The effects of border control and quarantine measures on global spread of COVID-19

M. Pear Hossain; Alvin Junus; Xiaolin Zhu; Pengfei Jia; Tzai-Hung Wen; Dirk Pfeiffer; Hsiang-Yu Yuan

where Imp and Sec represent the imported and secondary cases produced by the imported cases (we will use 77 secondary cases to denote this group in the remaining parts). We introduced an η(k, .) function to map the 78 number of the infected at the source i to the imported and secondary cases at j given different border control 79 5 and quarantine measures. The term η(k = 0, .) calculated the changes during first wave transmission (imported) 80 and η(k = 1, .) calculated the changes during second wave transmission (secondary infected cases produced by 81 the imported cases) under quarantine. The dot in η(k = 0, .) represents other epidemiological parameters. 82 During the early outbreak phase, because the susceptible population S was so close to the population size N , 83 therefore, we assumed S N ≈ 1. Because M ii and M jj are both near one (every day, more than 99.99% of 84 individuals stay in the same location), we thus ignored the variables M ii and M jj to increase readability in the 85 remaining sections. 86 Calculating the arrival rate of imported cases 87 In order to calculate the imported cases, we assumed that infected cases could pass the border screening or 88 move to another location only during their latent or incubation periods. We calculated the number of latent 89 cases at time s by including a latent period τ . Therefore, the number of cases I i in Eq(1) that were within the 90 latent period at a specific time s were