epidemic-modelling

[Computer Modeling] SIR/SIRS/SIRQ/ISIR/SEIR comparmental models for numerical epidemic modelling in MATLAB.

Homework/project in Practicum in Physics 2 (13E061PF2) at University of Belgrade, School of Electrical Engineering.

Comparmental models

SIR model

• S is the number of susceptible individuals
• I is the number of infectious individuals
• R is the number of removed individuals (either immune or deceased)
• α is a constant that describes the infection rate
• β is a constant that describes the recovery rate

This model (Solution/SIR.m) is described using the following system of first-order differential equations:

dS(t)/dt = -α * S * I
dI(t)/dt = α * S * I - β * I
dR(t)/dt = β * I

The number of S/I/R individuals (for α = 2.65 * 10^-6, β = 1) can be found below:

MATLAB scripts that use this model can be found in Solution/SIRepidemija.m, Solution/SIR_R0virus.m, and Solution/SIR_R0opseg.m.

SIRS model

• γ is a constant that describes the rate of immunity loss among recovered individuals (for example due to virus mutations)

This model (Solution/SIRS.m) is described using the following system of first-order differential equations:

dS(t)/dt = -α * S * I + γ * R
dI(t)/dt = α * S * I - β * I
dR(t)/dt = β * I - γ * R

The number of S/I/R individuals (for α = 2.65 * 10^-6, β = 1, γ = 0.35) can be found below:

A MATLAB script that uses this model can be found in Solution/SIRSepidemija.m.

SIRQ model

• q is a constant that describes the rate of removal of infected individuals from the population through preventive measures (for example quarantine)

This model (Solution/SIRQ.m) is described using the following system of first-order differential equations:

dS(t)/dt = -α * S * I
dI(t)/dt = α * S * I - (β + q) * I
dR(t)/dt = (β + q) * I

The number of S/I/R individuals (for α = 2.65 * 10^-6, β = 1, q = 0.5) can be found below:

A MATLAB script that uses this model can be found in Solution/SIRQepidemija.m.

ISIR model

• k is a constant that describes the impact of the transfer epidemic information (for example due to self-isolation and avoiding contact)

This model (Solution/ISIR.m) is described using the following system of first-order differential equations:

dS(t)/dt = -α(I) * S * I
dI(t)/dt = α(I) * S * I - β * I
dR(t)/dt = β * I

The number of S/I/R individuals (for α₀ = 2.65 * 10^-6, β = 1, k = 0.8 * 10^-5) can be found below:

A MATLAB script that uses this model can be found in Solution/ISIRepidemija.m.

SEIR model

• E is the number of exposed individuals
• δ is a constant that describes the rate of transition of individuals from exposed to infectious population (for example due to the incubation period)

This model (Solution/SEIR.m) is described using the following system of first-order differential equations:

dS(t)/dt = -α * S * I
dE(t)/dt = α * S * I - δ * E
dI(t)/dt = δ * E - β * I
dR(t)/dt = β * I

The number of S/E/I/R individuals (for α = 2.65 * 10^-6, β = 1, δ = 0.5) can be found below:

A MATLAB script that uses this model can be found in Solution/SEIRepidemija.m.