, genetics, luck).

Convalescent immunity Protection after recovering. Vaccinated survivors get the better of this and vaccinated immunity.

Other vaccine benefits Divides the chance of death for vaccinated people who do get ill. 1 = no benefit, 5 = five times fewer deaths.

Simulation length Maximum number of steps. 0 runs until nobody is infected.

Changes apply from the next step, so you can adjust a running outbreak. Population and coverage changes rebuild the grid.

Illustrative – click to load, then click a person:

Flu in a cityDense population, moderate contagiousness, 60 % vaccinated. Watch how the outbreak threads through the unvaccinated.

Lethal illness in remote areaVery deadly but people rarely meet (low density). Outbreaks burn out locally; try raising density to 0.3.

Measles in an under-vaccinated schoolExtremely contagious, excellent vaccine, only half covered. Nearly every unvaccinated person catches it.

Measles with 95 % coverage (herd protection)Same illness, 95 % covered. Chains of infection usually stop after a few cases, protecting the unvaccinated too.

New virus, no vaccine yetNobody is protected. Compare the final morbidity with the next preset.

Same virus, 75 % vaccinated with a leaky vaccineThe vaccine only halves the chance of infection but cuts deaths five-fold: fewer cases, far fewer deaths.

Inspired by real outbreaks (rough translations, see notes below) – click to load, then click a person:

COVID-19, early 2020 (no vaccine)R0 about 3, infection fatality around 1 %, nobody immune. Lower density mid-run to see what distancing did.

COVID-19, 2021 Delta wave, 70 % vaccinatedMore contagious variant; vaccine roughly 60 % against infection but about 90 % against death.

COVID-19, 2022 Omicron, 80 % vaccinatedVery contagious, much milder, vaccine leaky against infection, reinfections common (low convalescent immunity).

Pneumonic plague, Madagascar 2017Person-to-person lung form; short illness, R0 near 1.3, fatality about 9 % with antibiotics in 2017 (near 100 % untreated). Set mortality to 0.9 for no treatment.

Ebola, West Africa 2014 (no vaccine)Spreads only by close contact (low density), long illness, fatality around 50 %. The 2019 rVSV vaccine is about 97 % effective: try coverage 50 %, immunity 0.97.

Smallpox, 1960s outbreak with ring vaccinationR0 about 6, fatality 30 %, vaccine 95 % effective, 80 % covered. Eradicated in 1980; drop coverage to 20 % to see why it mattered.

Seasonal influenzaR0 about 1.3, fatality 0.1 %, vaccine about 50 % effective, many people partly immune from earlier seasons.

Inhalational anthrax, 2001 letters (does not spread)Anthrax is not transmitted person to person, so contagiousness is 0: click each exposed person yourself and nothing spreads. Fatality was 45 % (5 of 11) even with treatment.

		Count	Infected	Convalescent	Deceased	Unaffected	Tally infected	Exposed	I/E ratio	Case mortality %	Morbidity %	Overall mortality %
	Vaccinated
	Not vaccinated
All

Odds of infection (unvaccinated vs vaccinated): –
Odds of death (unvaccinated vs vaccinated): –

Over time Infected Convalescent Deceased

How it works

Each square is a person, vaccinated or not according to the coverage you choose. Click one to make it the index case. At every step each infected person may meet each of their eight neighbours (population density); a meeting spreads the illness with the contagiousness chance, unless the neighbour's immunity – vaccinated, unvaccinated, or convalescent after an earlier illness – blocks it. After the illness duration an infected person dies, recovers, or stays ill a little longer; vaccinated people divide their chance of dying by the “other benefits” factor. The table compares what happened to the vaccinated and unvaccinated groups, and the odds lines put the two side by side.

Reading the table

Count – people in the group at the start. Infected / Convalescent / Deceased / Unaffected – where they are right now.
Tally infected and Exposed – running totals of infections and of risky meetings. I/E ratio – infections per exposure, i.e. how often an exposure actually took; the gap between the two rows is the vaccine's protection against infection.
Case mortality % – deaths among people whose illness has ended (deaths ÷ (deaths + recovered)). Morbidity % – share of the group that has been ill at all. Overall mortality % – deaths ÷ group size.
Odds of infection / death – unvaccinated ÷ vaccinated risk per person; “per case” compares the risk only among people who were exposed or ill.

Things to try

Load Measles with 95 % coverage and seed several outbreaks: most fizzle. Then drag coverage down 5 % at a time and watch the point where it stops fizzling – that is herd protection.
Load New virus, no vaccine yet, run it to the end, note the morbidity, then load the leaky-vaccine preset: fewer cases, far fewer deaths, even though the vaccine is only 50 % protective.
Open Advanced settings while an outbreak runs and lower Population density – the model's version of distancing – and watch the curve bend.
Set Mortality high and Population density very low (Lethal illness in remote area): a deadly illness can be self-limiting simply because it kills faster than it spreads.

About the “real outbreak” presets

They are rough translations of published figures into this toy's knobs, not measured parameters. The mapping: expected secondary infections in a fully susceptible grid ≈ 8 neighbours × density × contagiousness × illness duration (the grid saturates, so the realised number is lower than the R₀ quoted); mortality ≈ case fatality; vaccinated immunity ≈ vaccine efficacy against infection; “other benefits” ≈ how much the vaccine cuts deaths among people who get ill anyway. Treatment, incubation, superspreading, travel and behaviour change are not modelled. Anthrax is included precisely because it does not spread between people: with contagiousness 0 every case is one you create yourself, which is what a point-source exposure looks like.

This is a teaching toy, not an epidemiological model: a square grid with eight neighbours, no movement, no incubation period and simple coin flips. The numbers illustrate ideas such as herd protection and case mortality; they do not predict anything.