A stochastic agent-based model to evaluate COVID-19 transmission influenced by human mobility

The paper empirically reports bistability, thresholds, and a hysteresis-like loop in an agent-based Mob–Cov model, but offers no rigorous mathematical argument for why these phase boundaries occur or when they should be expected; key mechanistic components (e.g., infection when multiple infectors are present) are also described inconsistently (text says Pj = sum_i Pij, while the pseudocode induces a 1−∏(1−Pij) rule) . The candidate model provides a plausible theoretical framework (finite-state absorbing Markov chain, quasi-stationarity, coupling/branching bounds leading to sub/supercritical regimes, and monotonicity of a Herfindahl-type co-location index) that qualitatively reproduces the paper’s findings on c1 thresholds (≈[0.25, 0.4]), low-mobility ratios (≈≥0.6), and population-size windows (≈[400, 500]) . However, the theoretical development remains at the level of proof sketches with rough bounds and additional unverified assumptions (e.g., independence, irreducibility of the nonabsorbing subchain, exponentially long metastability), so it is not yet a complete proof.