https://doi.org/10.1140/epjp/s13360-024-05168-1
Regular Article
Research on parameter identification of an epidemic-like network system based on optimization theory
1
Affiliated Hospital of Jiangsu University, Jiangsu University, Zhenjiang, People’s Republic of China
2
School of Mathematical Sciences, Jiangsu University, Zhenjiang, People’s Republic of China
Received:
31
January
2024
Accepted:
8
April
2024
Published online:
29
July
2024
In this paper, an 
(
) rumor propagation model based on reaction–diffusion is established. When building the model, we consider the influence of the second propagation of rumors on the model according to the practical significance. The necessary conditions of Turing instability are deduced in the theoretical analysis. After considering the stability of the system, the first-order necessary conditions and second-order conditions of the optimality of the system can be found through the optimal control method. The effect of the propagation rate on the system is analyzed by using the pattern dynamics in numerical simulation. It is found that the higher the propagation rate, the more the density distribution of the propagator in the space. We also have discussed the pattern evolution form without consideration of the cross-diffusion in the system. Further, the optimality condition is applied to the parameter identification experiment to study the accuracy of multi-parameter identification under different algorithms. Finally, this work has analyzed the decline process of the system loss function under different network structures.
Linhe Zhu and Shuling Shen have contributed equally, and they are co-first authors of this paper.
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