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Analysis of SEIR model with self-protection awareness in complex networks QIN Jiaxin, LI Shuping JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2025, 60 (4): 60-71.   DOI: 10.6040/j.issn.1671-9352.0.2024.061 Abstract （388）      PDF（pc） （3995KB）（179）       Save By considering media publicity and information dissemination among people, we establish an SEIR(susceptible-exposed-infectious-removed,)model with two types of susceptible compartments on complex networks to study the impact of self-protection awareness on the spread of infectious diseases. The basic reproduction number R0 is obtained by calculation, and it is proved that there is a unique endemic equilibrium point when R0>1. According to Hurwitz criterion and comparison theorem, the stability of the disease-free equilibrium is analyzed. Then it is proved that the disease is uniformly persistent when R0>1. Sensitivity analysis determines the importance of parameters for R0. Numerical simulation shows that improving self-protection awareness can effectively reduce the probability of being infected. Reference | Related Articles | Metrics

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High-order differentiability and sensitivity of vector variational inequalities MA Quanlu, XUE Xiaowei JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2025, 60 (2): 105-113.   DOI: 10.6040/j.issn.1671-9352.0.2023.400 Abstract （361）      PDF（pc） （412KB）（95）       Save The paper studies the higher-order differentiability and sensitivity of vector variational inequalities and weak vector variational inequalities. The basic definitions of contingent cones, higher-order tangent sets are introduced. The higher-order differential properties of a class of set-valued maps closely related to vector variational inequalities are studied, and the accurate calculation formula of its higher-order derivatives is obtained. By discussing the relationship between the higher-order derivatives of set-valued mapping and its profile mapping, the higher-order differentiability and sensitivity of vector variational inequalities are obtained. Reference | Related Articles | Metrics

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Coexistence solutions of a predator-prey model with Allee effect and density-dependent diffusion in the predator MA Tiantian, LI Shanbing JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2025, 60 (4): 84-92.   DOI: 10.6040/j.issn.1671-9352.0.2023.323 Abstract （257）      PDF（pc） （472KB）（173）       Save This paper is concerned with the coexistence solutions of a predator-prey model with Allee effect and density-dependent diffusion in the predator under homogeneous Dirichlet boundary conditions. Based on a priori estimate of coexistence solutions, the sufficient conditions for the existence of coexistence solutions are established by using the theory of fixed point index in positive cone. The results show that the density-dependent diffusion has a significant effect on the existence of coexistence solutions, and it is also find that the functional response function between the two species has an essential effect on the existence of coexistence solutions. Reference | Related Articles | Metrics