Fig. 1: Overall structure of this work.

a SIR Model. Each individual belongs to one of the three states: susceptible (S), infected (I), or removed (R). When infected (i), a susceptible individual will switch into the I state (ii) and gain the ability to infect others (iii). An infected individual is removed (through recovery or death) with a probability (iv). b Non-Markovian versus Markovian process. The infection capacity of an infected individual is characterized by the infection time distribution \({\psi }_{\inf }(\tau )\) and its removal can be described by the removal time distribution ψ_rem(τ). For the non-Markovian process, the distributions can assume quite general forms, while the distributions are exponential for a Markovian process. c Equivalence between non-Markovian and Markovian processes: (i) steady-state equivalence holds under all conditions; (ii) transient-state equivalence only holds when T_gen is equal to T_rem. d Markovian estimation of memory-dependent process. (i) The initial phase of the Monte Carlo simulation is used to fit the parameters according to the Markovian theory. (ii) Important issues such as the estimation of R₀, epidemic forecasting, and the evaluation of vaccination strategies can be addressed by the theory. (iii) The remaining data generated by the Monte Carlo simulation is used to test the accuracy of the estimated R₀, epidemic forecasting, and prevention evaluation.