This research investigates a novel approach to modeling an SIR epidemic in a heterogeneous environment by imposing certain restrictions on population mobility.Our study reveals the influence of partially restricting t...This research investigates a novel approach to modeling an SIR epidemic in a heterogeneous environment by imposing certain restrictions on population mobility.Our study reveals the influence of partially restricting the mobility of the infected population,who are allowed to diffuse locally and can be modeled using random dispersion.In contrast,the non-infective population,which includes susceptible and recovered individuals,has more freedom in their movements.This greater mobility can be modeled using nonlocal dispersion.Our approach is valid for a class of nonlocal dispersion kernels.For the analysis,we first establish the well-posedness of the solution,ensuring the existence,uniqueness,and positivity of this solution.Additionally,we identify the basic reproduction number R0 with its threshold role.Specifically,when R0<1,we prove the global asymptotic stability of the disease-free steady state.Conversely,when R0>1,we demonstrate the corresponding semiflow of the model is uniformly persistent and establish behavior at endemic steady state.Lastly,we examine the asymptotic profiles of the positive steady state as the rate at which susceptible or infected individuals disperse tends to zero or infinity.Our findings reveal that when the movement of infected individuals is restricted,the infection concentrates in specific locations that may be described as the infected preferred spots.展开更多
文摘This research investigates a novel approach to modeling an SIR epidemic in a heterogeneous environment by imposing certain restrictions on population mobility.Our study reveals the influence of partially restricting the mobility of the infected population,who are allowed to diffuse locally and can be modeled using random dispersion.In contrast,the non-infective population,which includes susceptible and recovered individuals,has more freedom in their movements.This greater mobility can be modeled using nonlocal dispersion.Our approach is valid for a class of nonlocal dispersion kernels.For the analysis,we first establish the well-posedness of the solution,ensuring the existence,uniqueness,and positivity of this solution.Additionally,we identify the basic reproduction number R0 with its threshold role.Specifically,when R0<1,we prove the global asymptotic stability of the disease-free steady state.Conversely,when R0>1,we demonstrate the corresponding semiflow of the model is uniformly persistent and establish behavior at endemic steady state.Lastly,we examine the asymptotic profiles of the positive steady state as the rate at which susceptible or infected individuals disperse tends to zero or infinity.Our findings reveal that when the movement of infected individuals is restricted,the infection concentrates in specific locations that may be described as the infected preferred spots.
文摘选取广西环江县喀斯特峰丛洼地:草丛(T)、灌丛(S)、原生林(PF)(中坡位)不同植被类型,原生林上、中、下不同坡位,按土壤发生层采集淋溶层(A层,0—10 cm)、过渡层(AB层,20—30 cm,草丛和灌丛;30—50 cm,原生林)、淀积层(B层,70—100cm)样品,研究土壤微生物量碳、氮(Soil microbial biomass carbon(SMBC)、soil microbial biomass nitrogen(SMBN))、微生物碳熵、氮熵(ratio of SMBC to soil organic carbon(qMBC)、ratio of SMBN to soil total nitrogen(qMBN))、土壤基础呼吸(soil basicrespiration(SBR))以及代谢熵(microbial metabolic quotient(qCO2))的剖面分异特征及其影响因素。结果表明,植被、土层深度显著影响土壤微生物量及基础呼吸,随植被恢复,SMBC、SMBN、SBR由草丛、灌丛、原生林依次上升,并随土壤发生层位的加深逐渐减少,qCO2在3种植被类型间差异显著:T>PF>S;原生林A层SMBC,SMBN在各坡位间均显著高于AB层、B层,SBR在A层由下坡位至上坡位递减,而在AB和B层的上、下坡位间无显著差异,qCO2坡位间无显著差异(P>0.05);SMBC与SMBN之间存在显著正相关(r=0.825,P<0.01,n=45),且SMBC、SMBN、SBR分别与有机碳、全氮、碱解氮均呈显著正相关。因此,随植被恢复,土壤质量明显改善,且坡位对A层土壤的影响较AB层和B层更显著,对于维持土壤微生物调节的土壤养分循环功能,调控土壤氮素营养与土壤有机质同等重要,这为合理制订喀斯特生态恢复措施提供了理论依据。
