Table 1 Algorithmic summary of our explicit–implicit time-discretion population growth model

Inputs:

- Increasing time sequence \(t_{1} = 0 < t_{2} < \cdots < t_{M - 1} < t_{M} = T\)

- Initial population size \(N_{1} = N_{0} > 0\)

- Given bounded function f:[0,∞)⟶[0,∞)

Steps:

- For all n∈{1,…,M − 1}, compute \(N_{n + 1} = N_{n} \cdot \frac{1 + A \cdot \Delta _{n + 1} + B \cdot \Delta _{n + 1} \cdot f_{n + 1} \cdot N_{n}}{1 + C \cdot \Delta _{n + 1} \cdot N_{n}^{2}}\) by (17)

Outputs:

- Population size sequence \(\{ N_{n} \} _{n = 1}^{M}\)