SIR model of epidemic spread with accumulated exposure

We study an extended and modified SIR model of epidemic spread in which susceptible agents during interactions with infectious neighbors are exposed to the disease and can consequently become infectious. The studied model is extended to include heterogeneity of interactions which is modelled assuming random character of the dose accumulated by susceptible agents in every interaction with infectious neighbors. When the accumulated exposure is larger than the individual’s resistance, an agent becomes infectious and consequently introduces a new source of an epidemic which is capable of passing the disease further. We study statistical properties characterizing the course of an epidemic. The examination of the modified SIR model reveals a possible “resonant activation”-like behavior of the system in the duration of the epidemic outbreak and a possible bistable behavior of the model with accumulated exposure. Furthermore, the linear scaling of the duration of the epidemic with the system size for a wide range of the model parameters is recorded.     

A predator–prey model with diseases in both prey and predator

In this paper, we present and analyze a predator–prey model, in which both predator and prey can be infected. Each of the predator and prey is divided into two categories, susceptible and infected. The epidemics cannot be transmitted between prey and predator by predation. The predation ability of susceptible predators is stronger than infected ones. Likewise, it is more difficult to catch a susceptible prey than an infected one. And the diseases cannot be hereditary in both of the predator and prey populations. Based on the assumptions above, we find that there are six equilibrium points in this model. Using the base reproduction number, we discuss the stability of the equilibrium points qualitatively. Then both of the local and global stabilities of the equilibrium points are analyzed quantitatively by mathematical methods. We provide numerical results to discuss some interesting biological cases that our model exhibits. Lastly, we discuss how the infectious rates affect the stability, and how the other parameters work in the five possible cases within this model.     

Minimizing the Spread of Negative Influence in SNIR Model by Contact Blocking

This paper presents a method to minimize the spread of negative influence on social networks by contact blocking. First, based on the infection-spreading process of COVID-19, the traditional susceptible, infectious, and recovered (SIR) propagation model is extended to the susceptible, non-symptomatic, infectious, and recovered (SNIR) model. Based on this model, we present a method to estimate the number of individuals infected by a virus at any given time. By calculating the reduction in the number of infected individuals after blocking contacts, the method selects the set of contacts to be blocked that can maximally reduce the affected range. The selection of contacts to be blocked is repeated until the number of isolated contacts that need to be blocked is reached or all infection sources are blocked. The experimental results on three real datasets and three synthetic datasets show that the algorithm obtains contact blockings that can achieve a larger reduction in the range of infection than other similar algorithms. This shows that the presented SNIR propagation model can more precisely reflect the diffusion and infection process of viruses in social networks, and can efficiently block virus infections.     

Epidemiological impact of waning immunization on a vaccinated population

This is an epidemiological SIRV model based study that is designed to analyze the impact of vaccination in containing infection spread, in a 4-tiered population compartment comprised of susceptible, infected, recovered and vaccinated agents. While many models assume a lifelong protection through vaccination, we focus on the impact of waning immunization due to conversion of vaccinated and recovered agents back to susceptible ones. Two asymptotic states exist, the “disease-free equilibrium” and the “endemic equilibrium” and we express the transitions between these states as function of the vaccination and conversion rates and using the basic reproduction number. We find that the vaccination of newborns and adults have different consequences on controlling an epidemic. Also, a decaying disease protection within the recovered sub-population is not sufficient to trigger an epidemic at the linear level. We perform simulations for a parameter set mimicking a disease with waning immunization like pertussis. For a diffusively coupled population, a transition to the endemic state can proceed via the propagation of a traveling infection wave, described successfully within a Fisher-Kolmogorov framework.     

Discovering network behind infectious disease outbreak

Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network and reveal the transmission parameters which govern the stochastic spreads over the network from a dataset on an infectious disease outbreak in the early growth phase. Populations in a combination of epidemiological compartment models and a meta-population network model are described by stochastic differential equations. Probability density functions are derived from the equations and used for the maximal likelihood estimation of the topology and parameters. The method is tested with computationally synthesized datasets and the WHO dataset on the SARS outbreak.     

Mobility matrix evolution for an SIS epidemic patch model

Intercommunity disease spread can be modeled using a collection of discrete community “patches” with continuous population flow between them. In a susceptible–infected–susceptible (SIS) model residents of a community may either be classified as susceptible or infected. Infected individuals may heal and become susceptible again but are not permitted to die or become immune. The spread of disease can be controlled by modifying the rate and direction of resident movement across patch boundaries. In this work we use genetic algorithms to evolve optimal connections between patch boundaries such that the total number of infected individuals is minimized.     

Effective vaccination strategies for realistic social networks

We consider the effectiveness of targeted vaccination at preventing the spread of infectious disease in a realistic social network. We compare vaccination strategies based on no information (random vaccination) to complete information (PageRank) about the network. The most effective strategy we find is to vaccinate those people with the most unvaccinated contacts. However, this strategy requires considerable information and computational effort which may not be practical. The next best strategies vaccinate people with many contacts who in turn have few contacts.     

SEIR Model of Rumor Spreading in Online Social Network with Varying Total Population Size

Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to describe the online social network with varying total number of users and user deactivation rate. We calculate the exact equilibrium points and reproduction number for this model. Furthermore, we perform the rumor spreading process in the online social network with increasing population size based on the original real world Facebook network. The simulation results indicate that the SEIR model of rumor spreading in online social network with changing total number of users can accurately reveal the inherent characteristics of rumor spreading process in online social network.     

A cellular automata model with probability infection and spatial dispersion

In this article, we have proposed an epidemic model based on the probability cellular automata theory. The essential mathematical features are analysed with the help of stability theory. We have given an alternative modelling approach for the spatiotemporal system which is more realistic from the practical point of view. A discrete and spatiotemporal approach is shown by using cellular automata theory. It is interesting to note that both the size of the endemic equilibrium and the density of the individuals increase with the increase of the neighbourhood size and infection rate, but the infections decrease with the increase of the recovery rate. The stability of the system around the positive interior equilibrium has been shown by using a suitable Lyapunov function. Finally, experimental data simulation for SARS disease in China in 2003 and a brief discussion are given.     

Scaling behavior of threshold epidemics

We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease from infected individuals, while infected ones recover from the disease at a constant rate and are never infected again. Our focus is the behavior at the epidemic threshold where the rates of the infection and recovery processes balance. In the infinite population limit, we establish analytically scaling rules for the time-dependent distribution functions that characterize the sizes of the infected and the recovered sub-populations. Using heuristic arguments, we also obtain scaling laws for the size and duration of the epidemic outbreaks as a function of the total population. We perform numerical simulations to verify the scaling predictions and discuss the consequences of these scaling laws for near-threshold epidemic outbreaks.     

Shift of percolation thresholds for epidemic spread between static and dynamic small-world networks

The study compares the epidemic spread on static and dynamic small-world networks. They are constructed as a 2-dimensional Newman and Watts model (500 × 500 square lattice with additional shortcuts), where the dynamics involves rewiring shortcuts in every time step of the epidemic spread. We assume susceptible-infectious-removed (SIR) model of the disease. We study the behaviour of the epidemic over the range of shortcut probability per underlying bond ϕ = 0–0.5. We calculate percolation thresholds for the epidemic outbreak, for which numerical results are checked against an approximate analytical model. We find a significant lowering of percolation thresholds on the dynamic network in the parameter range given. The result shows the behaviour of the epidemic on dynamic network is that of a static small world with the number of shortcuts increased by 20.7±1.4 %, while the overall qualitative behaviour stays the same. We derive corrections to the analytical model which account for the effect. For both dynamic and static small worlds we observe suppression of the average epidemic size dependence on network size in comparison with the finite-size scaling known for regular lattice. We also study the effect of dynamics for several rewiring rates relative to infectious period of the disease.     

Experimental and computational simulation of beta-dose heterogeneity in sediment

Interpreting the spread in equivalent-dose estimates is an important aspect of optically stimulated luminescence (OSL) dating. Ideally, prior to age estimation, an assessment should be made of the likely spread in equivalent dose due to dose-rate heterogeneity in the sediment. Such a procedure would greatly increase the validity of OSL ages, particularly for sediments susceptible to partial bleaching, and for sediments with coarse or poorly sorted grain-size distributions. In this paper we take a step towards a general model of dose-rate heterogeneity by simulating the ⁴⁰K-derived beta dose to quartz. We present an experimental simulation of the ⁴⁰K beta dose, and compare the results with a Monte Carlo simulation of the same experiment. The experiment uses artificially produced ²⁴Na to simulate the ⁴⁰K beta dose to quartz, allowing a large, heterogeneous dose to be administered in a short period of time. The Monte Carlo simulation correctly predicts the shape of the equivalent-dose distribution, but underestimates the spread in dose received by different grains. The experimental set-up provides a new avenue of research into beta-dose heterogeneity.     

Global analysis of multiple routes of disease transmission on heterogeneous networks

In this paper, we propose and study an SIS epidemic model with multiple transmission routes on heterogeneous networks. We focus on the dynamical evolution of the prevalence. Through mathematical analysis, we obtain the basic reproduction number _R0$R_0$ by investigating the local stability of the disease-free equilibrium and also investigate the effects of various immunization schemes on disease spread. We further obtain that the disease will die out independent of the initial infections if the basic reproduction number is less than one, otherwise if the basic reproduction number is larger than one, the system converges to a unique endemic equilibrium, which is globally stable and thus the disease persists in the population. Our theoretical results are conformed by a series of numerical simulations and suggest a promising way for the control of infectious diseases with multiple routes.     

一类SEIRS型流行病的细胞自动机模型

本文通过分析SEIRS类流行病，建立了该类疾病的二维概率细胞自动机模型。在二维中，每个细胞的状态代表易感者，潜伏者，患者，恢复者（或免疫者）和死亡者五个部分个体之一。我们研究了两种情况下，即对潜伏者和患者隔离与不隔离将对疾病转播的影响。经研究我们发现，如果不隔离疾病将持续流行，而及时的隔离则将会减缓疾病的流行。本模型给出了对具体疾病利用细胞自动进行仿真的算法。我们发现当恢复者的失去免疫力大于时，疾病潜伏者和患者的密度序列将在正平衡点附近振荡。最后，我们用计算机对模型进行了仿真。     

Epidemic threshold and immunization on generalized networks

The susceptible–infected–susceptible (SIS) model is widely adopted in the studies of epidemic dynamics. When it is applied on contact networks, these networks mostly consist of nodes connected by undirected and unweighted edges following certain statistical properties, whereas in this article we consider the threshold and immunization problem for the SIS model on generalized networks that may contain different kinds of nodes and edges which are very possible in the real situation. We proved that an epidemic will become extinct if and only if the spectral radius of the corresponding parameterized adjacent matrix (PAM) is smaller than 1. Based on this result, we can evaluate the efficiency of immune strategies and take several prevailing ones as examples. In addition, we also develop methods that can precisely find the optimal immune strategies for networks with the given PAM.     

Does Social Distancing Matter for Infectious Disease Propagation? An SEIR Model and Gompertz Law Based Cellular Automaton

In this paper, we present stochastic synchronous cellular automaton defined on a square lattice. The automaton rules are based on the SEIR (susceptible → exposed → infected → recovered) model with probabilistic parameters gathered from real-world data on human mortality and the characteristics of the SARS-CoV-2 disease. With computer simulations, we show the influence of the radius of the neighborhood on the number of infected and deceased agents in the artificial population. The increase in the radius of the neighborhood favors the spread of the pandemic. However, for a large range of interactions of exposed agents (who neither have symptoms of the disease nor have been diagnosed by appropriate tests), even isolation of infected agents cannot prevent successful disease propagation. This supports aggressive testing against disease as one of the useful strategies to prevent large peaks of infection in the spread of SARS-CoV-2-like diseases.     

Conservative Langevin dynamics of solid-on-solid interfaces

We study the dynamics of an interface between two phases in interaction with a wall in the case when the evolution is dominated by surface diffusion. For this, we use an SOS model governed by a conservative Langevin equation and suitable boundary conditions. In the partial wetting case, we study various scaling regimes and show oscillatory behavior in the relaxation of the interface toward its equilibrium shape. We also consider complete wetting and the structure of the precursor film.     

Steady States in SIRS Epidemical Model of Mobile Individuals

We consider an epidemical model within socially interacting mobile individuals to study the behaviors of steady states of epidemic propagation in 2D networks. Using mean-field approximation and large scale simulations, we recover the usual epidemic behavior with critical thresholds δ_c and p_c below which infectious disease dies out. For the population density δ far above δ_c, it is found that there is linear relationship between contact rate λ and the population density δ in the main. At the same time, the result obtained from mean-field approximation is compared with our numerical result, and it is found that these two results are similar by and large but not completely the same.     

A random walk evolution model of wireless sensor networks and virus spreading

In this paper, considering both cluster heads and sensor nodes, we propose a novel evolving a network model based on a random walk to study the fault tolerance decrease of wireless sensor networks (WSNs) due to node failure, and discuss the spreading dynamic behavior of viruses in the evolution model. A theoretical analysis shows that the WSN generated by such an evolution model not only has a strong fault tolerance, but also can dynamically balance the energy loss of the entire network. It is also found that although the increase of the density of cluster heads in the network reduces the network efficiency, it can effectively inhibit the spread of viruses. In addition, the heterogeneity of the network improves the network efficiency and enhances the virus prevalence. We confirm all the theoretical results with sufficient numerical simulations.