SIR Math Model of Virus Spread (Coronavirus or other)

You can change infection rate (transmission rate) and see how spread is affected (flatten the curve). Infection rate = beta = number of social contacts x probability of contracting virus each contact. When we socially isolate we reduce beta and therefore spread.

An individual is infectious for approximately 7 days. During this time they pass covid19 to approximately 2.5 people. These 2 basic parameters determine the model dynamics.

Simulink model is of the following system of three odes:

dS/dt = -β(I/N)S
dI/dt = β(I/N)S – γI
dR/dt = γI

S = Number Susceptible Individuals
I = Number Infectious Individuals
R = Number Recovered Individuals
N= Total Population
β = Ep = Number Social contacts x probability of transmitting disease each contact = Infection rate
γ = Recovery Rate

Key scenarios of dynamics:
If, during 7 days of being infectious, a person passes to 1 person then the disease will not grow, i.e., number of infectious individuals stays the same.
If, during 7 days of being infectious, a person passes to 2 or more people the disease grows, i.e., number of infectious individuals grows.
If, during 7 days of being infectious, a person does not pass to another person (or, say 10 people are sick at exact same time and pass to 9 people over 7 days) the disease will reduce, i.e., number of sick individuals goes to zero.
As individuals recover, the number of susceptible people decline, and therefore spread slows and eventually reduces to zero.