Jia Fengling, Gu Ziyu, Yang Lixin
School of Mathematics, Chengdu Normal University, Chengdu 611130, China.
School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi'an 710021, China.
Entropy (Basel). 2023 Oct 11;25(10):1437. doi: 10.3390/e25101437.
This paper proposes a SIQRS epidemic model with birth and death on a complex network, considering individual alertness. In particular, we investigate the influence of the individual behavior in the transmission of epidemics and derive the basic reproduction number depending on birth rate, death rate, alertness rate, quarantine rate. In addition, the stabilities of the disease-free equilibrium point and endemic equilibrium point are analyzed via stability theory. It is found that the emergence of individual behavior can influence the process of transmission of epidemics. Our results show that individual alertness rate is negatively correlated with basic reproduction number, while the impact of individual alertness on infectious factor is positively correlated with basic reproduction number. When the basic reproduction number is less than one, the system is stable and the disease is eventually eradicated. Nevertheless, there is an endemic equilibrium point under the condition that the basic reproduction number is more than one. Finally, numerical simulations are carried out to illustrate theoretical results.
本文提出了一个考虑个体警觉性的、具有出生和死亡的复杂网络上的SIQRS传染病模型。特别地，我们研究了个体行为在传染病传播中的影响，并推导了依赖于出生率、死亡率、警觉率、隔离率的基本再生数。此外，通过稳定性理论分析了无病平衡点和地方病平衡点的稳定性。发现个体行为的出现会影响传染病的传播过程。我们的结果表明，个体警觉率与基本再生数呈负相关，而个体警觉对感染因子的影响与基本再生数呈正相关。当基本再生数小于1时，系统是稳定的，疾病最终被根除。然而，在基本再生数大于1的条件下存在一个地方病平衡点。最后，进行了数值模拟以说明理论结果。
