Given the following SIR diagram, where h are some costly self-protective activities that people can take to avoid contracting the disease. h(p,It) =nIt -apIt +C. C is a constant, p is the price of costly self-protective activities.

a. Write down dS/dt.

b. Solve for the steady state infected population I*.

c. Which parameters do I* depend on? Among these related parameters, which are inversely related to I*.

d.What is the effect of price on the size of the steady-stated infected population I*? Solve for dI*/dp

c. Calculate the prevalence elasticity of self-protection