This model shows the possible spread of SARS.
We start this model with the following sliders:
k = mean # contacts per day an infectious person has with a susceptible person.Initially, individuals are all susceptible to catching the disease. This is shown in the susceptible stock. Some of the susceptible individuals, at a rate demonstrated by the flow sus to quar, will be quarantined so they cannot be exposed to the disease. This occurs at a rate of susceptible * q.
m = per capita death rate
N = initial population
p = fraction per day of exposed people who become infectious
q = fraction per day of suceptible individuals who go into quarantine
u = fraction per day of susceptible quarantined individuals who are allowed to leave quarantine
v = per capita recovery rate
w = fraction per day that people recover and become immune
b = transmission constant
Once in the susceptible quarantine stock, individuals can either remain there or move back to the susceptible stock if they are allowed out of quarantine at a rate of susceptible_quarantined * u.
Other susceptible individuals can become exposed to SARS via the sus to expos flow, which contains the formula susceptible_quarantined * u. They enter the exposed flow. But the people who are in the exposed stock do not always realize that they've been exposed to SARS. They go in the expos to undet flow: p * exposed, become infectious and enter the infectious undetected stock.
At the infectious undetected stage, some of them can become immune to SARS, and enter the recovered immune stock via the undet to im flow: infectious_undetected * v. Some of those who are in the infectious undetected stock die via the undet to death flow: infectious_undetected * m. Others are isolated through the undet to iso: infectious_undetected * w, and enter the infectious isolated stock.
Sometimes those in the infectious isolated stock recover and become immune: infectious_isolated * v, but other times, they die via the iso to death flow: infectious_isolated * m. They end up in the SARS death stock.
So what about those who are exposed to the disease and know it? They enter the exposed quarantine stock via the sus to expos quar flow: N * q * k. They then enter the infectious quarantined stock: exposed_quarantined * p, where they can remain infectious and isolated as part of the infectious isolated stock, join the recovered immune group through the inf quar to rec flow: infectious_quarantined * v, or die: infectious_quarantined * m.