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Models of epidemics: when contact repetition and clustering should be included
Timo Smieszek, Lena Fiebig, Roland W Scholz
Theoretical Biology and Medical Modelling , 2009, DOI: 10.1186/1742-4682-6-11
Abstract: We compare two different types of individual-based models: One assumes random mixing without repetition of contacts, whereas the other assumes that the same contacts repeat day-by-day. The latter exists in two variants, with and without clustering. We systematically test and compare how the total size of an outbreak differs between these model types depending on the key parameters transmission probability, number of contacts per day, duration of the infectious period, different levels of clustering and varying proportions of repetitive contacts.The simulation runs under different parameter constellations provide the following results: The difference between both model types is highest for low numbers of contacts per day and low transmission probabilities. The number of contacts and the transmission probability have a higher influence on this difference than the duration of the infectious period. Even when only minor parts of the daily contacts are repetitive and clustered can there be relevant differences compared to a purely random mixing model.We show that random mixing models provide acceptable estimates of the total outbreak size if the number of contacts per day is high or if the per-contact transmission probability is high, as seen in typical childhood diseases such as measles. In the case of very short infectious periods, for instance, as in Norovirus, models assuming repeating contacts will also behave similarly as random mixing models. If the number of daily contacts or the transmission probability is low, as assumed for MRSA or Ebola, particular consideration should be given to the actual structure of potentially contagious contacts when designing the model.The spread of infectious disease is determined by an interplay of biological and social factors [1]. Biological factors are, among others, the virulence of an infectious agent, pre-existing immunity and the pathways of transmission. A major social factor influencing disease spread is the arrangement of
Should tumor depth be included in prognostication of soft tissue sarcoma?
Anders Rydholm, Pelle Gustafson
BMC Cancer , 2003, DOI: 10.1186/1471-2407-3-17
Abstract: We analyzed the associations between tumor size and depth and the prognostic importance of grade, size and depth in a population-based series of 490 adult patients with soft tissue sarcoma of the extremity or trunk wall with complete, 4.5 years minimum, follow-up.Multivariate analysis showed no major prognostic effect of tumor depth when grade and size were taken into account. The mean size of small tumors was the same whether superficial or deep but the mean size of large and deep-seated tumors were one third larger than that of large but superficial tumors. Tumor depth influenced the prognosis in the subset of high-grade and large tumors. In this subset deep-seated tumors had poorer survival rate than superficial tumors, which could be explained by the larger mean size of the deep-seated tumors.Most of the prognostic value of tumor depth in soft tissue sarcomas of the extremity or trunk wall can be explained by the association between tumor size and depth.Most staging systems for soft tissue sarcoma are based on histologic malignancy grade, tumor size and tumor depth (the French (FNCLCC) system [1]; the Memorial Sloan Kettering (MSK) system [2]; the American Joint Committee on Cancer/International Union Against Cancer AJCC/UICC system 5th ed [3]. However, we think it is unlikely that tumor depth per se, all other things being equal, should influence the risk of metastatic spread from a soft tissue sarcoma. One explanation for the prognostic value of tumor depth could be the association between depth and tumor size, deep-seated tumors being larger. Most systems dichotomize size at 5 cm. Prognostic information from tumor depth may be obtained if each size group (1–5/>5 cm) is divided into superficial and deep-seated tumors if the mean size of the deep-seated tumors is larger than that of the superficial tumors. A prognostic effect of tumor depth could then be related to size and should be strongest in the large size group in which the size span is greater. We tested
Should anorectal ultrasonography be included as a diagnostic tool for chronic anal pain?
García-Montes,M. J.; Argüelles-Arias,F.; Jiménez-Contreras,S.; Sánchez-Gey,S.; Pellicer-Bautista,F.; Herrerías-Gutiérrez,J. M.;
Revista Espa?ola de Enfermedades Digestivas , 2010, DOI: 10.4321/S1130-01082010000100002
Abstract: objective: to assess the efficiency of endorectal ultrasound (erus) in the study of chronic idiopathic anal pain (ciap). material and method: this is a prospective and descriptive study in which 40 patients, 18 men and 22 women with an average of 47 years, were included. they had chronic anal pain of at least 3 months' duration. a complete colonoscopy was performed in all patients, which found no abnormalities to explain clinical symptoms. patients with anal fissure and internal hemorrhoids of any degree, perianal suppurative processes, and pelvic surgery were excluded from the study. an aloka prosound ssd-4000 ultrasound console attached to a multifrequency radial transductor asu-67 (7.5 and 10 mhz) was used. results: one patient could not tolerate the examination. in 8 patients (20% of cases) alterations were detected during ultrasonography: in 4 patients (10% of the cases; 1 man and 3 women) internal anal sphincter (ias) hypertrophy, and in 5 patients (4 women and 1 man) a torn sphincter complex. a tear in the upper ias canal and hypertrophy of the middle anal canal were observed in one patient (1 woman). conclusions: erus is a simple, economic and useful test to study anorectal pathologies. although in most studied cases no damage to the anal canal or rectal wall was detected, in a considerable number of patients we observed a thickening of the ias, a probable cause of anal pain. therefore, we understand that erus should be included in the study of ciap.
Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases  [PDF]
Jo?l Mossong ,Niel Hens,Mark Jit,Philippe Beutels,Kari Auranen,Rafael Mikolajczyk,Marco Massari,Stefania Salmaso,Gianpaolo Scalia Tomba,Jacco Wallinga,Janneke Heijne,Malgorzata Sadkowska-Todys,Magdalena Rosinska,W. John Edmunds
PLOS Medicine , 2008, DOI: 10.1371/journal.pmed.0050074
Abstract: Background Mathematical modelling of infectious diseases transmitted by the respiratory or close-contact route (e.g., pandemic influenza) is increasingly being used to determine the impact of possible interventions. Although mixing patterns are known to be crucial determinants for model outcome, researchers often rely on a priori contact assumptions with little or no empirical basis. We conducted a population-based prospective survey of mixing patterns in eight European countries using a common paper-diary methodology. Methods and Findings 7,290 participants recorded characteristics of 97,904 contacts with different individuals during one day, including age, sex, location, duration, frequency, and occurrence of physical contact. We found that mixing patterns and contact characteristics were remarkably similar across different European countries. Contact patterns were highly assortative with age: schoolchildren and young adults in particular tended to mix with people of the same age. Contacts lasting at least one hour or occurring on a daily basis mostly involved physical contact, while short duration and infrequent contacts tended to be nonphysical. Contacts at home, school, or leisure were more likely to be physical than contacts at the workplace or while travelling. Preliminary modelling indicates that 5- to 19-year-olds are expected to suffer the highest incidence during the initial epidemic phase of an emerging infection transmitted through social contacts measured here when the population is completely susceptible. Conclusions To our knowledge, our study provides the first large-scale quantitative approach to contact patterns relevant for infections transmitted by the respiratory or close-contact route, and the results should lead to improved parameterisation of mathematical models used to design control strategies.
The potential spread of highly pathogenic avian influenza virus via dynamic contacts between poultry premises in Great Britain
Jennifer E Dent, Istvan Z Kiss, Rowland R Kao, Mark Arnold
BMC Veterinary Research , 2011, DOI: 10.1186/1746-6148-7-59
Abstract: The model predicted that although large outbreaks are rare, they may occur, with long distances between infected premises. Final outbreak size was most sensitive to the probability of spread via slaughterhouse-linked movements whereas the probability of onward spread beyond an index premises was most sensitive to the frequency of company personnel movements.Results obtained from this study show that, whilst there is the possibility that HPAI virus will jump from one cluster of farms to another, movements made by catching teams connected fewer poultry premises in an outbreak situation than slaughterhouses and company personnel. The potential connection of a large number of infected farms, however, highlights the importance of retaining up-to-date data on poultry premises so that control measures can be effectively prioritised in an outbreak situation.For a wide range of epidemic infections, contact structures can be used to describe the potential transmission of infection in a population [1-4]. The validity of such models, however, depends on the parameterisation of the contact structures analysed. The existence of the animal movement licensing scheme and cattle tracing system in Great Britain (GB), for which the identification and movements of cattle, sheep, goats, pigs, deer and horses, must be recorded [5], allows for the reconstruction and analysis of the network of contacts in order to predict the spread of infectious disease across these industries. This is not the case for the poultry industry where, before 2005, there was no national register of poultry farms. Motivated by numerous outbreaks of H5N1 highly pathogenic avian influenza (HPAI) across the world and the occurrence of several incursions of avian influenza viruses (AIV) in GB [6,7], information was collected by the British government on poultry farm locations, and on the frequency and types of movements between farms.In GB, the poultry industry can be divided into the primary breeding sector and the
Epidemic Spread on Weighted Networks  [PDF]
Christel Kamp ,Mathieu Moslonka-Lefebvre,Samuel Alizon
PLOS Computational Biology , 2013, DOI: 10.1371/journal.pcbi.1003352
Abstract: The contact structure between hosts shapes disease spread. Most network-based models used in epidemiology tend to ignore heterogeneity in the weighting of contacts between two individuals. However, this assumption is known to be at odds with the data for many networks (e.g. sexual contact networks) and to have a critical influence on epidemics' behavior. One of the reasons why models usually ignore heterogeneity in transmission is that we currently lack tools to analyze weighted networks, such that most studies rely on numerical simulations. Here, we present a novel framework to estimate key epidemiological variables, such as the rate of early epidemic expansion () and the basic reproductive ratio (), from joint probability distributions of number of partners (contacts) and number of interaction events through which contacts are weighted. These distributions are much easier to infer than the exact shape of the network, which makes the approach widely applicable. The framework also allows for a derivation of the full time course of epidemic prevalence and contact behaviour, which we validate with numerical simulations on networks. Overall, incorporating more realistic contact networks into epidemiological models can improve our understanding of the emergence and spread of infectious diseases.
Spread of infectious diseases through clustered populations  [PDF]
Joel C. Miller
Quantitative Biology , 2008,
Abstract: Networks of person-person contacts form the substrate along which infectious diseases spread. Most network-based studies of the spread focus on the impact of variations in degree (the number of contacts an individual has). However, other effects such as clustering, variations in infectiousness or susceptibility, or variations in closeness of contacts may play a significant role. We develop analytic techniques to predict how these effects alter the growth rate, probability, and size of epidemics and validate the predictions with a realistic social network. We find that (for given degree distribution and average transmissibility) clustering is the dominant factor controlling the growth rate, heterogeneity in infectiousness is the dominant factor controlling the probability of an epidemic, and heterogeneity in susceptibility is the dominant factor controlling the size of an epidemic. Edge weights (measuring closeness or duration of contacts) have impact only if correlations exist between different edges. Combined, these effects can play a minor role in reinforcing one another, with the impact of clustering largest when the population is maximally heterogeneous or if the closer contacts are also strongly clustered. Our most significant contribution is a systematic way to address clustering in infectious disease models, and our results have a number of implications for the design of interventions.
Measuring Social Contacts in the Emergency Department  [PDF]
Douglas W. Lowery-North, Vicki Stover Hertzberg, Lisa Elon, George Cotsonis, Sarah A. Hilton, Christopher F. Vaughns, Eric Hill, Alok Shrestha, Alexandria Jo, Nathan Adams
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0070854
Abstract: Background Infectious individuals in an emergency department (ED) bring substantial risks of cross infection. Data about the complex social and spatial structure of interpersonal contacts in the ED will aid construction of biologically plausible transmission risk models that can guide cross infection control. Methods and Findings We sought to determine the number and duration of contacts among patients and staff in a large, busy ED. This prospective study was conducted between 1 July 2009 and 30 June 2010. Two 12-hour shifts per week were randomly selected for study. The study was conducted in the ED of an urban hospital. There were 81 shifts in the planned random sample of 104 (78%) with usable contact data, during which there were 9183 patient encounters. Of these, 6062 (66%) were approached to participate, of which 4732 (78%) agreed. Over the course of the year, 88 staff members participated (84%). A radiofrequency identification (RFID) system was installed and the ED divided into 89 distinct zones structured so copresence of two individuals in any zone implied a very high probability of contact <1 meter apart in space. During study observation periods, patients and staff were given RFID tags to wear. Contact events were recorded. These were further broken down with respect to the nature of the contacts, i.e., patient with patient, patient with staff, and staff with staff. 293,171 contact events were recorded, with a median of 22 contact events and 9 contacts with distinct individuals per participant per shift. Staff-staff interactions were more numerous and longer than patient-patient or patient-staff interactions. Conclusions We used RFID to quantify contacts between patients and staff in a busy ED. These results are useful for studies of the spread of infections. By understanding contact patterns most important in potential transmission, more effective prevention strategies may be implemented.
Inferring the Structure of Social Contacts from Demographic Data in the Analysis of Infectious Diseases Spread  [PDF]
Laura Fumanelli ,Marco Ajelli,Piero Manfredi,Alessandro Vespignani,Stefano Merler
PLOS Computational Biology , 2012, DOI: 10.1371/journal.pcbi.1002673
Abstract: Social contact patterns among individuals encode the transmission route of infectious diseases and are a key ingredient in the realistic characterization and modeling of epidemics. Unfortunately, the gathering of high quality experimental data on contact patterns in human populations is a very difficult task even at the coarse level of mixing patterns among age groups. Here we propose an alternative route to the estimation of mixing patterns that relies on the construction of virtual populations parametrized with highly detailed census and demographic data. We present the modeling of the population of 26 European countries and the generation of the corresponding synthetic contact matrices among the population age groups. The method is validated by a detailed comparison with the matrices obtained in six European countries by the most extensive survey study on mixing patterns. The methodology presented here allows a large scale comparison of mixing patterns in Europe, highlighting general common features as well as country-specific differences. We find clear relations between epidemiologically relevant quantities (reproduction number and attack rate) and socio-demographic characteristics of the populations, such as the average age of the population and the duration of primary school cycle. This study provides a numerical approach for the generation of human mixing patterns that can be used to improve the accuracy of mathematical models in the absence of specific experimental data.
Age-specific contacts and travel patterns in the spatial spread of 2009 H1N1 influenza pandemic  [PDF]
Andrea Apolloni,Chiara Poletto,Vittoria Colizza
Quantitative Biology , 2013, DOI: 10.1186/1471-2334-13-176
Abstract: Confirmed cases during the early stage of the 2009 H1N1 pdm in various countries showed an age shift between importations and local transmission cases, with adults mainly responsible for seeding unaffected regions and children most frequently driving community outbreaks. We introduce a multi-host stochastic metapopulation model with two age classes to analytically address the role of a heterogeneously mixing population and its associated non-homogeneous travel behaviors on the risk of a major epidemic. We inform the model with statistics on demography, mixing and travel behavior for Europe and Mexico, and calibrate it to the 2009 H1N1 pdm early outbreak. We varied model parameters to explore the invasion conditions under different scenarios. We derive the expression for the global invasion potential of the epidemic that depends on disease transmissibility, transportation network and mobility features, demographic profile and mixing pattern. Highly assortative mixing favor the spatial containment of the epidemic, this effect being contrasted by an increase in the social activity of adults vs. children. Heterogeneity of the mobility network topology and traffic flows strongly favor the disease invasion, as also a larger fraction of children traveling. Variations in the demography and mixing habits across countries lead to heterogeneous outbreak situations. Results are compatible with the H1N1 spatial spread observed. The work illustrates the importance of age-dependent mixing profiles and mobility features in the study of the conditions for the spatial invasion of an emerging influenza pandemic. Its results allow the immediate assessment of the risk of a major epidemic for a specific scenario upon availability of data, and the evaluation of the effectiveness of public health interventions targeting specific age groups, their interactions and mobility behaviors.
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