A metapopulation SIHURD model

We enhance our SIHURD model published in Bica et-al (2022) and propose a metapopulation infectious disease mathematical monitoring model where individuals move between discrete spatial patches. We divide the environment into a finite number of spatial patches (e.g., adjacent cities), which preserve homogeneity characteristics. We apply the enhanced SIHURD model presented in this article to each spatial patch. The novelty of this model lies in introducing parameters that represent individuals’ travel rates between spatial patches, which depend on their disease status. In addition, it assumes that individuals do not change their disease status while travelling between patches. Our study uses the reproduction number, R 0k , for each spatial patch, k = 1, 2, . . . , n, (n > 1) integer, which represents the average number of secondary cases produced by an infected individual in a susceptible population. The system has only a disease-free equilibrium point if R 0k ≤ 1. In contrast, if R 0k > 1, the system has an endemic equilibrium point. Reproduction numbers R 0k are crucial for understanding the spread of infectious diseases and can inform measures to control outbreaks effectively. Migration between patches fundamentally alters the behaviour of the endemic equilibrium within a patch, rendering it unstable in the proposed model.