In multistage SI(k)R models, the relationship between prevalence peak and weighted stage functional maxima varies with scaling of progression rates, converging under Erlang scaling to a delay model that justifies the factor-two approximation with error bounds and corrections.
MacDonald, Time lags in biological models , vol
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Erlang mixture approximations with the linear chain trick convert distributed delay DDEs into ODEs, with convergence proofs for bounded kernels and applications to stability analysis.
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On Erlang mixture approximations for differential equations with distributed time delays
Erlang mixture approximations with the linear chain trick convert distributed delay DDEs into ODEs, with convergence proofs for bounded kernels and applications to stability analysis.