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. 2024 May 23;19(5):e0303300.
doi: 10.1371/journal.pone.0303300. eCollection 2024.

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations

Sida Kang  1 , Tianhao Liu  2 , Hongyu Liu  1 , Yuhan Hu  3 , Xilin Hou  1
Affiliations

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations

Sida Kang et al. PLoS One. .

Abstract

Information dissemination has a significant impact on social development. This paper considers that there are many stochastic factors in the social system, which will result in the phenomena of information cross-dissemination and variation. The dual-system stochastic susceptible-infectious-mutant-recovered model of information cross-dissemination and variation is derived from this problem. Afterward, the existence of the global positive solution is demonstrated, sufficient conditions for the disappearance of information and its stationary distribution are calculated, and the optimal control strategy for the stochastic model is proposed. The numerical simulation supports the results of the theoretical analysis and is compared to the parameter variation of the deterministic model. The results demonstrate that cross-dissemination of information can result in information variation and diffusion. Meanwhile, white noise has a positive effect on information dissemination, which can be improved by adjusting the perturbation parameters.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. The flow diagram of the model.
Fig 2
Fig 2. The stability of information-free equilibrium E0 of system 1 with R0 < 1.
Fig 3
Fig 3. The stability of information-existence equilibrium E* of system 1 with R0 > 1.
Fig 4
Fig 4
Frequency histograms of (a)S1(t), (b)S2(t), (c)I1(t), (d)I2(t), (e)M1(t), (f)M2(t), (g)M3(t), (h)M4(t) when σi(i = 1 ∼ 8) = 0.0001.
Fig 5
Fig 5
Comparison between deterministic model and stochastic model of the densities of (a)S1(t), (b)S2(t), (c)I1(t), (d)I2(t), (e)M1(t), (f)M2(t), (g)M3(t), (h)M4(t) change over time when σi(i = 1 ∼ 8) = 0.0001.
Fig 6
Fig 6
Frequency histograms of (a)S1(t), (b)S2(t), (c)I1(t), (d)I2(t), (e)M1(t), (f)M2(t), (g)M3(t), (h)M4(t) when σi(i = 1 ∼ 8) = 0.00001.
Fig 7
Fig 7
Comparison between deterministic model and stochastic model of the densities of (a)S1(t), (b)S2(t), (c)I1(t), (d)I2(t), (e)M1(t), (f)M2(t), (g)M3(t), (h)M4(t) change over time when σi(i = 1 ∼ 8) = 0.00001.
Fig 8
Fig 8
Comparison between σi(i = 1 ∼ 8) = 0.0001 and σi(i = 1 ∼ 8) = 0.00001 of the densities of (a)S1(t), (b)S2(t), (c)I1(t), (d)I2(t), (e)M1(t), (f)M2(t), (g)M3(t), (h)M4(t) change over time.
Fig 9
Fig 9. The densities of I1(t) and I2(t) change over time when σi(i = 1 ∼ 8) = 0.0001 under constant control measure and optimal control.
Fig 10
Fig 10. The densities of I1(t) and I2(t) change over time when σi(i = 1 ∼ 8) = 0.00001 under constant control measure and optimal control.
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