Problem 1: Covid-19 Vaccination Campaign [6 Points] You wereiust hired by the CDC to lead the Covid19 vaccination campaign. The private payoff from getting vaccinated is 11' = c, where r: is cost parameter mat incorporates the risk of complications associated with vaccination (vaccines per 5e are free of charge). The private payoff associated with not getting vaccinated is 1r = bII'O[V\" V}, where: b is a cost parameter that incorporates the health risks associated with catching Covid19; R0 is the basic reproduction number (Le. how transmissible the disease is]; V\" is the critical level of immunity, or vaccination, the population needs to reach toeventually eradi cateCovid19{i.e. the herd immunity threshold]; V is the fraction of the population iat is currently imi'nune/vaccinated. Together, \"RV' V)" represents the probability of catching Covidl'). For simplicity, assume that the immunity one develops to Covid19 is permanent, and iat catching the disease provides you with the same immunity that the vaccine does,so that V includes both vaccinated and infected individuals. LA. [0.5 point] Let S denote the fraction of the population that is susceptible. Find R, the effective repro duction number and nd V\