The short answer is yes, and yes. According to the United States Centres for Disease Control and Prevention (CDC), those who do not get vaccinated after their recovery from Covid-19 are more likely to be infected again compared to those who get a jab after their recovery. It is for this reason that many health authorities advise a booster after infection. The guidelines vary from country to country with most recommending at least a 4-week wait after infection before getting a booster.