Epidemics, the Ising-model and percolation theory: A comprehensive review focused on Covid-19

General spatial photonic Ising machine based on the interaction matrix eigendecomposition method

The spatial photonic Ising machine has achieved remarkable advancements in solving combinatorial optimization problems. However, it still remains a huge challenge to flexibly map an arbitrary problem to the Ising model. In this paper, we propose a general spatial photonic Ising machine based on the interaction matrix eigendecomposition method. The arbitrary interaction matrix can be configured in the two-dimensional Fourier transformation based spatial photonic Ising model by using values generated by matrix eigendecomposition. The error in the structural representation of the Hamiltonian decreases substantially with the growing number of eigenvalues utilized to form the Ising machine. In combination with the optimization algorithm, as low as ∼65% of the eigenvalues are required by intensity modulation to guarantee the best probability of optimal solution for a 20-vertex graph Max-cut problem, and this percentage decreases to below ∼20% for near-zero probability. The 4-spin experiments and error analysis demonstrate the Hamiltonian linear mapping and ergodic optimization. Our work provides a viable approach for spatial photonic Ising machines to solve arbitrary combinatorial optimization problems with the help of the multi-dimensional optical property.

Random Lasers as Social Processes Simulators

In this work, we suggest a quantum-like simulator concept to study social processes related to the solution of NP-hard problems. The simulator is based on the solaser model recently proposed by us in the framework of information cascade growth and echo chamber formation in social network communities. The simulator is connected with the random laser approach that we examine in the A and D-class (superradiant) laser limits. Novel network-enforced cooperativity parameters of decision-making agents, which may be measured as a result of the solaser simulation, are introduced and justified for social systems. The innovation diffusion in complex networks is discussed as one of the possible impacts of our proposal.

Effect of carbons' structure and type on AC electrical properties of polymer composites: predicting the percolation threshold of permittivity through different models

The AC electrical properties of EVA- and NBR-based composites filled with different conductive fillers were investigated. Result shows several magnitudes of increment in AC electrical conductivity and dielectric permittivity after the addition of these conductive fillers, indicating that these materials can be used as supercapacitors. The magnitude of increment was varied according to polymer and filler types. Herein, we also have tested the applicability of different sigmoidal models to find out the percolation threshold value of permittivity for these binary polymer composite systems. It is observed that except sigmoidal-Boltzmann and sigmoidal-dose-response models, other sigmoidal models exhibit different values of percolation threshold when considered for any particular polymer composite system. The paper discusses the variation in results of percolation threshold with an emphasis on the advantages, disadvantages and limitations of these models. We also have applied the classical percolation theory to predict the percolation threshold of permittivity and compared with all the reported sigmoidal models. To judge the unanimous acceptability of these models, they tested vis-à-vis the permittivity results of various polymer composites reported in published literature. To comprehend, all the models except the sigmoidal-logistic-1 model were successfully applicable for predicting the percolation threshold of permittivity for polymer composites.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00396-023-05120-2.

Dynamics of a Fractional-Order Delayed Model of COVID-19 with Vaccination Efficacy

In this study, we provide a fractional-order mathematical model that considers the effect of vaccination on COVID-19 spread dynamics. The model accounts for the latent period of intervention strategies by incorporating a time delay τ. A basic reproduction number, R0, is determined for the model, and prerequisites for endemic equilibrium are discussed. The model’s endemic equilibrium point also exhibits local asymptotic stability (under certain conditions), and a Hopf bifurcation condition is established. Different scenarios of vaccination efficacy are simulated. As a result of the vaccination efforts, the number of deaths and those affected have decreased. COVID-19 may not be effectively controlled by vaccination alone. To control infections, several non-pharmacological interventions are necessary. Based on numerical simulations and fitting to real observations, the theoretical results are proven to be effective.

Analysis of mobility based COVID-19 epidemic model using Federated Multitask Learning

Aggregating a massive amount of disease-related data from heterogeneous devices, a distributed learning framework called Federated Learning(FL) is employed. But, FL suffers in distributing the global model, due to the heterogeneity of local data distributions. To overcome this issue, personalized models can be learned by using Federated multitask learning(FMTL). Due to the heterogeneous data from distributed environment, we propose a personalized model learned by federated multitask learning (FMTL) to predict the updated infection rate of COVID-19 in the USA using a mobility-based SEIR model. Furthermore, using a mobility-based SEIR model with an additional constraint we can analyze the availability of beds. We have used the real-time mobility data sets in various states of the USA during the years 2020 and 2021. We have chosen five states for the study and we observe that there exists a correlation among the number of COVID-19 infected cases even though the rate of spread in each case is different. We have considered each US state as a node in the federated learning environment and a linear regression model is built at each node. Our experimental results show that the root-mean-square percentage error for the actual and prediction of COVID-19 cases is low for Colorado state and high for Minnesota state. Using a mobility-based SEIR simulation model, we conclude that it will take at least 400 days to reach extinction when there is no proper vaccination or social distance.

Mean-field theory of social laser

In this work we suggest a novel paradigm of social laser (solaser), which can explain such Internet inspired social phenomena as echo chambers, reinforcement and growth of information cascades, enhancement of social actions under strong mass media operation. The solaser is based on a well-known in quantum physics laser model of coherent amplification of the optical field. Social networks are at the core of the solaser model; we define them by means of a network model possessing power–law degree distribution. In the solaser the network environment plays the same role as the gain medium has in a physical laser device. We consider social atoms as decision making agents (humans or even chat bots), which possess two (mental) states and occupy the nodes of a network. The solaser establishes communication between the agents as absorption and spontaneous or stimulated emission of socially actual information within echo chambers, which mimic an optical resonator of a convenient (physical) laser. We have demonstrated that social lasing represents the second order nonequilibrium phase transition, which evokes the release of coherent socially stimulated information field represented with the order parameter. The solaser implies the formation of macroscopic social polarization and results in a huge social impact, which is realized by viral information cascades occurring in the presence of population imbalance (social bias). We have shown that decision making agents follow an adiabatically time dependent mass media pump, which acts in the network community reproducing various reliable scenarios for information cascade evolution. We have also shown that in contrast to physical lasers, due to node degree peculiarities, the coupling strength of decision making agents with the network may be enhanced \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{\langle k\rangle }$$\end{document}⟨k⟩ times. It leads to a large increase of speed, at which a viral message spreads through a social media. In this case, the mass media pump supports additional reinforcement and acceleration of cascade growth. We have revealed that the solaser model in some approximations possesses clear links with familiar Ising and SIS (susceptible-infected-susceptible) models typically used for evaluating a social impact and information growth, respectively. However, the solaser paradigm can serve as a new platform for modelling temporal social events, which originate from “microscopic” (quantum-like) processes occurring in the society. Our findings open new perspectives for interdisciplinary studies of distributed intelligence agents behavior associated with information exchange and social impact.

Population density impact on COVID-19 mortality rate: A multifractal analysis using French data

The current COVID-19 pandemic caught everyone off guard and is an excellent case study to investigate the real impact of population density on emerging highly contagious infectious diseases. The relationship between the threat of COVID-19 and population density has been widely debated not only in scientific articles, but also in magazines and reports around the world. It appeared both in the columns of experts and in the speeches of politicians, yet without reaching any consensus. In this study, using COVID-19 data from France, we try to shed light on this debate. An alternative density measure, weighted by population, is used. This novel density measure clearly outperforms the commonly used density in terms of relationship with COVID-19 deaths and proved to be competitive with some of the best known predictors, including population. A multifractal analysis, characterizing different space distributions of population in France, is used to further understand the relation between density and COVID-19 mortality rate.

Dynamics of a stochastic COVID-19 epidemic model considering asymptomatic and isolated infected individuals

Coronavirus disease (COVID-19) has a strong influence on the global public health and economics since the outbreak in 2020. In this paper, we study a stochastic high-dimensional COVID-19 epidemic model which considers asymptomatic and isolated infected individuals. Firstly we prove the existence and uniqueness for positive solution to the stochastic model. Then we obtain the conditions on the extinction of the disease as well as the existence of stationary distribution. It shows that the noise intensity conducted on the asymptomatic infections and infected with symptoms plays an important role in the disease control. Finally numerical simulation is carried out to illustrate the theoretical results, and it is compared with the real data of India.

The impact of vaccination on the spread of COVID-19: Studying by a mathematical model

The global spread of COVID-19 has not been effectively controlled, posing a huge threat to public health and the development of the global economy. Currently, a number of vaccines have been approved for use and vaccination campaigns have already started in several countries. This paper designs a mathematical model considering the impact of vaccination to study the spread dynamics of COVID-19. Some basic properties of the model are analyzed. The basic reproductive number ℜ 1 of the model is obtained, and the conditions for the existence of endemic equilibria are provided. There exist two endemic equilibria when ℜ 1 < 1 under certain conditions, which will lead to backward bifurcation. The stability of equilibria are analyzed, and the condition for the backward bifurcation is given. Due to the existence of backward bifurcation, even if ℜ 1 < 1 , COVID-19 may remain prevalent. Sensitivity analysis and simulations show that improving vaccine efficacy can control the spread of COVID-19 faster, while increasing the vaccination rate can reduce and postpone the peak of infection to a greater extent. However, in reality, the improvement of vaccine efficacy cannot be realized in a short time, and relying only on increasing the vaccination rate cannot quickly achieve the control of COVID-19. Therefore, relying only on vaccination may not completely and quickly control COVID-19. Some non-pharmaceutical interventions should continue to be enforced to combat the virus. According to the sensitivity analysis, we improve the model by including some non-pharmaceutical interventions. Combining the sensitivity analysis with the simulation of the improved model, we conclude that together with vaccination, reducing the contact rate of people and increasing the isolation rate of infected individuals will greatly reduce the number of infections and shorten the time of COVID-19 spread. The analysis and simulations in this paper can provide some useful suggestions for the prevention and control of COVID-19.

Assessing vaccination priorities for different ages and age-specific vaccination strategies of COVID-19 using an SEIR modelling approach

In the past year, the global epidemic situation is still not optimistic, showing a trend of continuous expansion. With the research and application of vaccines, there is an urgent need to develop some optimal vaccination strategies. How to make a reasonable vaccination strategy to determine the priority of vaccination under the limited vaccine resources to control the epidemic and reduce human casualties? We build a dynamic model with vaccination which is extended the classical SEIR model. By fitting the epidemic data of three countries—China, Brazil, Indonesia, we have evaluated age-specific vaccination strategy for the number of infections and deaths. Furthermore, we have evaluated the impact of age-specific vaccination strategies on the number of the basic reproduction number. At last, we also have evaluated the different age structure of the vaccination priority. It shows that giving priority to vaccination of young people can control the number of infections, while giving priority to vaccination of the elderly can greatly reduce the number of deaths in most cases. Furthermore, we have found that young people should be mainly vaccinated to reduce the number of infections. When the emphasis is on reducing the number of deaths, it is important to focus vaccination on the elderly. Simulations suggest that appropriate age-specific vaccination strategies can effectively control the epidemic, both in terms of the number of infections and deaths.

Heterogeneity matters: Contact structure and individual variation shape epidemic dynamics

In the recent COVID-19 pandemic, mathematical modeling constitutes an important tool to evaluate the prospective effectiveness of non-pharmaceutical interventions (NPIs) and to guide policy-making. Most research is, however, centered around characterizing the epidemic based on point estimates like the average infectiousness or the average number of contacts. In this work, we use stochastic simulations to investigate the consequences of a population's heterogeneity regarding connectivity and individual viral load levels. Therefore, we translate a COVID-19 ODE model to a stochastic multi-agent system. We use contact networks to model complex interaction structures and a probabilistic infection rate to model individual viral load variation. We observe a large dependency of the dispersion and dynamical evolution on the population's heterogeneity that is not adequately captured by point estimates, for instance, used in ODE models. In particular, models that assume the same clinical and transmission parameters may lead to different conclusions, depending on different types of heterogeneity in the population. For instance, the existence of hubs in the contact network leads to an initial increase of dispersion and the effective reproduction number, but to a lower herd immunity threshold (HIT) compared to homogeneous populations or a population where the heterogeneity stems solely from individual infectivity variations.