Spatial Spread Of Infectious Diseases Research Articles

Stabilization of a reaction–diffusion system modelling a class of spatially structured epidemic systems via feedback control

A two-component reaction–diffusion system modelling a class of spatially structured epidemic systems is considered. The system describes the spatial spread of infectious diseases mediated by environmental pollution. A relevant problem, related to the possible eradication of the epidemic, is the so called zero stabilization. In a series of papers, necessary conditions, and sufficient conditions of stabilizability have been obtained. It has been proved that it is possible to diminish exponentially the epidemic process in the whole habitat, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain. The stabilizability with a feedback control of the harvesting type is related to the magnitude of the principal eigenvalue of a certain operator which is not selfadjoint. In this paper, we have proposed an approximating method for this principal eigenvalue. Further, we have faced the problem of finding the optimal position (by translation) of the support of the feedback stabilizing control in order to minimize both the infected population and the pollutant at a certain finite time.

Natural Human Mobility Patterns and Spatial Spread of Infectious Diseases

We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of the model on regular and complex metapopulation network topologies and show that significant dynamical differences exist to ordinary reaction-diffusion and effective force of infection models. On a lattice we calculate an expression for the velocity of the propagating epidemic front and find that in contrast to the diffusive systems, our model predicts a saturation of the velocity with increasing traveling rate. Furthermore, we show that a fully stochastic system exhibits a novel threshold for attack ratio of an outbreak absent in diffusion and force of infection models. These insights not only capture natural features of human mobility relevant for the geographical epidemic spread, they may serve as a starting point for modeling important dynamical processes in human and animal epidemiology, population ecology, biology and evolution.

Phase transitions in contagion processes mediated by recurrent mobility patterns

Human mobility and activity patterns mediate contagion on many levels, including: spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations and recurrent flows and poorly modeled by the random diffusive dynamics generally used to study them. Here we develop a theoretical framework to analyze contagion within a network of locations where individuals recall their geographic origins. We find a phase transition between a regime in which the contagion affects a large fraction of the system and one in which only a small fraction is affected. This transition cannot be uncovered by continuous models due to the stochastic features of the contagion process and defines an invasion threshold that depends on mobility parameters, providing guidance for controlling contagion spread by constraining mobility processes. We recover the threshold behavior by analyzing diffusion processes mediated by real human commuting data.

The Structure of Borders in a Small World

Territorial subdivisions and geographic borders are essential for understanding phenomena in sociology, political science, history, and economics. They influence the interregional flow of information and cross-border trade and affect the diffusion of innovation and technology. However, it is unclear if existing administrative subdivisions that typically evolved decades ago still reflect the most plausible organizational structure of today. The complexity of modern human communication, the ease of long-distance movement, and increased interaction across political borders complicate the operational definition and assessment of geographic borders that optimally reflect the multi-scale nature of today's human connectivity patterns. What border structures emerge directly from the interplay of scales in human interactions is an open question. Based on a massive proxy dataset, we analyze a multi-scale human mobility network and compute effective geographic borders inherent to human mobility patterns in the United States. We propose two computational techniques for extracting these borders and for quantifying their strength. We find that effective borders only partially overlap with existing administrative borders, and show that some of the strongest mobility borders exist in unexpected regions. We show that the observed structures cannot be generated by gravity models for human traffic. Finally, we introduce the concept of link significance that clarifies the observed structure of effective borders. Our approach represents a novel type of quantitative, comparative analysis framework for spatially embedded multi-scale interaction networks in general and may yield important insight into a multitude of spatiotemporal phenomena generated by human activity.

Modeling the spatial spread of infectious diseases: The GLobal Epidemic and Mobility computational model

Here we present the Global Epidemic and Mobility (GLEaM) model that integrates sociodemographic and population mobility data in a spatially structured stochastic disease approach to simulate the spread of epidemics at the worldwide scale. We discuss the flexible structure of the model that is open to the inclusion of different disease structures and local intervention policies. This makes GLEaM suitable for the computational modeling and anticipation of the spatio-temporal patterns of global epidemic spreading, the understanding of historical epidemics, the assessment of the role of human mobility in shaping global epidemics, and the analysis of mitigation and containment scenarios.

On the stabilization of reaction–diffusion systems modeling a class of man‐environment epidemics: A review

AbstractA two‐component reaction–diffusion system modeling a class of spatially structured epidemic systems is considered. The system describes the spatial spread of infectious diseases mediated by environmental pollution. A relevant problem, related to the possible eradication of the epidemic, is the so‐called zero‐stabilization. In a series of papers, necessary conditions and sufficient conditions of stabilizability have been obtained. It has been proved that it is possible to diminish exponentially the epidemic process, in the whole habitat, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain.In order to model the possible seasonal variability of the environmental conditions, the relevant parameters need to be assumed to be periodic, all with the same period. Corresponding results for the time homogeneous case are presented too. Copyright © 2010 John Wiley & Sons, Ltd.

Multiscale mobility networks and the spatial spreading of infectious diseases

Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. To study the interplay between short-scale commuting flows and long-range airline traffic in shaping the spatiotemporal pattern of a global epidemic we ( i ) analyze mobility data from 29 countries around the world and find a gravity model able to provide a global description of commuting patterns up to 300 kms and ( ii ) integrate in a worldwide-structured metapopulation epidemic model a timescale-separation technique for evaluating the force of infection due to multiscale mobility processes in the disease dynamics. Commuting flows are found, on average, to be one order of magnitude larger than airline flows. However, their introduction into the worldwide model shows that the large-scale pattern of the simulated epidemic exhibits only small variations with respect to the baseline case where only airline traffic is considered. The presence of short-range mobility increases, however, the synchronization of subpopulations in close proximity and affects the epidemic behavior at the periphery of the airline transportation infrastructure. The present approach outlines the possibility for the definition of layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multiscale framework.

Modeling Spatial Spread of Infectious Diseases with a Fixed Latent Period in a Spatially Continuous Domain

In this paper, with the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of the population may diffuse, we formulate an SIR model with a simple demographic structure for the population living in a spatially continuous environment. The model is given by a system of reaction-diffusion equations with a discrete delay accounting for the latency and a spatially non-local term caused by the mobility of the individuals during the latent period. We address the existence, uniqueness, and positivity of solution to the initial-value problem for this type of system. Moreover, we investigate the traveling wave fronts of the system and obtain a critical value c * which is a lower bound for the wave speed of the traveling wave fronts. Although we can not prove that this value is exactly the minimal wave speed, numeric simulations seem to suggest that it is. Furthermore, the simulations on the PDE model also suggest that the spread speed of the disease indeed coincides with c *. We also discuss how the model parameters affect c *.

A stabilization strategy for a reaction–diffusion system modelling a class of spatially structured epidemic systems ( think globally, act locally)

A two-component reaction–diffusion system modelling a class of spatially structured epidemic systems is considered. The system describes the spatial spread of infectious diseases mediated by environmental pollution. The internal zero stabilization is investigated. We provide necessary conditions of stabilizability and sufficient conditions of stabilizability. In the affirmative case a simple feedback stabilizing control is indicated. It shows that it is possible to diminish exponentially the epidemic process, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain ( think globally, act locally).

Note on the stabilization of a reaction–diffusion model in epidemiology

In this paper we investigate a stabilization problem for a spatially structured epidemic system, modelling the spatial spread of infectious diseases mediated by environmental pollution. We provide an internal stabilizability result and in affirmative case a simple feedback stabilizing control, i.e., we show that it is possible to diminish exponentially the epidemic process, by reducing the concentration of the pollutant in a nonempty and large enough subset of the spatial domain.

Effect of variability in infection period on the persistence and spatial spread of infectious diseases.

The effects of the mean infection (incubation plus infectious) period on the dynamics of infectious diseases are well understood. We examine the dynamics and persistence of epidemics when the distribution of the infection period also is modelled, using the well-documented childhood disease measles as a test case. We pay particular attention to the differences between exponentially distributed and constant periods. The use of constant periods increases the persistence of epidemics by reducing the individual stochasticity. The infection period distribution is also shown to have a significant effect on the spatial spread of disease.

A diffusive age-structured SEIRS epidemic model

A model of an epidemic disease is analyzed with the following fea- tures: (1) the susceptible and infective populations are diffusing in a spatial region and (2) infected individuals pass through an incubation period before becoming infectives throughout the spatial region. The model consists of a system of nonlin- ear partial differential equations in which the infective population is structured by age since first infected. It is proved that the infective population converges to zero and the susceptible population converges to a constant positive value throughout the region. The extinction of the infective population is due to the uniformly positive rate of their removal. We analyze a system of partial differential equations modeling the spatial spread of infectious disease through a population structured by age of infection. The population is confined to a bounded region in R n . We divide the population into susceptible, exposed, and infective subclasses, having density functions S(x, t), E(x, t), and I(x, t) respectively, for x ∈ and t ≥ 0. The total populations of the subclasses at time t are obtained by integrating the densities over . We envision the following scenario. The susceptible class consists of individuals capable of becoming infected, the exposed class is made up of individuals who have contracted the disease but who are not yet capable of transmitting it, and the infective class consists of individuals capable of transmitting the disease. We shall assume that at a rate proportional to the product of the susceptible and the infective populations, individuals leave the susceptible class and enter the exposed class. We stipulate that individuals, after remaining in the exposed class for a fixed incubation or latency period of length τ, enter the infective class where they remain for the finite length of time σ. Individuals are removed from both the latent and infective phases of the disease with a constant mortality rate λ and the probability of mortality is independent of the length of time the individual has been in either of these phases. At the conclusion of the infective period, individuals pass back into the susceptible class and do not enter a removed or immune class. Properly speaking, this process may be described as an SEIRS (susceptible, exposed, infective, removed, susceptible) disease model which describes the progression of a potentially fatal disease offering the possibility of recovery but no immunity. However, because the individuals comprising the removed class no longer affect the dynamics of the spread of the disease, we do not need to include the removed class in the modeling process.

Host Dispersal and the Spatial Spread of Insect Pathogens

Empirical studies of the spatial spread of insect pathogens have emphasized the importance of high dispersal rates, but typically rely strictly on observational data. In contrast, existing mathematical models on the spatial spread of infectious diseases have suggested that a highly infectious disease can spread rapidly even if the dispersal rate of its host is low; such models, however, are largely untested. To understand how host dispersal and disease infectiousness affect the spatial spread of infectious disease, we performed a field experiment in which we released a nuclear polyhedrosis virus (NPV) into two experimentally established, disease—free gypsy moth (Lymantria dispar) populations. We simultaneously and independently measured the long—distance dispersal of ballooning, first—instar, gypsy moth larvae, the stage in which dispersal is by far the greatest. Surprisingly, dispersal by ballooning was a good predictor of NPV spread only in the first few weeks of spread. Subsequently, the virus spread much farther and less directionally than did ballooning larvae. No infections appeared in control plots that started with only uninfected larvae, confirming that the virus we released caused the epizootic in our experimental populations. On the theory that additional spread was due to a combination of small—scale larval dispersal and a high rate of disease transmission, we compared our data to the predictions of a mathematical model for the spatial spread of insect pathogens that combines disease transmission and small—scale host dispersal. By using independent estimates of each of the model parameters, we used the model to make post hoc predictions of the rate of spread of the virus from an initial distribution dictated by larval ballooning. Although the model included both initial long—distance dispersal by larval ballooning and subsequent short—distance dispersal by larval crawling, it poorly matched the observed distribution of the virus. An alternative and as yet untested hypothesis is that the observed spread of the virus may be due to mechanical vectoring by a parasitoid fly, a mechanism for which there are as yet no available mathematical theory or relevant field data.