Table 2 The Hybrid Simulation Algorithm (Algorithm 1)

1: set the initial state to (T₀, E₀, I(t₀)) and the initial time t to t₀;

2: while t < t _stop do

3:    let x be the current state, for $j\in \mathcal{S}$ evaluate a _j (x), define $a_0^{\mathcal{S}}={\sum }_{j\in \mathcal{S}}{a}_j\left(\mathbf{x}\right)$;

4:    let χ be a random number with distribution Exp(1), solve the transcendental equation

   $A_4\left(\tau \right)+a_0^S\tau +A_7\left(\tau \right)=\chi$

   and then define $a_0=a_0^S+a_4\left(t+\tau \right)+a_7\left(t+\tau \right)$;

5:    let r be a random number U[0, 1], for the next event to fire find j by solving

   $\sum _{i=1}^{j-1}{a}_i\left(t+\tau \right)<r\cdot a_0\le \sum _{i=1}^j{a}_i\left(t+\tau \right)$

   where if $i\in \mathcal{S}$ then a _i (t + τ ) = a _i (x);

6:    update (T, E, I(t)) to (T + ν_T,j, E + ν_E,j, I(t + τ )) and change clock to t + τ ;

7: end while