Mitigation and herd immunity strategy for COVID-19 is likely to fail

Wolfgang Bock; Barbara Adamik; Marek Bawiec; Viktor Bezborodov; Marcin Bodych; Jan Pablo Burgard; Thomas Goetz; Tyll Krueger; Agata Migalska; Barbara Pabjan; Tomasz Ozanski; Ewaryst Rafajlowicz; Wojciech Rafajlowicz,; Ewa Skubalska-Rafajlowicz; Sara Ryfczynska; Ewa Szczurek; Piotr Szymanski

The time till hospitalisation from the onset of symptoms is assumed to be Gamma distributed with median 1.67 and variance 7.424 [gamma parameters: shape=0.874, loc=0.0, scale=2.915] 10 Patients with non severe progression eventually stay at home and the time from onset of symptoms till staying at home is also assumed to be Gamma distributed with median 2.31. and variance 8.365 [gamma parameters: shape=0.497, loc=0.0, scale=3.923] 11 . The maximal duration of the infectious period is assumed to be 14 days 12 . Contact structure and infection transport: Within the households we assume a clique contact structure. Empirical studies have shown that a large fraction of secondary infections are taking place within households 13 . We hence assumed that the probability of a household member to become infected by an already infected household member, who is infectious within a time interval of length T , scales as 1 − exp(−T /L) and L + 1 is the household size. Here, the time T is measured in days. Outside of the households we assume that infected individuals create on average c · T secondary infections, given that all contacts of these individuals are susceptible, where c is an intrinsic parameter. Note the time T being infectious is different for contacts inside and outside the household. The out-reproduction number R* is defined as the expectation of c · T , which is equal to 2.34c under our assumptions of disease progression within patients. The actual number of secondary infections of an individual outside the household is assumed to be Poisson distributed with mean (c · T ). The total reproduction number R 0 is given by the sum of R* and the number of secondary infections generated inside the household. The duration of the infectivity time T implicitly depends on age. This is due to the fact that infectivity time is reduced for individuals with severe disease progression, as those patients become hospitalized. Se-5 . CC-BY-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.