Analysis and Monte Carlo simulations of a model for the spread of infectious diseases in heterogeneous metapopulations

We present a study of the continuous-time equations governing the dynamics of a susceptible infected-susceptible model on heterogeneous metapopulations. These equations have been recently proposed as an alternative formulation for the spread of infectious diseases in metapopulations in a continuous-time framework. Individual-based Monte Carlo simulations of epidemic spread in uncorrelated networks are also performed revealing a good agreement with analytical predictions under the assumption of simultaneous transmission or recovery and migration processes

Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

Epidemic models with an infected-infectious period

The introduction of an infective-infectious period on the geographic spread of epidemics is considered in two different models. The classical evolution equations arising in the literature are generalized and the existence of epidemic wave fronts is revised. The asymptotic speed is obtained and improves previous results for the Black Death plague

The Three Horsemen of Growth: Plague, War and Urbanization in Early Modern Europe

How did Europe overtake China? We construct a simple Malthusian model with two sectors, and use it to explain how European per capita incomes and urbanization rates could surge ahead of Chinese ones. That living standards could exceed subsistence levels at all in a Malthusian setting should be surprising. Rising fertility and falling mortality ought to have reversed any gains. We show that productivity growth in Europe can only explain a small fraction of rising living standards. Population dynamics - changes of the birth and death schedules - were far more important drivers of the longrun Malthusian equilibrium. The Black Death raised wages substantially, creating important knock-on effects. Because of Engel's Law, demand for urban products increased, raising urban wages and attracting migrants from rural areas. European cities were unhealthy, especially compared to Far Eastern ones. Urbanization pushed up aggregate death rates. This effect was reinforced by more frequent wars (fed by city wealth) and disease spread by trade. Thus, higher wages themselves reduced population pressure. Without technological change, our model can account for the sharp rise in European urbanization as well as permanently higher per capita incomes. We complement our calibration exercise with a detailed analysis of intra-European growth in the early modern period. Using a panel of European states in the period 1300-1700, we show that war frequency can explain a good share of the divergent fortunes within Europe.

The three horsemen of riches: Plague, war and urbanization in early modern Europe

How did Europe escape the "Iron Law of Wages?" We construct a simple Malthusian model withtwo sectors and multiple steady states, and use it to explain why European per capita incomes andurbanization rates increased during the period 1350-1700. Productivity growth can only explain a smallfraction of the rise in output per capita. Population dynamics changes of the birth and death schedules were far more important determinants of steady states. We show how a major shock to population cantrigger a transition to a new steady state with higher per-capita income. The Black Death was such ashock, raising wages substantially. Because of Engel's Law, demand for urban products increased, andurban centers grew in size. European cities were unhealthy, and rising urbanization pushed up aggregatedeath rates. This effect was reinforced by diseases spread through war, financed by higher tax revenues.In addition, rising trade also spread diseases. In this way higher wages themselves reduced populationpressure. We show in a calibration exercise that our model can account for the sustained rise in Europeanurbanization as well as permanently higher per capita incomes in 1700, without technological change.Wars contributed importantly to the "Rise of Europe", even if they had negative short-run effects. We thustrace Europe s precocious rise to economic riches to interactions of the plague shock with the belligerentpolitical environment and the nature of cities.

Dispersal probability distributions and the wave-front speed problem

The speed and width of front solutions to reaction-dispersal models are analyzed both analytically and numerically. We perform our analysis for Laplace and Gaussian distribution kernels, both for delayed and nondelayed models. The results are discussed in terms of the characteristic parameters of the models

Monitoring mortality as an indicator of influenza in Catalonia, Spain.

This study aimed to investigate the behaviour of two indicators of influenza activity in the area of Barcelona and to evaluate the usefulness of modelling them to improve the detection of influenza epidemics. DESIGN: Descriptive time series study using the number of deaths due to all causes registered by funeral services and reported cases of influenza-like illness. The study concentrated on five influenza seasons, from week 45 of 1988 to week 44 of 1993. The weekly number of deaths and cases of influenza-like illness registered were processed using identification of a time series ARIMA model. SETTING: Six large towns in the Barcelona province which have more than 60,000 inhabitants and funeral services in all of them. MAIN RESULTS: For mortality, the proposed model was an autoregressive one of order 2 (ARIMA (2,0,0)) and for morbidity it was one of order 3 (ARIMA (3,0,0)). Finally, the two time series were analysed together to facilitate the detection of possible implications between them. The joint study of the two series shows that the mortality series can be modelled separately from the reported morbidity series, but the morbidity series is influenced as much by the number of previous cases of influenza reported as by the previous mortality registered. CONCLUSIONS: The model based on general mortality is useful for detecting epidemic activity of influenza. However, because there is not an absolute gold standard that allows definition of the beginning of the epidemic, the final decision of when it is considered an epidemic and control measures recommended should be taken after evaluating all the indicators included in the influenza surveillance programme.

Time-delayed fronts from biased random walks

We generalize a previous model of time-delayed reaction–diffusion fronts (Fort and Méndez 1999 Phys. Rev. Lett. 82 867) to allow for a bias in the microscopic random walk of particles or individuals. We also present a second model which takes the time order of events (diffusion and reproduction) into account. As an example, we apply them to the human invasion front across the USA in the 19th century. The corrections relative to the previous model are substantial. Our results are relevant to physical and biological systems with anisotropic fronts, including particle diffusion in disordered lattices, population invasions, the spread of epidemics, etc

Actualización sobre la gripe del virus A: experiencia de una pandemia desde la perspectiva enfermera

En abril de 2009 la Organización Mundial de la Salud (OMS) emite su primer comunicado, donde advierte la presencia de un brote epidémico por un nuevo virus de gripe A (H1N1) en EE.UU y México, declarando una Emergencia de Salud Pública de importancia internacional. Dos meses después la OMS elevó la alerta por este virus a nivel 6, el máximo de la escala que configura una pandemia, tras comprobar la transmisión elevada y sostenida del virus en el mundo. Actualmente, los Comités y Subcomités de Expertos están trabajando en la elaboración y actualización de protocolos específicos y en la implementación de medidas, tanto clínicas como sociales, que ayuden a gestionar la pandemia. Los objetivos de este trabajo son realizar una revisión de los antecedentes y situación actual de la gripe del virus A, para reflexionar sobre los aspectos más controvertidos que han aparecido en el transcurso de esta pandemia y reforzar los conocimientos de los profesionales enfermeros.

La modelización de la propagación de epidemias

Sobre l' estudi de la propagació de les epidèmies utilitzant models matemàtics

Approximate solution to the speed of spreading viruses

Recently, it has been shown that the speed of virus infections can be explained by time-delayed reactiondiffusion [J. Fort and V. Me´ndez, Phys. Rev. Lett. 89, 178101 (2002)], but no analytical solutions were found. Here we derive formulas for the front speed, valid in appropriate limits. We also integrate numerically the evolution equations of the system. There is good agreement with both numerical and experimental speeds

Time-Delayed Spread of Viruses in Growing Plaques

The spread of viruses in growing plaques predicted by classical models is greater than that measured experimentally. There is a widespread belief that this discrepancy is due to biological factors. Here we show that the observed speeds can be satisfactorily predicted by a purely physical model that takes into account the delay time due to virus reproduction inside infected cells. No free or adjustable parameters are used