The flow of the population.

The flow of the population.</p

Time evolution of the population.

Λ = 2, μ = 0.05, d = 0.9, α = 0.05, φ = 0.3, ω = 0.8, p = 0.4, q = 0.4, such that S = 30, E = 0, I+ = 5, I− = 5, R = 0, when t = 10−2.</p

Time evolution of the population.

Λ = 2, μ = 0.05, d = 0.9, α = 0.05, φ = 0.3, ω = 0.8, p = 1, q = 1, such that S = 30, E = 0, I+ = 5, I− = 5, R = 0, when t = 10−2.</p

The optimal proportion of recovery resources <i>q</i>₀ assigned to the active informed people as a function of <i>p</i>, when <i>μ</i> = 0.01.

(a) ω = 0.6, d = 0.2. (b) ω = 0.2, d = 0.6.</p

The critical points <i>p</i>⁽⁰⁾ and <i>p</i>⁽¹⁾ as functions of <i>ω</i> and <i>d</i>, when <i>μ</i> = 0.01.

The critical points p(0) and p(1) as functions of ω and d, when μ = 0.01.</p

(color online). The relationships of five species in the Jungle game.

<p>Arrows point from predator to prey. <i>S</i>₁ and <i>S</i>₂ can prey three species and be hunt by one species; <i>S</i>₃ can prey two species and be hunt by two species; <i>S</i>₄ and <i>S</i>₅ can prey one species and be hunt by three species.</p

(color online) Densities of five species in Monte Carlo simulation. <i>L</i> = 200,<i>k</i>_{<i>i</i>, <i>j</i>} = 1.

<p>After about 500 time steps, the species <i>S</i>₄ and <i>S</i>₃ extinct and species <i>S</i>₁, <i>S</i>₂ and <i>S</i>₅ coexist.</p

(color online) Coexistence of species in example 1 using Monte Carlo simulation. <i>L</i> = 400.

<p>All five species coexist in the red region. Species <i>S</i>₁<i>S</i>₄<i>S</i>₅ coexist in the orange region. Species <i>S</i>₁<i>S</i>₂<i>S</i>₅ coexist in the light yellow region. Species <i>S</i>₁<i>S</i>₃<i>S</i>₅ coexist in the deep yellow region. Only <i>S</i>₅ remains in the green region. Only <i>S</i>₁ or <i>S</i>₂ remains in the blue region.</p

The area of region II in Fig 3 with different <i>p</i>₁.

<p>There exists <i>P</i> ≈ 1.149 making the smallest area at <i>p</i>₁ = <i>P</i>. When <i>p</i>₁ < <i>P</i>, the area decreases with the increasing <i>p</i>₁; when <i>p</i>₁ > <i>P</i>, the area increases with the increasing <i>p</i>₁.</p

(color online) Densities of five species in Monte Carlo simulation. <i>L</i> = 200,<i>k</i>_{<i>i</i>, <i>j</i>} = 1.

<p>After about 500 time steps, the species <i>S</i>₄ and <i>S</i>₃ extinct and species <i>S</i>₁, <i>S</i>₂ and <i>S</i>₅ coexist.</p