Narrow Results

We consider epidemic transmission in a finite population with both scale-free network structure and heterogeneous infection rates related to both susceptibility and infectiousness of individuals. The restriction to a finite population size and heterogeneity are included so that the model more closely matches reality. In particular, the arithmetic average behavior of heterogeneous infection rates with node-degree correlation is discussed. Through numerical simulations, we find that the average infection rate presents robust small-amplitude oscillations. Based on this property, we propose a statistical measure of the system dynamics — the epidemic spreading efficiency (ESE) — and discuss its phase transitions as a function of the various system parameters. The results show that the ESE presents a non-continuous phase transition and the ESE threshold is an extension of the epidemic threshold from the case of homogeneous infection rate (for homogeneous populations, the two quantities exhibit the same behavior). By comparing the ESE threshold and the epidemic threshold, we find that ESE threshold is larger than epidemic threshold for a sufficiently large network size. This implies that the traditional homogeneous assumption of infection rates in many epidemiological models overestimates the likelihood of epidemic disease survival.

We investigate the spreading of SARS-CoV-2 in the state of Alagoas, northeast of Brazil, via an adaptive susceptible-infected-removed (SIR) model featuring dynamic recuperation and propagation rates. Input parameters are defined based on data made available by Alagoas Secretary of Health from April 19, 2020 on. We provide with the evolution of the basic reproduction number $R_0$ and reproduce the historical series of the number of confirmed cases with less than $10\%$ error. We offer predictions, from November 16 forward, over the epidemic situation in the near future and show that it will keep decelerating. Furthermore, the same model can be used to study the epidemic dynamics in other countries with great easiness and accuracy.

We study the combined effects of aging and links removal on epidemic dynamics in the Barabási–Albert scale-free networks. The epidemic is described by a susceptible-infected-refractory (SIR) model. The aging effect of a node introduced at time t_i is described by an aging factor of the form (t-t_i)^-β in the probability of being connected to newly added nodes in a growing network under the preferential attachment scheme based on popularity of the existing nodes. SIR dynamics is studied in networks with a fraction 1-p of the links removed. Extensive numerical simulations reveal that there exists a threshold p_c such that for p≥p_c, epidemic breaks out in the network. For p<p_c, only a local spread results. The dependence of p_c on β is studied in detail. The function p_c(β) separates the space formed by β and p into regions corresponding to local and global spreads, respectively.

In order to propose a more realistic epidemic dynamics model and effective medical resource allocation strategy, this paper constructs an improved SEIR model combined with a dynamical medical resource allocation model and individual behavior sharing medical resources. Simultaneously, a genetic algorithm to solve the medical resource allocation model is proposed to obtain the optimum resource allocation strategy. In this SEIR model, there is an important critical value of the stored medical resources, when the number of stored medical resources is more than the critical value, the inhibition of epidemic can be continuously enhanced until it reaches a minimum threshold, and then stabilizes near a minimum value, but when the resource surplus is below the critical value, the inhibitory effect on epidemic will weaken. The results demonstrate that the number of patients in the proposed method decreased more than 40% compared with the conventional control experiment. Moreover, the algorithm can automatically make decisions according to individual behavior in sharing preferences and the epidemic development trend.

It is crucial to capture the actual infection scale of communicable diseases. However, the official case numbers cannot equal to actual infection scale in society, because a large number of asymptomatic individuals are not recognized. To deal with this challenge, this paper takes COVID-19 as the object, and develops an improved SEIR dynamics model to estimate its actual infection scale. Generalized to the circumstances in this work, we improve the classical SEIR model by considering three implicit factors: self-recovered asymptomatic individuals, recovered individuals, and deceased individuals. The dynamics process inside the improved model is expressed using mathematical formulas, and the parameter estimation scheme is given accordingly. To evaluate the estimation effect of the proposal, we employ pandemic data from 10 representative countries to build experimental scenario. The results obtained through model fitting demonstrate that the estimated actual infection scale is approximately 10–30 times higher than the reported average “newly confirmed cases”. Furthermore, our findings reveal a noteworthy negative correlation between the transmission coefficient and vaccination rate, confirming the beneficial role of vaccination in mitigating COVID-19 spreading.

Epidemic dynamics in networks have attracted a great deal of attention from many fields. Based on the previous work, we propose a weak discrete mean-field approximation, and the difference with the previous approximation approach is that it can result in more simple difference equations. We mainly consider the minimal SIS epidemic model in complex networks, and make comparisons amongst two kinds of approximation formulations on the prediction of epidemic prevalence and find that they are effective to model epidemic spreading. Moreover, we investigate its application to the risk feedback case and simulations indicate its effectiveness.

Epidemic dynamics in networks have attracted a great deal of attention from researchers of many fields. In this paper, we mainly study the global behaviors of discrete-time epidemic model in heterogenous networks. By theoretical analysis, we show that the model can be characterized by the basic reproduction number R₀. When R₀ is smaller than unit, the disease-free equilibrium is globally stable, while R₀ is larger than unit, the unique positive equilibrium is globally attractive.

In this paper, an SIRS epidemic model with high-risk immunization was investigated, where a susceptible neighbor of an infected node is immunized with rate h. Through analyzing the discrete-time model, we found that the epidemic threshold above which an epidemic can prevail and persist in a population is inversely proportional to 1 - h value. We also studied the continuous-time epidemic model and obtained a different result: the epidemic threshold does not depend on the immunization parameter h. Our results suggest that the difference between the discrete-time epidemic model and the continuous-time epidemic model exists in the high-risk immunization.

In this paper, we study the spreading of infections on complex heterogeneous networks based on an SEIRS epidemic model with nonlinear infectivity. By mathematical analysis, the basic reproduction number R₀ is obtained. When R₀ is less than one, the disease-free equilibrium is globally asymptotically stable and the disease dies out, while R₀ is greater than one, the disease-free equilibrium becomes unstable and the disease is permanent, and in the meantime there exists a unique endemic equilibrium which is globally attractive under certain conditions. Finally, the effects of various immunization schemes are studied. To verify our theoretical results, the corresponding numerical simulations are also included.

This work studies and numerically simulates a logistic-type model for the dynamics of Chagas disease, which is caused by the parasite T. cruzi and affects millions of humans and domestic mammals throughout rural areas in Central and South America. A basic model for the disease dynamics that includes insecticide spraying was developed in Spagnuolo et al. (2010) [27] and consists of a delay-differential equation for the vectors and three nonlinear ordinary differential equations for the populations of the infected vectors, infected humans and infected domestic mammals. In this work, the vector equation is modified by using a logistic term with zero, one or two delays or time lags. The aim of this study is three-fold: to numerically study the effects of using different numbers of delays on the model behavior; to find if twice yearly insecticide spraying schedules improve vector control; and to study the sensitivity of the system to the delays in the case of two delays, by introducing randomness in the delays. It is found that the vector equation with different number of delays has very different solutions. The “best” day of spraying is the middle of Spring and twice annual sprayings cause only minor improvements in disease control. Finally, the model is found to be insensitive to the values of the delays, when the delays are randomly distributed within rather narrow intervals or ranges centered on the parameter values used in Coffield et al. (2014) [8].