Some relatively mild illnesses, like the common cold, return to infect you again and again. For a while, right after you recover from a cold, you are immune. But that doesn't last; after some weeks or months, depending on the illness, you become susceptible again. This means there is now a flow from the recovered population to the susceptible. These exercises ask you to modify the basic S-I-R model to describe an illness where immunity is temporary.
R to S. Call this immunity
loss, and use c to denote the coefficient of
immunity loss.
c = 1/42 per day, and explain your reasoning carefully. A
suggestion: adapt the discussion of recovery in the text.
S, I, and R.
S in the sense that when
S is above the threshold, I increases, but when it is below, I
decreases. Does this model have the same feature? If so, what
is the threshold value?
R increase or decrease if
S = 25400 and R = 22500), leaving I unchanged. Will R increase
or decrease?
S, I, and R that lead to a decreasing R.
I and R determine whether R
will increase or decrease. Show that
Explain your argument clearly. A suggestion: consider the rate equation for R'.
I compartment
are to balance?
R compartment
are to balance?
I nor R is changing, then the model must be at the
steady state. Why?
S at the steady state?
R at the steady state? A suggestion: you
know 
. You also
have a connection between I and R at the steady state.