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In this paper, a nitrogen fixation game system with two time delays under nitrogen limitation is investigated. Firstly, we discuss the existence and local stability of the equilibrium points for the nondelay system. Then the nitrogen fixation delay and strategy-dependent delay are used as bifurcation parameters to analyze the local stability and the Hopf bifurcation. In addition, we obtain the direction of Hopf bifurcation, the change of the period for periodic solution and the stability of periodic solution via center manifold theory and normal form method. Finally, numerical simulation is employed to visualize the theoretical analysis results and we find that the nitrogen fixation strategy is the dominant strategy when the values of the two time delays are large enough. This study promotes the investigation of the effects of two time delays on the dynamics of evolutionary games with environmental feedback, especially on stability and bifurcation.

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Aim To summarize the whole process management measures for caregivers of inpatients in a non‐new coronavirus pneumonia designated hospital in China during the novel coronavirus pneumonia epidemic. The implementation of these measures is mainly to prevent the virus pandemic caused by crowd gathering. Design A quasi‐experimental study. Methods Novel coronavirus pneumonia prevention and control measures were implemented in the ‘pre‐hospital link, hospitalization link and discharge link’ for the whole process of the hospitalized patients’ caregivers. To evaluate the effects by time point inspection, the results were fed back using information technology for quality improvement. Results The results of three time point inspections indicated that the management quality of many projects improved continuously ( p < 0.05). From January to June of 2021, 20 departments implemented a facial recognition information management system. The ratio of patients/caregivers admitted was 1:0.528~1:0.965; It was found that it is effective to implement the whole process management measures. The facial recognition system plays a key role in the comprehensive management of the caregivers.