اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAnalysis of an epidemic model with awareness decay on regular random networks
173
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The existence of a die-out threshold (different from the classic disease-invasion one) defining a region of slow extinction of an epidemic has been proved elsewhere for susceptible-aware-infectious-susceptible models without awareness decay, through bifurcation analysis. By means of an equivalent mean-field model defined on regular random networks, we interpret the dynamics of the system in this region and prove that the existence of bifurcation for this second epidemic threshold crucially depends on the absence of awareness decay. We show that the continuum of equilibria that characterizes the slow die-out dynamics collapses into a unique equilibrium when a constant rate of awareness decay is assumed, no matter how small, and that the resulting bifurcation from the disease-free equilibrium is equivalent to that of standard epidemic models. We illustrate these findings with continuous-time stochastic simulations on regular random networks with different degrees. Finally, the behaviour of solutions with and without decay in awareness is compared around the second epidemic threshold for a small rate of awareness decay.
قيم البحث
اقرأ أيضاً
In the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether a disease will eventually infect a large fraction of a population. Because network structure typically changes in time, which fundamen
tally influences the dynamics of spreading processes on them and in turn affects epidemic thresholds for disease propagation, it is important to examine epidemic thresholds in temporal networks. Most existing studies of epidemic thresholds in temporal networks have focused on models in discrete time, but most real-world networked systems evolve continuously in time. In our work, we encode the continuous time-dependence of networks into the evaluation of the epidemic threshold of a susceptible--infected--susceptible (SIS) process by studying an SIS model on tie-decay networks. We derive the epidemic-threshold condition of this model, and we perform numerical experiments to verify it. We also examine how different factors---the decay coefficients of the tie strengths in a network, the frequency of interactions between nodes, and the sparsity of the underlying social network in which interactions occur---lead to decreases or increases of the critical values of the threshold and hence contribute to facilitating or impeding the spread of a disease. We thereby demonstrate how the features of tie-decay networks alter the outcome of disease spread.
In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentially between interactions. Specifica
lly, we formulate continuous-time Laplacian dynamics and a discrete-time DeGroot model of opinion dynamics on these tie-decay networks, and we carry out numerical computations for the continuous-time Laplacian dynamics. We examine the speed of convergence by studying the spectral gaps of combinatorial Laplacian matrices of tie-decay networks. First, we compare the spectral gaps of the Laplacian matrices of tie-decay networks that we construct from empirical data with the spectral gaps for corresponding randomized and aggregate networks. We find that the spectral gaps for the empirical networks tend to be smaller than those for the randomized and aggregate networks. Second, we study the spectral gap as a function of the tie-decay rate and time. Intuitively, we expect small tie-decay rates to lead to fast convergence because the influence of each interaction between two nodes lasts longer for smaller decay rates. Moreover, as time progresses and more interactions occur, we expect eventual convergence. However, we demonstrate that the spectral gap need not decrease monotonically with respect to the decay rate or increase monotonically with respect to time. Our results highlight the importance of the interplay between the times that edges strengthen and decay in temporal networks.
Public health services are constantly searching for new ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine (isolation) and treatment of symptomatic individuals. Epidemic models have a
long history of assisting in public health planning and policy making. In this paper, we introduce epidemic models including variable population size, degree-related imperfect vaccination and quarantine on scale-free networks. More specifically, the models are formulated both on the population with and without permanent natural immunity to infection, which corresponds respectively to the susceptible-vaccinated-infected-quarantined-recovered (SVIQR) model and the susceptible-vaccinated-infected-quarantined (SVIQS) model. We develop different mathematical methods and techniques to study the dynamics of two models, including the basic reproduction number, the global stability of disease-free and endemic equilibria. For the SVIQR model, we show that the system exhibits a forward bifurcation. Meanwhile, the disease-free and unique endemic equilibria are shown to be globally asymptotically stable by constructing suitable Lyapunov functions. For the SVIQS model, conditions ensuring the occurrence of multiple endemic equilibria are derived. Under certain conditions, this system cannot undergo a backward bifurcation. The global asymptotical stability of disease-free equilibrium, and the persistence of the disease are proved. The endemic equilibrium is shown to be globally attractive by using monotone iterative technique. Finally, stochastic network simulations yield quantitative agreement with the deterministic mean-field approach.
In this paper, we propose two novel immunization strategies, i.e., combined immunization and duplex immunization, for SIS model in directed scale-free networks, and obtain the epidemic thresholds for them with linear and nonlinear infectivities. With
the suggested two new strategies, the epidemic thresholds after immunization are greatly increased. For duplex immunization, we demonstrate that its performance is the best among all usual immunization schemes with respect to degree distribution. And for combined immunization scheme, we show that it is more effective than active immunization. Besides, we give a comprehensive theoretical analysis on applying targeted immunization to directed networks. For targeted immunization strategy, we prove that immunizing nodes with large out-degrees are more effective than immunizing nodes with large in-degrees, and nodes with both large out-degrees and large in-degrees are more worthy to be immunized than nodes with only large out-degrees or large in-degrees. Finally, some numerical analysis are performed to verify and complement our theoretical results. This work is the first to divide the whole population into different types and embed appropriate immunization scheme according to the characteristics of the population, and it will benefit the study of immunization and control of infectious diseases on complex networks.
ANDy , Activity Networks with Delays, is a discrete time framework aimed at the qualitative modelling of time-dependent activities. The modular and concise syntax makes ANDy suitable for an easy and natural modelling of time-dependent biological syst
ems (i.e., regulatory pathways). Activities involve entities playing the role of activators, inhibitors or products of biochemical network operation. Activities may have given duration, i.e., the time required to obtain results. An entity may represent an object (e.g., an agent, a biochemical species or a family of thereof) with a local attribute, a state denoting its level (e.g., concentration, strength). Entities levels may change as a result of an activity or may decay gradually as time passes by. The semantics of ANDy is formally given via high-level Petri nets ensuring this way some modularity. As main results we show that ANDy systems have finite state representations even for potentially infinite processes and it well adapts to the modelling of toxic behaviours. As an illustration, we present a classification of toxicity properties and give some hints on how they can be verified with existing tools on ANDy systems. A small case study on blood glucose regulation is provided to exemplify the ANDy framework and the toxicity properties.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
