A hierarchical intervention scheme based on epidemic severity in a community network - He, Runzi; Luo, Xiaofeng; Asamoah, Joshua Kiddy K.; Zhang, Yongxin; Li, Yihong; Jin, Zhen; Sun, Gui-Quan (Journal of mathematical biology, 2023)
As there are no targeted medicines or vaccines for newly emerging infectious diseases, isolation among communities (villages, cities, or countries) is one of the most effective intervention measures. As such, the number of intercommunity edges ( NIE ) becomes one of the most important factor in isolating a place since it is closely related to normal life. Unfortunately, how NIE affects epidemic spread is still poorly understood. In this paper, we quantitatively analyzed the impact of NIE on infectious disease transmission by establishing a four-dimensional SIR edge-based compartmental model with two communities. The basic reproduction number R 0 ( ⟨ l ⟩ ) is explicitly obtained subject to NIE ⟨ l ⟩ . Furthermore, according to R 0 ( 0 ) with zero NIE , epidemics spread could be classified into two cases. When R 0 ( 0 ) > 1 for the case 2, epidemics occur with at least one of the reproduction numbers within communities greater than one, and otherwise when R 0 ( 0 ) < 1 for case 1, both reproduction numbers within communities are less than one. Remarkably, in case 1, whether epidemics break out strongly depends on intercommunity edges. Then, the outbreak threshold in regard to NIE is also explicitly obtained, below which epidemics vanish, and otherwise break out. The above two cases form a severity-based hierarchical intervention scheme for epidemics. It is then applied to the SARS outbreak in Singapore, verifying the validity of our scheme. In addition, the final size of the system is gained by demonstrating the existence of positive equilibrium in a four-dimensional coupled system. Theoretical results are also validated through numerical simulation in networks with the Poisson and Power law distributions, respectively. Our results provide a new insight into controlling epidemics.