The coronavirus is different from the kind of infectious disease modeled in the SIR (Susceptible Infected-Recovered) framework discussed in class in at least 2 ways: c There is no way to completely recover from coronavirus, so there is no recovered pop- ulation (i.e., Rt 2 O : AIR for all t). Full immunity for the infected is not guaranteed. c There is no vaccine for coronavirus that has been proven to be 100% effective yet (i.e., at : 0). Fortunately, there are some costly selfprotective actions such as wearing surgical masks; call it m that people can take to reduce the likelihood of contracting coronavirus. Assume that such maskprotection is 90% effective, so that it can lower the infection rate from Asa (: [t] to Asia 0.91mi. Assume also that the rate of use of masks mt depends on both its cost (pt) and the prevalence of the disease (It) as follows: mt 2 \"1(1): 3 It) I 771 6!th + GUI: (-l (H 1. Given these assumptions about the coronavirus, write down the two equations that govern the dynamics of the Susceptible (S) and the Infected (I) in terms of their current values (St, It) and the underlying parametersiviz\" the birth rate (Ab), the death rates (63,61) , the infectivity parameter ([3) , and the mask-wearing parameters (m, a?\" a1) . 2. What conditions must hold when the populations of both infected and uninfected people are in the steady state? 3. Economic interpretations of parameter conditions: (a) What does it mean for a; : O? (b) What does it mean for a; > ,8? 4. Assume a; > [3, use the 2 steadystate conditions from part 2 above to solve for the steadystate value of the Infected (P') as a function of the cost of self-protection (p) and other underlying parameters. How would a change in p affect I\"? On this basis, would you recommend the govermnent to provide face masks to the public for free