A review of sequential Monte Carlo methods for real-time disease modeling

The paper states, using the next generation matrix method, an explicit closed-form for Reff(t) in Eq. (22) and specifies the infectious compartments, transition structure, and per-compartment infectivity weights in Eqs. (14)–(16). The candidate solution reconstructs the same expression by computing βt·(St/N) times the expected total weighted infectious time of a single index case, decomposed into pre-symptomatic, symptomatic (with testing/self-isolation branches), and asymptomatic contributions. The algebra matches the paper’s Eq. (22) exactly. One caveat: the candidate notes that τc − τl and related durations may be negative, but the model’s binomial transition rates require these durations to be strictly positive (as also reflected by the parameter table), so that particular remark is incorrect. Otherwise, both arrive at the same formula—paper via NGM, model via expected-time/branching—hence both correct with different proofs. Supporting evidence: model compartments and transitions (Eqs. (14)–(16) with weights) and the target Reff(t) expression (Eq. (22)) ; parameter meanings/values (Table 1) confirm positivity of durations .