Sir Epidemic Model

The Three compartments of the SIR Model

SIR model consists of three compartments:

• S for the number of Susceptible.
• I for the number of Infectious.
• R for the number of recovered that includes both immune and death.

Each compartment is considered as function of time t in number of days, denoted as S(t), I(t) and R(t). The model will project the value of these three functions on given time t. The model is a reasonable prediction for infectious diseases where recovery confers lasting resistance, such as Coronavirus, measles, mumps and rubella.

Transition Rates in SIR model

The SIR model will need two inputs that represent the two transition rates:

• Contact Rate: is a transition rate from susceptible to infectious that is defined as the average number of contacts per person times the probability of disease transmission in a contact between a susceptible and an infectious subject.
• Recover Rate: is a transition rate from infectious to recovered that is defined as the reciprocal the duration in number of days for the infection duration.

Basic Reproduction Number

Basic reproduction number or basic reproduction ratio is defined as the ratio of the contact rate to the recover rate. This number reflects the number of contacts by an infected individual with others before the infected has recovered. If this number is greater than 1, the infection will spread in a population. The higher the number is, the harder to control the epidemic. For example, SARS has a basic reproduction number in the range of 2-5.

Wuhan Coronavirus

new corona virus, COVID-19, is highly contagious and caused world wide pandemic. The basic reproduction number for COVID-19 is estimated in the range of 2.13 to 3.11. The average number of days of the infection is about 14. Using that number we can input a recover rate at 0.07. Using 2.62 as the basic reproduction number, then we can input the contact rate as 0.182. Then you can input different values of the total population into the model to view the peak and number of infectious by day. By trying different population values, you can get an rough estimation of the total population infected.