The population dynamics underlying the diffusion of ideas hold many qualitative similarities to those involved in the spread of infections. In spite of much suggestive evidence this analogy is hardly ever quantified in useful ways. The standard benefit of modeling epidemics is the ability to estimate quantitatively population average parameters, such as interpersonal contact rates, incubation times, duration of infectious periods, etc. In most cases such quantities generalize naturally to the spread of ideas and provide a simple means of quantifying sociological and behavioral patterns. Here we apply several paradigmatic models of epidemics to empirical data on the advent and spread of Feynman diagrams through the theoretical physics communities of the USA, Japan, and the USSR in the period immediately after World War II. This test case has the advantage of having been studied historically in great detail, which allows validation of our results. We estimate the effectiveness of adoption of the idea in the three communities and find values for parameters reflecting both intentional social organization and long lifetimes for the idea. These features are probably general characteristics of the spread of ideas, but not of common epidemics.
The aim of this paper consists in the application of a recent epidemiological model, namely SEIR with Social Distancing (SEIR--SD), extended here through the definition of a social distancing function varying over time, to assess the situation related to the spreading of the coronavirus Covid--19 in Italy and in two of its most important regions, i.e., Lombardy and Campania. To profitably use this model, the most suitable values of its parameters must be found. The estimation of the SEIR--SD model parameters takes place here through the use of Differential Evolution, a heuristic optimization t…
Motivated by our intention to use SIR-type epidemiological models in the context of dynamic networks as provided by large-scale highly interacting inhomogeneous human crowds, we investigate in this framework possibilities to reduce the classical SIR model to a representative evolution model for a suitably chosen observable. For selected scenarios, we provide practical {\em a priori} error bounds between the approximate and the original observables. Finally, we illustrate numerically the behavior of the reduced models compared to the original ones.
In this work, we adapt the epidemiological SIR model to study the evolution of the dissemination of COVID-19 in Germany and Brazil (nationally, in the State of Paraiba, and in the City of Campina Grande). We prove the well posedness and the continuous dependence of the model dynamics on its parameters. We also propose a simple probabilistic method for the evolution of the active cases that is instrumental for the automatic estimation of parameters of the epidemiological model. We obtained statistical estimates of the active cases based the probabilistic method and on the confirmed cases data. …
Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc. is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous …
An epidemiological model is developed for the spread of COVID-19 in South Africa. A variant of the classical compartmental SEIR model, called the SEIQRDP model, is used. As South Africa is still in the early phases of the global COVID-19 pandemic with the confirmed infectious cases not having peaked, the SEIQRDP model is first parameterized on data for Germany, Italy, and South Korea - countries for which the number of infectious cases are well past their peaks. Good fits are achieved with reasonable predictions of where the number of COVID-19 confirmed cases, deaths, and recovered cases will …
As a large-scale instance of dramatic collective behaviour, the 2005 French riots started in a poor suburb of Paris, then spread in all of France, lasting about three weeks. Remarkably, although there were no displacements of rioters, the riot activity did travel. Access to daily national police data has allowed us to explore the dynamics of riot propagation. Here we show that an epidemic-like model, with just a few parameters and a single sociological variable characterizing neighbourhood deprivation, accounts quantitatively for the full spatio-temporal dynamics of the riots. This is the firs…
The unprecedented coronavirus disease 2019 (COVID-19) pandemic is still a worldwide threat to human life since its invasion into the daily lives of the public in the first several months of 2020. Predicting the size of confirmed cases is important for countries and communities to make proper prevention and control policies so as to effectively curb the spread of COVID-19. Different from the 2003 SARS epidemic and the worldwide 2009 H1N1 influenza pandemic, COVID-19 has unique epidemiological characteristics in its infectious and recovered compartments. This drives us to formulate a new infecti…
We develop a multiple compartment Susceptible-Infected-Recovered (SIR) model to analyze the spread of several infectious diseases through different geographic areas. Additionally, we propose a data-quality sensitive optimization framework for fitting this model to observed data. We fit the model to the temporal profile of the number of people infected by one of six influenza strains in Europe over $7$ influenza seasons. In addition to describing the temporal and spatial spread of influenza, the model provides an estimate of the inter-country and intra-country infection and recovery rates of ea…
We introduce a Python package for modeling and studying the spread of infectious diseases using an agent-based SEIR style epidemiological model with a focus on university campuses. This document explains the epidemiological model used in the package and gives examples highlighting the ways that the package can be used.
The outbreak of the coronavirus disease 2019 (COVID-19) has now spread throughout the globe infecting over 150 million people and causing the death of over 3.2 million people. Thus, there is an urgent need to study the dynamics of epidemiological models to gain a better understanding of how such diseases spread. While epidemiological models can be computationally expensive, recent advances in machine learning techniques have given rise to neural networks with the ability to learn and predict complex dynamics at reduced computational costs. Here we introduce two digital twins of a SEIRS model a…
Mathematical epidemiological models have a broad use, including both qualitative and quantitative applications. With the increasing availability of data, large-scale quantitative disease spread models can nowadays be formulated. Such models have a great potential, e.g., in risk assessments in public health. Their main challenge is model parameterization given surveillance data, a problem which often limits their practical usage. We offer a solution to this problem by developing a Bayesian methodology suitable to epidemiological models driven by network data. The greatest difficulty in obtainin…
We propose a compartmental mathematical model for the spread of the COVID-19 disease, showing its usefulness with respect to the pandemic in Portugal, from the first recorded case in the country till the end of the three states of emergency. New results include the compartmental model, described by a system of seven ordinary differential equations; proof of positivity and boundedness of solutions; investigation of equilibrium points and their stability analysis; computation of the basic reproduction number; and numerical simulations with official real data from the Portuguese health authoritie…
In this paper, we develop an extension of standard epidemiological models, suitable for COVID-19. This extension incorporates the transmission due to pre-symptomatic or asymptomatic carriers of the virus. Furthermore, this model also captures the spread of the disease due to the movement of people to/from different administrative boundaries within a country. The model describes the probabilistic rise in the number of confirmed cases due to the concomitant effects of (incipient) human transmission and multiple compartments. The associated parameters in the model can help architect the public he…
In [Ecological Complexity 44 (2020) Art. 100885, DOI: 10.1016/j.ecocom.2020.100885] a continuous-time compartmental mathematical model for the spread of the Coronavirus disease 2019 (COVID-19) is presented with Portugal as case study, from 2 March to 4 May 2020, and the local stability of the Disease Free Equilibrium (DFE) is analysed. Here, we propose an analogous discrete-time model and, using a suitable Lyapunov function, we prove the global stability of the DFE point. Using COVID-19 real data, we show, through numerical simulations, the consistence of the obtained theoretical results.
Understanding individual decisions in a world where communications and information move instantly via cell phones and the internet, contributes to the development and implementation of policies aimed at stopping or ameliorating the spread of diseases. In this manuscript, the role of official social network perturbations generated by public health officials to slow down or stop a disease outbreak are studied over distinct classes of static social networks. The dynamics are stochastic in nature with individuals (nodes) being assigned fixed levels of education or wealth. Nodes may change their ep…
Nowcasting and forecasting of epidemic spreading rely on incidence series of reported cases to derive the fundamental epidemiological parameters for a given pathogen. Two relevant drawbacks for predictions are the unknown fractions of undocumented cases and levels of nonpharmacological interventions, which span highly heterogeneously across different places and times. We describe a simple data-driven approach using a compartmental model including asymptomatic and presymptomatic contagions that allows to estimate both the level of undocumented infections and the value of effective reproductive …
We present a compartmental meta-population model for the spread of Covid-19 in India. Our model simulates populations at a district or state level using an epidemiological model that is appropriate to Covid-19. Different districts are connected by a transportation matrix developed using available census data. We introduce uncertainties in the testing rates into the model that takes into account the disparate responses of the different states to the epidemic and also factors in the state of the public healthcare system. Our model allows us to generate qualitative projections of Covid-19 spread …
The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations (ODE's) in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account…
To curb the spread of COVID-19, many governments around the world have implemented tiered lockdowns with varying degrees of stringency. Lockdown levels are typically increased when the disease spreads and reduced when the disease abates. A predictive control approach is used to develop optimized lockdown strategies for curbing the spread of COVID-19. The strategies are then applied to South African data. The South African case is of interest as the South African government has defined five distinct levels of lockdown, which serves as a discrete control input. An epidemiological model for the s…
In this work, we simulate the COVID-19 pandemic dynamics in a population modeled as a network of groups wherein infection can propagate both via intra-group and via inter-group interactions. Our results emphasize the importance of diminishing the inter-group infections in the effort of substantial flattening and delaying of the epi(demiologic) curve with concomitant mitigation of disastrous economy and social consequences. To exemplify with a limiting case, splitting a population into m (say, 5 or 10) noninteracting groups while keeping intra-group interaction unchanged yields a stretched epid…
Without vaccines and treatments, societies must rely on non-pharmaceutical intervention strategies to control the spread of emerging diseases such as COVID-19. Though complete lockdown is epidemiologically effective, because it eliminates infectious contacts, it comes with significant costs. Several recent studies have suggested that a plausible compromise strategy for minimizing epidemic risk is periodic closure, in which populations oscillate between wide-spread social restrictions and relaxation. However, no underlying theory has been proposed to predict and explain optimal closure periods …
Understanding the impact of collective social phenomena in epidemic dynamics is a crucial task to effectively contain the disease spread. In this work we build a mathematical description for assessing the interplay between opinion polarization and the evolution of a disease. The proposed kinetic approach describes the evolution of aggregate quantities characterizing the agents belonging to epidemiologically relevant states, and will show that the spread of the disease is closely related to consensus dynamics distribution in which opinion polarization may emerge. In the present modelling framew…
The COVID-19 pandemic has forced public health experts to develop contingent policies to stem the spread of infection, including measures such as partial/complete lockdowns. The effectiveness of these policies has varied with geography, population distribution, and effectiveness in implementation. Consequently, some nations (e.g., Taiwan, Haiti) have been more successful than others (e.g., United States) in curbing the outbreak. A data-driven investigation into effective public health policies of a country would allow public health experts in other nations to decide future courses of action to…
We performed a thorough sensitivity analysis of the herd immunity threshold for discrete-time SIR compartmental models with a static network structure. We find unexpectedly that these models violate classical intuition which holds that the herd immunity threshold should monotonically increase with the transmission parameter. We find the existence of bifurcations in the herd immunity threshold in the high transmission probability regime. The extent of these bifurcations is modulated by the graph heterogeneity, the recovery parameter, and the network size. In the limit of large, well-mixed netwo…
Passenger contact in public transit (PT) networks can be a key mediate in the spreading of infectious diseases. This paper proposes a time-varying weighted PT encounter network to model the spreading of infectious diseases through the PT systems. Social activity contacts at both local and global levels are also considered. We select the epidemiological characteristics of coronavirus disease 2019 (COVID-19) as a case study along with smart card data from Singapore to illustrate the model at the metropolitan level. A scalable and lightweight theoretical framework is derived to capture the time-v…
Using the notion of effective distance proposed by Brockmann and Helbing, complex spatiotemporal processes of epidemic spreading can be reduced to circular wave propagation patterns with well-defined wavefronts. This hidden homogeneity of contagion phenomena enables the mapping of virtual mobility networks to physical propagation channels. Subsequently, we propose a novel communications-inspired model of epidemic spreading and mitigation by establishing the one-to-one correspondence between the essential components comprising information and disease transmissions. The epidemic processes can be…
Epidemiological contact network models have emerged as an important tool in understanding and predicting the spread of infectious disease, due to their capacity to engage individual heterogeneity that may underlie essential dynamics of a particular host-pathogen system. Just as fundamental are the changes that real-world contact networks undergo over time, both independently of and in response to pathogen spreading. These dynamics play a central role in determining whether a disease will die out or become an epidemic within a population, known as the epidemic threshold. In this paper, we provi…
We study a dynamics of the epidemiological infection spreading at different values of the risk factor $β$ (a control parameter) with the using of dynamic Monte Carlo approach (DMC). In our toy model, the infection transmits due to contacts of randomly moving individuals. We show that the behavior of recovereds critically depends on the $β$ value. For sub-critical values $β<β_{c}\sim 0.6$, the number of infected cases asymptotically converges to zero, such that for a moderate risk factor the infection may disappear with time. Our simulations shown that over time, the properties of such a system…
