Validity of Markovian modeling for transient memory-dependent epidemic dynamics

Abstract

The initial transient phase of an emerging epidemic is of critical importance for data-driven model building, model-based prediction of the epidemic trend, and articulation of control/prevention strategies. Quantitative models for real-world epidemics need to be memory-dependent or non-Markovian, but this presents difficulties for data collection, parameter estimation, computation, and analyses. In contrast, such difficulties do not arise in the traditional Markovian models. To uncover the conditions under which Markovian and non-Markovian models are equivalent, we develop a comprehensive computational and analytic framework. We show that the transient-state equivalence holds when the average generation time matches the average removal time, resulting in minimal Markovian estimation errors in the basic reproduction number, epidemic forecasting, and evaluation of control strategy. The errors depend primarily on the generation-to-removal time ratio, while rarely on the specific values and distributions of these times. Overall, our study provides a general criterion for modeling memory-dependent processes using Markovian frameworks.