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Original Articles

Derivation of stochastic partial differential equations for size- and age-structured populations

Pages 73-86 | Received 02 Jan 2008, Published online: 10 Nov 2008

Figures & data

Figure 1. A Brownian Sheet on [0, 5]×[0, 5].

Figure 1. A Brownian Sheet on [0, 5]×[0, 5].

Table 1. Possible changes in population level u k (t) for k > 1 for time Δ t.

Table 2. Possible changes in population level u 1(t) for time Δ t.

Table 3. Possible changes in population level u j, k (t) for j > 1 in time Δ t.

Table 4. Possible changes in population level u 1, k (t) in time Δ t.

Figure 2. Calculated distribution of populations levels at time t = 0.5 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(10) and Equation(11).

Figure 2. Calculated distribution of populations levels at time t = 0.5 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(10) and Equation(11).

Figure 3. Calculated distribution of average size at time t = 0.5 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(10) and Equation(11).

Figure 3. Calculated distribution of average size at time t = 0.5 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(10) and Equation(11).

Table 5. Monte Carlo (MC) and SPDEs Equation(10) and Equation(11) calculational results at time t = 0.5.

Figure 4. Calculated distribution of populations levels at time t = 1.0 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(21) and Equation(22).

Figure 4. Calculated distribution of populations levels at time t = 1.0 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(21) and Equation(22).

Figure 5. Calculated distribution of average size at time t = 1.0 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(21) and Equation(22).

Figure 5. Calculated distribution of average size at time t = 1.0 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(21) and Equation(22).

Figure 6. Calculated distribution of average age at time t = 1.0 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(21) and Equation(22).

Figure 6. Calculated distribution of average age at time t = 1.0 for 500 sample paths using Monte Carlo (MC) and the SPDE Equation(21) and Equation(22).

Table 6. Monte Carlo (MC) and SPDE Equation(21) and Equation(22) calculational results at time t = 1.0.

Table 7. Monte Carlo (MC) and SPDE Equation(21) and Equation(22) calculational results at time t = 1.0.

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