Susceptible Exposed Infected Recovered Vaccinated Dead (SEIRVD) Model Simulator

Description

Simulation of a SEIRVD model written in C#. Writes per day outputs to CSV for easy ingestion into a visualizer.

Compartments

• Susceptible: The population of people that are suceptible to infection.

• Exposed: The population of people that have been exposed to disease and are infectious without showing symptoms

• Infected: The population of people that are actively infected and infectious.

• Recovered: The population of people that have recovered from the infection.

• Vaccinated: The population of otherwise susceptible people that are vaccinated against the disease

• Dead: The population of people that have died from infection

Simulation Math

Formulas for Constituent Terms

infectionFromVTerm = previousState.V * (previousState.E + (previousState.I * (1-infectedQuarantineRate))) * infectionRate * (1-vaccineEffectiveness);
infectionFromSTerm = previousState.S * (previousState.E + (previousState.I * (1-infectedQuarantineRate))) * infectionRate;
diseaseMortalityTerm = previousState.I * diseaseMortalityRate;
vaccineImmunityDecayTerm = previousState.V * vaccineImmunityDecay;
recoveredImmuneDecayTerm = previousState.R * recoveredImmunityDecay;
vaccinationRateTerm = previousState.S * vaccinationRate;
incubationRateTerm = previousState.E * incubationRate;
recoveryRateTerm = previousState.I * recoveryRate;

New Populaton Delta Equations

S = previousState.S + (vaccineImmunityDecayTerm + recoveredImmuneDecayTerm - vaccinationRateTerm - infectionFromSTerm);
E = previousState.E + (infectionFromVTerm + infectionFromSTerm - incubationRateTerm);
I = previousState.I + (incubationRateTerm - recoveryRateTerm - diseaseMortalityTerm);
R = previousState.R + (recoveryRateTerm - recoveredImmuneDecayTerm);
V = previousState.V + (vaccinationRateTerm - vaccineImmunityDecayTerm - infectionFromVTerm);
D = previousState.D + (diseaseMortalityTerm);

Values are normalized to force values to sum to ~99% at the end of each iteration. This prevents compounding floating point multiplication errors.

double sum = newS + newE + newI + newR + newV + newD;
newS /= sum;
newE /= sum;
newI /= sum;
newR /= sum;
newV /= sum;
newD /= sum;

Usage

seirvd.exe --days 100 --infectionRate 0.3 --incubationRate 0.07 --diseaseMortalityRate 0.05 --recoveryRate 0.03 --vaccinationRate 0.08 --infectedQuarantineRate 0.2 --recoveredImmunityDecay 0.15 --vaccineImmunityDecay 0.05 --vaccineEffectiveness 0.3 -s 0.98 -e 0.02 -i 0.0 -r 0.0 -v 0.0 -d 0.0 -o results.csv

Model Inputs

Input Parameter	Description	Default Value
--days	Duration of the simulation	100
--infectionRate	Transmission rate of disease	0.0
--incubationRate	how fast exposed incubate to infected	0.0
--diseaseMortalityRate	rate at which infected die	0.0
--recoveryRate	Recovery rate of infected	0.0
--vaccinationRate	Rate of vaccination of Susceptible	0.0
--infectedQuarantineRate	rate at which infected are quarantined and not longer contribute to exposures	0.0
--recoveredImmunityDecay	rate of decay for immunity gained from disease recovery	0.0
--vaccineImmunityDecay	rate of decay for immunity gained from vaccination	0.0
--vaccineEffectiveness	Vaccine effectiveness	0.0
-s, --susceptible	Initial susceptible population	0.0
-e, --exposed	Initial exposed population	0.0
-i, --infected	Initial infectious population	0.0
-r, --recovered	Initial recovered population	0.0
-v, --vaccinated	Initial vaccinated population	0.0
-d, --dead	Initial dead population	0.0
-o, --outputPath	Path to the simulation output file.	"output.csv"

Model Limitations

• The model does not consider natural birth and death rates within the population.
• Similar to the typical SIR model, it assumes a homogeneously mixed population.