Alemtuzumab is the a sledgehammer drug that depresses the immune system such that your T and B cells, monocytes and sometime neutrophils drop, leaving you open to infection. However, the cells rapidly recover and the infection risk will drop.
The 6 year follow up of the alemtuzumab trials says
Wray S, Havrdova E, Snydman DR, Arnold DL, Cohen JA, Coles AJ, Hartung HP, Selmaj KW, Weiner HL, Daizadeh N, Margolin DH, Chirieac MC, Compston DAS. Infection risk with alemtuzumab decreases over time: pooled analysis of 6-year data from the CAMMS223, CARE-MS I, and CARE-MS II studies and the CAMMS03409 extension study. Mult Scler. 2018 Oct 5:1352458518796675. doi: 10.1177/1352458518796675. [Epub ahead of print]
BACKGROUND: Reduced MS disease activity with alemtuzumab versus subcutaneous interferon beta-1a (SC IFNB-1a) in core phase 2/3 studies was accompanied by increased incidence of infections that were mainly nonserious and responsive to treatment. Alemtuzumab efficacy was durable over 6 years.
OBJECTIVE: To evaluate infections over 6 years in alemtuzumab-treated patients.
METHODS:Three randomized trials (CAMMS223, Comparison of Alemtuzumab and Rebif Efficacy in Multiple Sclerosis (CARE-MS) I, and CARE-MS II) compared two courses of alemtuzumab 12 mg with SC IFNB-1a 44 μg in patients with active relapsing-remitting MS. An extension study (CAMMS03409) provided further evaluation and as-needed alemtuzumab retreatment.
RESULTS: Infections occurred more frequently with alemtuzumab 12 mg than SC IFNB-1a during Years 1 (58.7% vs 41.3%) and 2 (52.6% vs 37.7%), but declined for alemtuzumab-treated patients in Years 3 (46.6%), 4 (42.8%), 5 (40.9%), and 6 (38.1%). Serious infections were uncommon (1.0%-1.9% per year). Infections were predominantly (>95%) mild to moderate and included upper respiratory tract infections, urinary tract infections, and mucocutaneous herpetic infections. Prophylactic acyclovir reduced herpetic infections. Lymphocyte counts after alemtuzumab therapy did not predict infection risk.
CONCLUSION: Infections with alemtuzumab were mostly mild to moderate and decreased over time, consistent with preservation of components of protective immunity.
I guess you can read and with time infection risk drops. Whilst they say these are usually mild, if you are one of the unlucky 1-2%, then it is a problem.