How long do people stick to a diet resolution? A digital epidemiological estimation of weight loss diet persistence.

OBJECTIVE: To use Internet search data to compare duration of compliance for various diets. DESIGN: Using a passive surveillance digital epidemiological approach, we estimated the average duration of diet compliance by examining monthly Internet searches for recipes related to popular diets. We fit a mathematical model to these data to estimate the time spent on a diet by new January dieters (NJD) and to estimate the percentage of dieters dropping out during the American winter holiday season between Thanksgiving and the end of December. SETTING: Internet searches in the USA for recipes related to popular diets over a 15-year period from 2004 to 2019. PARTICIPANTS: Individuals in the USA performing Internet searches for recipes related to popular diets. RESULTS: All diets exhibited significant seasonality in recipe-related Internet searches, with sharp spikes every January followed by a decline in the number of searches and a further decline in the winter holiday season. The Paleo diet had the longest average compliance times among NJD (5.32 ± 0.68 weeks) and the lowest dropout during the winter holiday season (only 14 ± 3 % dropping out in December). The South Beach diet had the shortest compliance time among NJD (3.12 ± 0.64 weeks) and the highest dropout during the holiday season (33 ± 7 % dropping out in December). CONCLUSIONS: The current study is the first of its kind to use passive surveillance data to compare the duration of adherence with different diets and underscores the potential usefulness of digital epidemiological approaches to understanding health behaviours.

Dynamics of population communities with prey migrations and Allee effects: a bifurcation approach.

The population dynamics of predator-prey systems in the presence of patch-specific predators are explored in a setting where the prey population has access to both habitats. The emphasis is in situations where patch-prey abundance drives prey dispersal between patches, with the fragile prey populations, i.e. populations subject to the Allee effect. The resulting 3D and 4D non-linear systems depending on some parameters, which reflect 'measures' of factors under consideration, support rich dynamics and in particular a diverse number of predator-prey life history outcomes. The model's mathematical analysis is carried out via submodels that focus in lower-dimensional settings. The outcomes depend on and, in fact, are quite sensitive to the structure of the system, the range of parameter values and initial conditions. We show that the system can support multistability and a diverse set of predator-prey life-history dynamics that include rather complex dynamical system outcomes. It is argued that, in general, evolution should favour heterogeneous settings including Allee effects, prey refuges and patch-specific predators.

Transmission potential of the new influenza A(H1N1) virus and its age-specificity in Japan.

On 16 May 2009, Japan confirmed its first three cases of new influenza A(H1N1) virus infection without a history of overseas travel, and by 1 June, 361 cases, owing to indigenous secondary transmission, have been confirmed. Of these, 287 cases (79.5%) were teenagers (i.e. between 10 and 19 years of age). The reproduction number is estimated at 2.3 (95% confidence interval: 2.0, 2.6). The average number of secondary transmissions involving minors (those under 20 years of age) traced back to infected minors is estimated at 2.8. That is, minors can sustain transmission even in the absence of adults. Estimates of the effective reproduction number Rt moved below 1 by 17 May. Active surveillance and public health interventions, including school closures most likely have contributed to keeping Rt below one.

Spatial and temporal dynamics of dengue fever in Peru: 1994-2006.

SUMMARYThe weekly number of dengue cases in Peru, South America, stratified by province for the period 1994-2006 were analysed in conjunction with associated demographic, geographic and climatological data. Estimates of the reproduction number, moderately correlated with population size (Spearman rho=0.28, P=0.03), had a median of 1.76 (IQR 0.83-4.46). The distributions of dengue attack rates and epidemic durations follow power-law (Pareto) distributions (coefficient of determination >85%, P<0.004). Spatial heterogeneity of attack rates was highest in coastal areas followed by mountain and jungle areas. Our findings suggest a hierarchy of transmission events during the large 2000-2001 epidemic from large to small population areas when serotypes DEN-3 and DEN-4 were first identified (Spearman rho=-0.43, P=0.03). The need for spatial and temporal dengue epidemic data with a high degree of resolution not only increases our understanding of the dynamics of dengue but will also generate new hypotheses and provide a platform for testing innovative control policies.

Estimation of the reproduction number of dengue fever from spatial epidemic data.

Dengue, a vector-borne disease, thrives in tropical and subtropical regions worldwide. A retrospective analysis of the 2002 dengue epidemic in Colima located on the Mexican central Pacific coast is carried out. We estimate the reproduction number from spatial epidemic data at the level of municipalities using two different methods: (1) Using a standard dengue epidemic model and assuming pure exponential initial epidemic growth and (2) Fitting a more realistic epidemic model to the initial phase of the dengue epidemic curve. Using Method I, we estimate an overall mean reproduction number of 3.09 (95% CI: 2.34,3.84) as well as local reproduction numbers whose values range from 1.24 (1.15,1.33) to 4.22 (2.90,5.54). Using Method II, the overall mean reproduction number is estimated to be 2.0 (1.75,2.23) and local reproduction numbers ranging from 0.49 (0.0,1.0) to 3.30 (1.63,4.97). Method I systematically overestimates the reproduction number relative to the refined Method II, and hence it would overestimate the intensity of interventions required for containment. Moreover, optimal intervention with defined resources demands different levels of locally tailored mitigation. Local epidemic peaks occur between the 24th and 35th week of the year, and correlate positively with the final local epidemic sizes (rho=0.92, P-value<0.001). Moreover, final local epidemic sizes are found to be linearly related to the local population size (P-value<0.001). This observation supports a roughly constant number of female mosquitoes per person across urban and rural regions.

On the role of cross-immunity and vaccines on the survival of less fit flu-strains.

A pathogen's route to survival involves various mechanisms including its ability to invade (host's susceptibility) and its reproductive success within an invaded host ("infectiousness"). The immunological history of an individual often plays an important role in reducing host susceptibility or it helps the host mount a faster immunological response de facto reducing infectiousness. The cross-immunity generated by prior infections to influenza A strains from the same subtype provide a significant example. The results of this paper are based on the analytical study of a two-strain epidemic model that incorporates host isolation (during primary infection) and cross-immunity to study the role of invasion mediated cross-immunity in a population where a precursor related strain (within the same subtype, i.e. H3N2, H1N1) has already become established. An uncertainty and sensitivity analysis is carried out on the ability of the invading strain to survive for given cross-immunity levels. Our findings indicate that it is possible to support coexistence even in the case when invading strains are "unfit", that is, when the basic reproduction number of the invading strain is less than one. However, such scenarios are possible only in the presence of isolation. That is, appropriate increments in isolation rates and weak cross-immunity can facilitate the survival of less fit strains. The development of "flu" vaccines that minimally enhance herd cross-immunity levels may, by increasing genotype diversity, help facilitate the generation and survival of novel strains.

An age-structured epidemic model of rotavirus with vaccination.

The recent approval of a rotavirus vaccine in Mexico motivates this study on the potential impact of the use of such a vaccine on rotavirus prevention and control. An age-structured model that describes the rotavirus transmission dynamics of infections is introduced. Conditions that guarantee the local and global stability analysis of the disease-free steady state distribution as well as the existence of an endemic steady state distribution are established. The impact of maternal antibodies on the implementation of vaccine is evaluated. Model results are used to identify optimal age-dependent vaccination strategies. A convergent numerical scheme for the model is introduced but not implemented. This paper is dedicated to Prof. K. P. Hadeler, who continues to push the frontier of knowledge in mathematical biology.

Modelling the transmission dynamics of acute haemorrhagic conjunctivitis: application to the 2003 outbreak in Mexico.

We model an outbreak of acute haemorrhagic conjunctivitis (AHC) using a simple epidemic model that includes susceptible, infectious, reported, and recovered classes. The model's framework considers the impact of underreporting and behaviour changes on the transmission rate and is applied to a recent epidemic of AHC in Mexico, using a fit to the cumulative number of cases to estimate model parameters, which agree with those derived from clinical studies. The model predicts a 'mean time from symptomatic onset to diagnosis' of 1.43 days (95 per cent CI: 1-2.5) and that the final size of the Mexican epidemic was underreported by 39 per cent. We estimate that a primary infectious case generates approximately 3 secondary cases (R0* = 2.64, SD 0.65). We explore the impact of interventions on the final epidemic size, and estimate a 36 per cent reduction in the transmission rate due to behaviour changes. The effectiveness of the behaviour changes in slowing the epidemic is evident at 21.90 (SD 0.19) days after the first reported case. Results therefore support current public health policy including expeditious announcement of the outbreak and public health information press releases that instruct individuals on avoiding contagion and encourage them to seek diagnosis in hospital clinics.

The role of spatial mixing in the spread of foot-and-mouth disease.

A model of epidemic dispersal (based on the assumption that susceptible cattle were homogeneously mixed over space, or non-spatial model) was compared to a partially spatially explicit and discrete model (the spatial model), which was composed of differential equations and used geo-coded data (Euclidean distances between county centroids). While the spatial model accounted for intra- and inter-county epidemic spread, the non-spatial model did not assess regional differences. A geo-coded dataset that resembled conditions favouring homogeneous mixing assumptions (based on the 2001 Uruguayan foot-and-mouth disease epidemic), was used for testing. Significant differences between models were observed in the average transmission rate between farms, both before and after a control policy (animal movement ban) was imposed. They also differed in terms of daily number of infected farms: the non-spatial model revealed a single epidemic peak (at, approximately, 25 epidemic days); while the spatial model revealed two epidemic peaks (at, approximately, 12 and 28 days, respectively). While the spatial model fitted well with the observed cumulative number of infected farms, the non-spatial model did not (P<0.01). In addition, the spatial model: (a) indicated an early intra-county reproductive number R of approximately 87 (falling to <1 within 25 days), and an inter-county R<1; (b) predicted that, if animal movement restrictions had begun 3 days before/after the estimated initiation of such policy, cases would have decreased/increased by 23 or 26%, respectively. Spatial factors (such as inter-farm distance and coverage of vaccination campaigns, absent in non-spatial models) may explain why partially explicit spatial models describe epidemic spread more accurately than non-spatial models even at early epidemic phases. Integration of geo-coded data into mathematical models is recommended.

Effects of behavioral changes in a smallpox attack model.

The impact of individual and community behavioral changes in response to an outbreak of a disease with high mortality is often not appreciated. Response strategies to a smallpox bioterrorist attack have focused on interventions such as isolation of infectives, contact tracing, quarantine of contacts, ring vaccination, and mass vaccination. We formulate and analyze a mathematical model in which some individuals lower their daily contact activity rates once an epidemic has been identified in a community. Transmission parameters are estimated from data and an expression is derived for the effective reproduction number. We use computer simulations to analyze the effects of behavior change alone and in combination with other control measures. We demonstrate that the spread of the disease is highly sensitive to how rapidly people reduce their contact activity rates and to the precautions that the population takes to reduce the transmission of the disease. Even gradual and mild behavioral changes can have a dramatic impact in slowing an epidemic. When behavioral changes are combined with other interventions, the epidemic is shortened and the number of smallpox cases is reduced. We conclude that for simulations of a smallpox outbreak to be useful, they must consider the impact of behavioral changes. This is especially true if the model predictions are being used to guide public health policy.

Pediatric electrocardiograph abnormalities following Centruroides limpidus tecomanus scorpion envenomation.

Scorpionism is an endemic public health problem in Mexico [Hoffmann, C.C., 1936. La distribucion geografica de los alacranes peligrosos en la Republica Mexicana. Bol. Inst. Hygiene Mex. 2, 321; Hoffmann, C.C., Nieto, D.R., 1939. Segunda contribucion al conocimiento de los alacranes mexicanos. Anal. Inst. Biol. 10, 83-92; Mazzoti, L., Bravo-Becherelle, M.A., 1963. Scorpionism in the Mexican Republic. In: Keegan, H.L., McFarlane, W.V. (Eds.), Venomous and Poissonous Animals and Noxious Plants of the Pacific Area. Pergamon Press, London, pp. 119-131; Monroy-Velasco, J., 1961. Alacranes venenosos de Mexico. Rev. Mex. Cien. Med. Biol., Mex. 1, 1-23; Diaz-Najera, A., 1975. Listas y datos de distribucion geografica de los alacranes de Mexico. Rev. Inv. Salud. Publica. (Mex.) 35, 1; Velasco-Castrejon, O., Lara-Aguilera, R., Alatorre, H., 1976. Aspectos epidemiologicos y clinicos de la picadura de alacran en una area hiperendemica. Rev. Inv. Salud Publica. (Mex.) 36, 93-103; Dehesa-Davila, M., Possani, L.D., 1994. Scorpionism and serotherapy in Mexico. Toxicon 32 (9), 1015-1018]. In this prospective study, we assess cardiovascular disorders in children via electrocardiographic (ECG) recordings following envenomation by scorpion species Centruroides limpidus tecomanus found in the state of Colima, Mexico. We analyzed 113 cases between the ages of 5 and 14 years. Among the most frequent symptoms presented included local pain (99.1%) and paresthesia (75.2%), pruritus (36.3%), sialorrhoea (35.4%), and nystagmus (24.8%). Cardiovascular disorders were observed in 39.8% of cases, 71% of which were rhythm abnormalities. We find a significant association between the frequency of ECG alterations and age, whereby 8-9-year-old children are more likely to experience ECG alterations when compared with other tested age groups.

The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda.

Despite improved control measures, Ebola remains a serious public health risk in African regions where recurrent outbreaks have been observed since the initial epidemic in 1976. Using epidemic modeling and data from two well-documented Ebola outbreaks (Congo 1995 and Uganda 2000), we estimate the number of secondary cases generated by an index case in the absence of control interventions R0. Our estimate of R0 is 1.83 (SD 0.06) for Congo (1995) and 1.34 (SD 0.03) for Uganda (2000). We model the course of the outbreaks via an SEIR (susceptible-exposed-infectious-removed) epidemic model that includes a smooth transition in the transmission rate after control interventions are put in place. We perform an uncertainty analysis of the basic reproductive number R0 to quantify its sensitivity to other disease-related parameters. We also analyse the sensitivity of the final epidemic size to the time interventions begin and provide a distribution for the final epidemic size. The control measures implemented during these two outbreaks (including education and contact tracing followed by quarantine) reduce the final epidemic size by a factor of 2 relative the final size with a 2-week delay in their implementation.

Critical response time (time available to implement effective measures for epidemic control): model building and evaluation.

The time available to implement successful control measures against epidemics was estimated. Critical response time (CRT), defined as the time interval within which the number of epidemic cases remains stationary (so that interventions implemented within CRT may be the most effective or least costly), was assessed during the early epidemic phase, when the number of cases grows linearly over time. The CRT was calculated from data of the 2001 foot-and-mouth disease (FMD) epidemic that occurred in Uruguay. Significant regional CRT differences (ranging from 1.4 to 2.7 days) were observed. The CRT may facilitate selection of control measures. For instance, a CRT equal to 3 days would support the selection of measures, such as stamping-out, implementable within 3 days, but rule out measures, such as post-outbreak vaccination, because intervention and immunity building require more than 3 days. Its use in rapidly disseminating diseases, such as FMD, may result in regionalized decision-making.

SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism.

In this article we use global and regional data from the SARS epidemic in conjunction with a model of susceptible, exposed, infective, diagnosed, and recovered classes of people ("SEIJR") to extract average properties and rate constants for those populations. The model is fitted to data from the Ontario (Toronto) in Canada, Hong Kong in China and Singapore outbreaks and predictions are made based on various assumptions and observations, including the current effect of isolating individuals diagnosed with SARS. The epidemic dynamics for Hong Kong and Singapore appear to be different from the dynamics in Toronto, Ontario. Toronto shows a very rapid increase in the number of cases between March 31st and April 6th, followed by a significant slowing in the number of new cases. We explain this as the result of an increase in the diagnostic rate and in the effectiveness of patient isolation after March 26th. Our best estimates are consistent with SARS eventually being contained in Toronto, although the time of containment is sensitive to the parameters in our model. It is shown that despite the empirically modeled heterogeneity in transmission, SARS' average reproductive number is 1.2, a value quite similar to that computed for some strains of influenza (J. Math. Biol. 27 (1989) 233). Although it would not be surprising to see levels of SARS infection higher than 10% in some regions of the world (if unchecked), lack of data and the observed heterogeneity and sensitivity of parameters prevent us from predicting the long-term impact of SARS. The possibility that 10 or more percent of the world population at risk could eventually be infected with the virus in conjunction with a mortality rate of 3-7% or more, and indications of significant improvement in Toronto support the stringent measures that have been taken to isolate diagnosed cases.

Scaling laws for the movement of people between locations in a large city.

Large scale simulations of the movements of people in a "virtual" city and their analyses are used to generate insights into understanding the dynamic processes that depend on the interactions between people. Models, based on these interactions, can be used in optimizing traffic flow, slowing the spread of infectious diseases, or predicting the change in cell phone usage in a disaster. We analyzed cumulative and aggregated data generated from the simulated movements of 1.6 x 10(6) individuals in a computer (pseudo-agent-based) model during a typical day in Portland, Oregon. This city is mapped into a graph with 181,206 nodes representing physical locations such as buildings. Connecting edges model individual's flow between nodes. Edge weights are constructed from the daily traffic of individuals moving between locations. The number of edges leaving a node (out-degree), the edge weights (out-traffic), and the edge weights per location (total out-traffic) are fitted well by power-law distributions. The power-law distributions also fit subgraphs based on work, school, and social/recreational activities. The resulting weighted graph is a "small world" and has scaling laws consistent with an underlying hierarchical structure. We also explore the time evolution of the largest connected component and the distribution of the component sizes. We observe a strong linear correlation between the out-degree and total out-traffic distributions and significant levels of clustering. We discuss how these network features can be used to characterize social networks and their relationship to dynamic processes.

Dispersal, disease and life-history evolution.

Discrete-time susceptible-infective-susceptible (S-I-S) disease transmission models can exhibit bistability (alternative stable equilibria) over a wide range of parameter values. We illustrate the richness generated by such 'simple' non-linear systems in the study of two patch epidemic models with disease-enhanced or disease-suppressed dispersal. Dispersal between patches can have a profound impact on local patch disease dynamics. In fact, dispersal between patches may give rise to bistability in parameter regimes without bistability in single patch models.

El transporte público y la dinámica de la tuberculosis a nivel poblacional / The public transporte and the dinamic of the tuberculosis in population level

En este artículo hemos introducido, por primera vez, un modelo matemático para el estudio de la dinámica de enfermedades transmisibles, que toma en consideración el impacto de transmisión en dos ambientes diferentes para una población heterogénea. Calculamos el número reproductivo básico y determinamos el impacto de homotransmisiones y heterotransmisiones en el número de infecciones secundarias

El transporte público y la dinámica de la tuberculosis a nivel poblacional / The public transporte and the dinamic of the tuberculosis in population level

En este artículo hemos introducido, por primera vez, un modelo matemático para el estudio de la dinámica de enfermedades transmisibles, que toma en consideración el impacto de transmisión en dos ambientes diferentes para una población heterogénea. Calculamos el número reproductivo básico y determinamos el impacto de homotransmisiones y heterotransmisiones en el número de infecciones secundarias

Transmission and dynamics of tuberculosis on generalized households.

Tuberculosis (TB) transmission is enhanced by systematic exposure to an infectious individual. This enhancement usually takes place at either the home, workplace, and/or school (generalized household). Typical epidemiological models do not incorporate the impact of generalized households on the study of disease dynamics. Models that incorporate cluster (generalized household) effects and focus on their impact on TB's transmission dynamics are developed. Detailed models that consider the effect of casual infections, that is, those generated outside a cluster, are also presented. We find expressions for the Basic Reproductive Number as a function of cluster size. The formula for R0 separates the contributions of cluster and casual infections in the generation of secondary TB infections. Relationships between cluster and classical epidemic models are discussed as well as the concept of critical cluster size.

A model for tuberculosis with exogenous reinfection.

Following primary tuberculosis (TB) infection, only approximately 10% of individuals develop active T.B. Most people are assumed to mount an effective immune response to the initial infection that limits proliferation of the bacilli and leads to long-lasting partial immunity both to further infection and to reactivation of latent bacilli remaining from the original infection. Infected individuals may develop active TB as a consequence of exogenous reinfection, i.e., acquiring a new infection from another infectious individual. Our results in this paper suggest that exogenous reinfection has a drastic effect on the qualitative dynamics of TB. The incorporation of exogenous reinfection into our TB model allows the possibility of a subcritical bifurcation at the critical value of the basic reproductive number R(0)=1, and hence the existence of multiple endemic equilibria for R(0)<1 and the exogenous reinfection rate larger than a threshold. Our results suggest that reducing R(0) to be smaller than one may not be sufficient to eradicate the disease. An additional reduction in reinfection rate may be required. These results may also partially explain the recently observed resurgence of TB.