Dynamic Analysis of an Epidemic Model Considering Personal Alert on a Complex Network

Abstract

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.

Keywords

• epidemic model
• complex networks
• individual alertness
• quarantine
• stability