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We analyze the critical transitions (a) to endemic states in an SIS epidemiological model, and (b) to full synchronization in an ensemble of coupled chaotic maps, on networks where, at any given time, each node is connected to just one neighbour. In these “monogamous” populations, the lack of connectivity in the instantaneous interaction pattern—that would prevent both the propagation of an infection and the collective entrainment into synchronization—is compensated by occasional random reconnections which recombine interacting couples by exchanging their partners. The transitions to endemic states and to synchronization are recovered if the recombination rate is sufficiently large, thus giving rise to a bifurcation as this rate varies. We study this new critical phenomenon both analytically and numerically. 相似文献
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The dynamics of an SIR epidemic model is explored in this paper in order to understand how the limited medical resources and their supply efficiency affect the transmission of infectious diseases. The study reveals that, with varying amount of medical resources and their supply efficiency, the target model admits both backward bifurcation and Hopf bifurcation. Sufficient criteria are established for the existence of backward bifurcation, the existence, the stability and the direction of Hopf bifurcation. The mechanism of backward bifurcation and its implication for the control of the infectious disease are also explored. Numerical simulations are presented to support and complement the theoretical findings. 相似文献
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G. Saccomandi 《Mathematical and Computer Modelling》1997,25(12):83-95
Using the linear theory of semigroups, existence and uniqueness of the solution are studied for an S → E → I model which takes into account spatial inhomogeneity, nonlocal interactions, and an open population. 相似文献
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Miaohua Jiang 《Journal of Difference Equations and Applications》2016,22(10):1438-1451
In the Markov chain model of infectious diseases in a connected network of heterogeneous individuals, the computation of the risk of infection for each individual and the expected size of the infected population over time is an NP-hard problem. We show that the individual risk of infection over time can be approximated by orbits of a nonlinear discrete dynamical system on a phase space of dimension equal to the number of individuals in the network. An upper bound for the eradication rate of the infectious disease in the network is also obtained. 相似文献
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Alberto dOnofrio 《Nonlinear Analysis: Real World Applications》2008,9(4):1567-1572
In this note we introduce the study of the global behaviour of the network-based SIS epidemic model recently proposed by Pastor-Satorras and Vespignani [Epidemic spreading in scale-free networks, Phys. Rev. Lett. 86 (2001) 3200], characterized in case of homogeneous scale-free networks by a very small epidemic threshold, and extended by Olinky and Stone [Unexpected epidemic threshold in heterogeneous networks: the role of disease transmission, Phys. Rev. E 70 (2004) 03902(r)]. We show that the above model may be read as a particular case of the classical multi-group SIS model proposed by Lajmainovitch and Yorke [A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci. 28 (1976) 221] and extended by Aronsson and Mellander [A deterministic model in biomathematics. Asymptotic behaviour and threshold conditions, Math. Biosci. 49 (1980) 207]. Thus, by applying the methods used for SIS multi-group models, we straightforwardly show, for the first time, that the local conditions identified in the physics literature also determine the global behaviour of a disease spreading on a network. Finally, we briefly study the case in which the force of infection is non-linear, by showing that multiple coexisting equilibria are possible, and by giving a global threshold condition for the extinction. 相似文献
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Yérali Gandica 《Physica A》2010,389(19):4172-4176
The effect of directionality on the information propagation in a contagion model with complex propagation, i.e., that takes into account the need for simultaneous exposure to multiple activation sources, is studied. While it is known that complex propagation is blocked with increasing network randomness, here it is shown that network directionality affects such a result, leading to several different behaviors depending on the preservation of the in-degree or out-degree. The critical points for the occurrence of complex propagation in 1D directed small world networks are determined. It is shown that these points only depend on the number of outgoing links. 相似文献
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Modelling and stability of epidemic model with free-living pathogens growing in the environment
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To understand the impact of free-living pathogens (FLP) on the epidemics, an epidemic model with FLP is constructed. The global dynamics of our model are determined by the basic reproduction number $R_0$. If $R_0<1$, the disease free equilibrium is globally asymptotically stable, and if $R_0>1$, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also carried out to illustrate our analytical results. 相似文献
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Jonathan P. Caulkins Gustav Feichtinger Gernot Tragler Dagmar Wallner 《European Journal of Operational Research》2010
A heated debate in drug policy concerns the relative merits of “harm reduction” (e.g., reducing drug-related HIV/AIDS transmission) vs. “use reduction” (controlling drug use per se). This paper models whether shifting emphasis between these goals over the course of a drug epidemic might reduce social costs relative to pursuing one or the other exclusively. Results suggest different answers for different drugs and/or countries. In particular, harm reduction may have always been effective for Australia’s injection drug use problem, but for US cocaine it may not have been in the past even if it could be so today. In certain circumstances harm reduction may “tip” an epidemic toward a high- rather than low-use equilibrium. The location in state space of regions where this occurs can be sensitive to parameter changes, suggesting caution may be in order when advocating harm reduction, unless there is confidence the epidemic has been modeled and parameterized accurately. 相似文献