In this paper,we propose a size-stage-structured cooperation model which has two distinct life stages in facultative cooperator.The primary feature of this model is to consider size structure,stage structure and oblig...In this paper,we propose a size-stage-structured cooperation model which has two distinct life stages in facultative cooperator.The primary feature of this model is to consider size structure,stage structure and obligate and facultative symbiosis at the same time in a cooperation system.We use the method of characteristic to show that this new model can be reduced to a threshold delay equations(TDEs)model,which can be further transformed into a functional differential equations(FDEs)model by a simple change of variables.Such simplification allows us to apply the classical theory of FDEs and establish a set of sufficient conditions to investigate the qualitative analysis of solutions of the FDEs model,including the global existence and uniqueness,positivity and boundedness.What's more,we use the geometric criteria to get the conclusions about stability and Hopf bifurcation of positive equilibrium because the coefficients of the characteristic equation depend on the bifurcation parameter.Finally,numerical simulations are carried out as supporting evidences of our analytical results.Our results show that the presence of size structure and stage structure plays an important role in the dynamic behavior of the model.展开更多
目的探讨冷冻治疗阈值或阈值前期(1型)早产儿视网膜病变(retinopathy of pre-maturity,ROP)的治疗效果。方法对筛查过程中发现的25例(50只眼)阈值或阈值前期(1型)ROP进行冷凝手术。全麻后在间接检眼镜直视下冷凝周边视网膜无血管区,术...目的探讨冷冻治疗阈值或阈值前期(1型)早产儿视网膜病变(retinopathy of pre-maturity,ROP)的治疗效果。方法对筛查过程中发现的25例(50只眼)阈值或阈值前期(1型)ROP进行冷凝手术。全麻后在间接检眼镜直视下冷凝周边视网膜无血管区,术后局部应用皮质类固醇和睫状肌麻痹剂2周。病变继续发展者补充冷凝手术,或进行间接检眼镜直视下光凝治疗,发生视网膜脱离或有玻璃体积血者进行玻璃体手术治疗。结果第一次手术后21例(42只眼)病变控制;4例(8只眼)病变仍继续发展,其中2例(4只眼)第2次冷凝手术后病变控制,最后冷凝治疗成功率为92%。1例(2只眼)第2次冷凝手术后1只眼玻璃体积血,3个月后对侧眼发生视网膜脱离,进行了玻璃体视网膜手术病变控制;另外1例(2只眼)一次冷凝治疗后病变继续发展,遂进行激光治疗、玻璃体手术,最后病变控制。结论冷凝是阻止阈值或阈值前期(1型)ROP发展的有效方法,术后玻璃体出血是冷凝的主要并发症之一。冷凝治疗长期疗效有待进一步随访。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.:11871007,11811530272 and 12071297)the Fundamental Research Funds for the Central Universities.
文摘In this paper,we propose a size-stage-structured cooperation model which has two distinct life stages in facultative cooperator.The primary feature of this model is to consider size structure,stage structure and obligate and facultative symbiosis at the same time in a cooperation system.We use the method of characteristic to show that this new model can be reduced to a threshold delay equations(TDEs)model,which can be further transformed into a functional differential equations(FDEs)model by a simple change of variables.Such simplification allows us to apply the classical theory of FDEs and establish a set of sufficient conditions to investigate the qualitative analysis of solutions of the FDEs model,including the global existence and uniqueness,positivity and boundedness.What's more,we use the geometric criteria to get the conclusions about stability and Hopf bifurcation of positive equilibrium because the coefficients of the characteristic equation depend on the bifurcation parameter.Finally,numerical simulations are carried out as supporting evidences of our analytical results.Our results show that the presence of size structure and stage structure plays an important role in the dynamic behavior of the model.
文摘目的探讨冷冻治疗阈值或阈值前期(1型)早产儿视网膜病变(retinopathy of pre-maturity,ROP)的治疗效果。方法对筛查过程中发现的25例(50只眼)阈值或阈值前期(1型)ROP进行冷凝手术。全麻后在间接检眼镜直视下冷凝周边视网膜无血管区,术后局部应用皮质类固醇和睫状肌麻痹剂2周。病变继续发展者补充冷凝手术,或进行间接检眼镜直视下光凝治疗,发生视网膜脱离或有玻璃体积血者进行玻璃体手术治疗。结果第一次手术后21例(42只眼)病变控制;4例(8只眼)病变仍继续发展,其中2例(4只眼)第2次冷凝手术后病变控制,最后冷凝治疗成功率为92%。1例(2只眼)第2次冷凝手术后1只眼玻璃体积血,3个月后对侧眼发生视网膜脱离,进行了玻璃体视网膜手术病变控制;另外1例(2只眼)一次冷凝治疗后病变继续发展,遂进行激光治疗、玻璃体手术,最后病变控制。结论冷凝是阻止阈值或阈值前期(1型)ROP发展的有效方法,术后玻璃体出血是冷凝的主要并发症之一。冷凝治疗长期疗效有待进一步随访。
