Evolution of group behaviour in the ecological snowdrift game-level-headed and impatient delayed epidemic model under emergencies

Major emergencies generate negative emotions within a group. Therefore, the topic of the spread of emotions leading to the coexistence of cooperation and defection within a group has attracted much attention. We introduced the influence of the external environment and constructed an ecological snowdrift game model to explore the evolution of cooperation and defection in this paper. On this basis, the ecological snowdrift game-level-headed and impatient delayed epidemic model was developed. This model considers the differences in individual personalities by categorizing individuals into level-headed and impatient groups, and also incorporates a delay in the spread of panic within groups. We computed a threshold value for panic spread and analysed the qualitative behaviour of the epidemic model, such as locally and globally asymptotically stable equilibria. The results indicated that cooperation is more likely to emerge in a group as the probability of a cooperator encountering an individual with the same strategy increases. Comparison with the level-headed and impatient delayed epidemic model revealed that group behaviour (i.e., cooperation and defection) can influence the evolutionary process of populations within a group. Numerical simulations verified the effectiveness of the derived results. The proposed model was analysed and validated through a practical example and visualization for sentiment analysis using the Naive Bayes algorithm. The findings of the paper can help to further explore the evolution of group behaviour.