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We create and analyze a stochastic heterosexual agent-based bipartite network model to help understand the spread of chlamydia trachomatis. Chlamydia is the most common sexually transmitted infection in the United States and is major cause of infertility, pelvic inflammatory disease, and ectopic pregnancy among women. We use an agent-based network model to capture the complex heterogeneous assortative sexual mixing network of men and women. Both long-term and casual partnerships are modeled with different sexual contact frequencies and condom use. We use simulations to compare the effectiveness of intervention strategies based on randomly screening people for infection, treating the partners of infected people, and rescreening for infection after treatment. We compare the difference between treating the partners of an infected person both with, and without, testing them first for infection. The highest prevalence is among young sexually active individuals. We calibrate the model parameters to agree with recent survey data showing chlamydia prevalence of 14% of the women and 9% of the men in the 15 – 25 year-old African American residents of New Orleans, Louisiana. We observed that although increased chlamydia screening and treating most of the partners of infected people will reduce the incidence, these mitigations alone are not sufficient to control the epidemic. The model predicts that the current epidemic can brought under control once over half of the partners of infected people are tested and treated.

The feedback-related negativity (FRN) refers to a difference in the human event-related potential (ERP) elicited by feedback indicating success versus failure: the difference appears negative when subtracting the success ERP from the failure ERP (Miltner et al., 1997). Although source localization techniques (e.g., BESA) suggest that the FRN is produced in the ACC, the inverse problem (that any given scalp distribution can be produced by an infinite number of possible dipole configurations) limits the certainty of this conclusion. The inverse problem can be circumvented by directly recording from the ACC in animal models. Although a non-human primate homologue of the FRN has been observed in the macaque monkey (e.g. Emeric et al., 2008), a homologue of the FRN has yet to be identified in rodents. We recorded local field potentials (LFPs) directly from the ACC in 6 rodents in a task based on the FRN paradigm. The animals were trained to poke their nose into a lighted port and received a feedback smell indicating whether or not a reward pellet would drop 1.5 s later. We observed a FRN-like effect time-locked to the feedback scent whereby the LFP to feedback predicting no-reward was significantly more negative than the LFP to feedback predicting reward. This deflection began on average 130 ms before behavioral changes in response to the feedback. Thus, we provide the first evidence of the existence of a rodent homologue of the FRN.

Once Aedes aegypti and Aedes albopictus mosquitoes that spread Chikungunya virus, dengue virus, and Zika virus are infected with Wolbachia, they have reduced egg laying rates, reduced transmission abilities, and shorter lifespans. Since most infected mosquitoes are only infectious in the last few days of their lives, shortening a mosquito’s lifespan by a day or two can greatly reduce their abilities to spread mosquito-borne viral diseases, such as Chikungunya, dengue fever, and Zika. We developed a mathematical model to compare the effectiveness of the wMel and wAlbB strains of Wolbachia for controlling the spread of these viruses. The differences among the diseases, mosquitoes, and Wolbachia strains are captured by the model parameters for the mosquito-human transmission cycle. Moreover, the model accounts for the behavior changes of infectious population created by differences in the malaise caused by these viruses. We derived the effective and basic reproduction numbers for the model that are used to estimate the number of secondary infections from the infectious populations. In the same density of Wolbachia-free Aedes aegypti or Aedes albopictus mosquitoes, we observed that wMel and wAlbB strains of Wolbachia can reduce the transmission rates of these diseases effectively., Author summary Mosquitoes infected with Wolbachia bacteria are less capable of transmitting dengue virus, Chikungunya virus, and Zika virus. We use a mathematical model to quantify the impact of infecting wild Aedes aegypti and Aedes albopictus mosquitoes with wAlbB and wMel strains of Wolbachia in reducing the transmission of these viruses. The model is a system of ordinary differential equations that accounts for reduced fitness of the Wolbachia-infected mosquitoes, reduced transmissibility of an infection, and the behavior changes of infected individuals caused by the infection. We derived an explicit formula for the effective reproduction number for when the host population are partially immune to new infections, as occurs in seasonal outbreaks. We compared the effectiveness of different species of mosquitoes, different strains of Wolbachia, and different diseases. Our model is a general model that can produce outputs for a specific location, once the data for the location are available to parameterize the model. The spatial heterogeneity of the populations must be considered before using this model to help guide policy decisions.

The dynamics of hepatitis C virus (HCV) RNA during translation and replication were added to an age-based multiscale mathematical model of HCV infection and treatment. The model allows the study of the production of HCV inside infected cells, which are later released as virus in the plasma, available to infect other cells. This is the first model to our knowledge to consider both positive and negative strands of HCV RNA with an age-based multiscale approach. Simulation of the effectiveness of direct acting antiviral (DAA) drugs in blocking HCV RNA intracellular production and release of new virions, and enhancing their depletion were performed. Changes on the set of parameters allowed the validation of the model comparing it to distinct experiments: in vitro and in vivo under therapy.

The function of a given brain region is often defined by the coding properties of its individual neurons, yet how this information is combined at the ensemble level is an equally important consideration. In the present study, multiple neurons from the anterior cingulate cortex (ACC) and the dorsal striatum (DS) were recorded simultaneously as rats performed different sequences of the same three actions. Sequence and lever decoding was remarkably similar on a per-neuron basis in the two regions. At the ensemble level, sequence-specific representations in the DS appeared synchronously but transiently along with the representation of lever location, while these two streams of information appeared independently and asynchronously in the ACC. As a result the ACC achieved superior ensemble decoding accuracy overall. Thus, the manner in which information was combined across neurons in an ensemble determined the functional separation of the ACC and DS on this task.

We present and characterize a multi-host epidemic model of Rift Valley fever (RVF) virus in East Africa with geographic spread on a network, rule-based mitigation measures, and mosquito infection and population dynamics. Susceptible populations are depleted by disease and vaccination and are replenished with the birth of new animals. We observe that the severity of the epidemics is strongly correlated with the duration of the rainy season and that even severe epidemics are abruptly terminated when the rain stops. Because naturally acquired herd immunity is established, total mortality across 25 years is relatively insensitive to many mitigation approaches. Strong reductions in cattle mortality are expected, however, with sufficient reduction in population densities of either vectors or susceptible (ie. unvaccinated) hosts. A better understanding of RVF epidemiology would result from serology surveys to quantify the importance of herd immunity in epidemic control, and sequencing of virus from representative animals to quantify the realative importance of transportation and local reservoirs in nucleating yearly epidemics. Our results suggest that an effective multi-layered mitigation strategy would include vector control, movement control, and vaccination of young animals yearly, even in the absence of expected rainfall.

We present two ordinary differential equation models for Rift Valley fever (RVF) transmission in cattle and mosquitoes. We extend existing models for vector-borne diseases to include an asymptomatic host class and vertical transmission in vectors. We define the basic reproductive number, ℛ(0), and analyse the existence and stability of equilibrium points. We compute sensitivity indices of ℛ(0) and a reactivity index (that measures epidemicity) to parameters for baseline wet and dry season values. ℛ(0) is most sensitive to the mosquito biting and death rates. The reactivity index is most sensitive to the mosquito biting rate and the infectivity of hosts to vectors. Numerical simulations show that even with low equilibrium prevalence, increases in mosquito densities through higher rainfall, in the presence of vertical transmission, can result in large epidemics. This suggests that vertical transmission is an important factor in the size and persistence of RVF epidemics.

The spread of an infectious disease is sensitive to the contact patterns in the population and to precautions people take to reduce the transmission of the disease. We investigate the impact that different mixing assumptions have on the spread an infectious disease in an age-structured ordinary differential equation model. We consider the impact of heterogeneity in susceptibility and infectivity within the population on the disease transmission. We apply the analysis to the spread of a smallpox-like disease, derive the formula for the reproduction number, R0, and based on this threshold parameter, show the level of human behavioral change required to control the epidemic. We analyze how different mixing patterns can affect the disease prevalence, the cumulative number of new infections, and the final epidemic size. Our analysis indicates that the combination of residual immunity and behavioral changes during a smallpox-like disease outbreak can play a key role in halting infectious disease spread; and that realistic mixing patterns must be included in the epidemic model for the predictions to accurately reflect reality.

We present a numerical study of the nonlinear mechanical model for morphogenesis proposed by Oster et al. (1983) with the aim of establishing the pattern forming capability of the model. We present a technique for mode selection based on linear analysis and show that, in many cases, it is a reliable predictor for nonlinear mode selection. In order to determine the set of model parameters that can generate a particular pattern we develop a technique based on nonlinear least square fitting to a dispersion relation. As an application we present a scenario for sequential pattern formation of dermal aggregations in chick embryos which leads to the hexagonal array of cell aggregations observed in feather germ formation in vivo.

Epidemiological modeling for infectious disease is important for disease management and its routine implementation needs to be facilitated through better description of models in an operational context. A standardized model characterization process that allows selection or making manual comparisons of available models and their results is currently lacking. A key need is a universal framework to facilitate model description and understanding of its features. Los Alamos National Laboratory (LANL) has developed a comprehensive framework that can be used to characterize an infectious disease model in an operational context. The framework was developed through a consensus among a panel of subject matter experts. In this paper, we describe the framework, its application to model characterization, and the development of the Biosurveillance Analytics Resource Directory (BARD; http://brd.bsvgateway.org/brd/), to facilitate the rapid selection of operational models for specific infectious/communicable diseases. We offer this framework and associated database to stakeholders of the infectious disease modeling field as a tool for standardizing model description and facilitating the use of epidemiological models.

We create a compartmental mathematical model to analyze the role of behavior change in slowing the spread of the Ebola virus disease (EVD) in the 2014–2015 Western Africa epidemic. Our model incorporates behavior change, modeled as decreased contact rates between susceptible and infectious individuals, the prevention of traditional funerals, and/or increased access to medical facilities. We derived the basic reproductive number for the model, and approximated the parameter values for the spread of the EVD in Monrovia. We used sensitivity analysis to quantify the relative importance of the timing, and magnitude, of the population reducing their contact rates, avoiding the traditional burial practices, and having access to medical treatment facilities. We found that reducing the number of contacts made by infectious individuals in the general population is the most effective intervention method for mitigating an EVD epidemic. While healthcare interventions delayed the onset of the epidemic, healthcare alone is insufficient to stop the epidemic in the model.

Chlamydia trachomatis, CT, infection is the most frequently reported sexually transmitted infection in the United States. To better understand the recent increase in disease prevalence, and help guide in mitigation efforts, we created and analyzed a multi-risk model for the spread of chlamydia in the heterosexual community. The model incorporates the heterogeneous mixing between men and women with different number of partners and the parameters are defined to approximate the disease transmission in the 15–25 year-old New Orleans African American community. We use sensitivity analysis to assess the relative impact of different levels of screening interventions and behavior changes on the basic reproduction number. Our results quantify, and validate, the impact that reducing the probability of transmission per sexual contact, such as using prophylactic condoms, can have on CT prevalence.

Although there are numerous theories regarding anterior cingulate cortex (ACC) function, most suggest that it is involved in some form of action or outcome processing. The present study characterized the dominant patterns of ACC activity on a task in which actions and outcomes could vary independently. Patterns of activity were detected using a modified form of principal component analysis (PCA), termed constrained PCA in which a regression procedure was applied prior to PCA to eliminate the contribution of nontask-related activity. When trials were grouped according to outcome, a PC was found in all subjects and sessions that had large fluctuations during actions but only differentiated correct versus error trials prior to the end of the delay and again at time of the outcome. Another PC was always present that separated right from left lever presses, but only around the time of the actual lever press. Individual neurons exhibited significant selectivities for trials involving different actions and/or outcomes. Of the ACC neurons that exhibited significant outcome selectivity, the majority fired more on error trials. The present study revealed separate as well as integrated action and outcome monitoring in the ACC, especially, although not exclusively, under conditions when an error is likely.

Contextual representations serve to guide many aspects of behavior and influence the way stimuli or actions are encoded and interpreted. The medial prefrontal cortex (mPFC), including the anterior cingulate subregion, has been implicated in contextual encoding, yet the nature of contextual representations formed by the mPFC is unclear. Using multiple single-unit tetrode recordings in rats, we found that different activity patterns emerged in mPFC ensembles when animals moved between different environmental contexts. These differences in activity patterns were significantly larger than those observed for hippocampal ensembles. Whereas ≈11% of mPFC cells consistently preferred one environment over the other across multiple exposures to the same environments, optimal decoding (prediction) of the environmental setting occurred when the activity of up to ≈50% of all mPFC neurons was taken into account. On the other hand, population activity patterns were not identical upon repeated exposures to the very same environment. This was partly because the state of mPFC ensembles seemed to systematically shift with time, such that we could sometimes predict the change in ensemble state upon later reentry into one environment according to linear extrapolation from the time-dependent shifts observed during the first exposure. We also observed that many strongly action-selective mPFC neurons exhibited a significant degree of context-dependent modulation. These results highlight potential differences in contextual encoding schemes by the mPFC and hippocampus and suggest that the mPFC forms rich contextual representations that take into account not only sensory cues but also actions and time.

Many different algorithms have been developed in the last few decades for solving complex real-world search and optimization problems. The main focus in this research has been on the development of a single universal genetic operator for population evolution that is always efficient for a diverse set of optimization problems. In this paper, we argue that significant advances to the field of evolutionary computation can be made if we embrace a concept of self-adaptive multimethod optimization in which multiple different search algorithms are run concurrently, and learn from each other through information exchange using a common population of points. We present an evolutionary algorithm, entitled A Multialgorithm Genetically Adaptive Method for Single Objective Optimization (AMALGAM-SO), that implements this concept of self adaptive multimethod search. This method simultaneously merges the strengths of the covariance matrix adaptation (CMA) evolution strategy, genetic algorithm (GA), and particle swarm optimizer (PSO) for population evolution and implements a self-adaptive learning strategy to automatically tune the number of offspring these three individual algorithms are allowed to contribute during each generation. Benchmark results in 10, 30, and 50 dimensions using synthetic functions from the special session on real-parameter optimization of CEC 2005 show that AMALGAM-SO obtains similar efficiencies as existing algorithms on relatively simple unimodal problems, but is superior for more complex higher dimensional multimodal optimization problems. The new search method scales well with increasing number of dimensions, converges in the close proximity of the global minimum for functions with noise induced multimodality, and is designed to take full advantage of the power of distributed computer networks.

We propose a population dynamics model for quantifying the effects of polling data on the outcome of multi-party elections decided by a majority-rule voting process. We divide the population into two groups: committed voters impervious to polling data, and susceptible voters whose decision to vote is influenced by data, depending on its reliability. This population-based approach to modeling the process sidesteps the problem of upscaling models based upon the choices made by individuals. We find releasing poll data is not advan- tageous to leading candidates, but it can be exploited by those closely trailing. The analysis identifies the particular type of voting impetus at play in different stages of an election and could help strategists optimize their influence on susceptible voters.

We present a closed form solution for the upscaled diffusion coefficient and derive a first-order homogenized approximation to linear flow equations with periodic and rapidly oscillating coefficients. The coefficients are defined as step functions describing inclusions of various shapes in a main matrix. This constitutes the n-dimensional upscaled version of Darcy’s law for linear flow in such systems. We consider the two-scale asymptotic expansion of the solution of the flow equation, and develop a corrector to an analytical approximation for the solution of the periodic cell-problem. We demonstrate that the proposed analytical form for the effective coefficient satisfies the generalized Voigt–Reiss’ inequality and is in agreement with other known theoretical results, including the geometric average for the checkerboard geometry, and with some published numerical results. The zeroth-order approximation in H1(Ω) is readily obtained and the first-order approximation in L2(Ω) is derived from the proposed analytical approximation to the basis functions. The analytical basis functions are also used to define a correction function that incorporates the heterogeneous features into the zeroth-order approximation to the gradient and flux, which considerably improves the convergence results. We illustrate the procedure with coefficients describing square inclusions with contrast ratios between the inclusion and the matrix as 10:1, 100:1, 1000:1 and 1:10, respectively. We demonstrate numerically that the convergence properties of the proposed approximations agree with the classical theoretical results in homogenization theory.

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 ρ=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%, PP=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.

We perform sensitivity analyses on a mathematical model of malaria transmission to determine the relative importance of model parameters to disease transmission and prevalence. We compile two sets of baseline parameter values: one for areas of high transmission and one for low transmission. We compute sensitivity indices of the reproductive number (which measures initial disease transmission) and the endemic equilibrium point (which measures disease prevalence) to the parameters at the baseline values. We find that in areas of low transmission, the reproductive number and the equilibrium proportion of infectious humans are most sensitive to the mosquito biting rate. In areas of high transmission, the reproductive number is again most sensitive to the mosquito biting rate, but the equilibrium proportion of infectious humans is most sensitive to the human recovery rate. This suggests strategies that target the mosquito biting rate (such as the use of insecticide-treated bed nets and indoor residual spraying) and those that target the human recovery rate (such as the prompt diagnosis and treatment of infectious individuals) can be successful in controlling malaria.

We consider the effectiveness of targeted vaccination at preventing the spread of infectious disease in a realistic social network. We compare vaccination strategies based on no information (random vaccination) to complete information (PageRank) about the network. The most effective strategy we find is to vaccinate those people with the most unvaccinated contacts. However, this strategy requires considerable information and computational effort which may not be practical. The next best strategies vaccinate people with many contacts who in turn have few contacts.

We present a method for estimating transmission matrices that describe the mixing and the probability of infection between age groups. Transmission matrices can be used to estimate age-dependent forces of infection in age-structured, compartmental models for the study of infectious diseases. We analyze the social network generated by the synthetic population of Portland and extract mixing patterns. Our results show that the mixing within the population consists of two groups, children and adults. Children interact most frequently with other children close to their own age, while adults interact with a wider range of age groups and the durations of typical adult contacts are shorter than typical contacts between children. Furthermore, the transmission matrix shows that children are more likely to acquire infection than adults.

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-value0.001). Moreover, final local epidemic sizes are found to be linearly related to the local population size (P-value0.001). This observation supports a roughly constant number of female mosquitoes per person across urban and rural regions.

For a self-adjoint linear operator with a discrete spectrum or a Hermitian matrix, the “extreme” eigenvalues define the boundaries of clusters in the spectrum of real eigenvalues. The outer extreme ones are the largest and the smallest eigenvalues. If there are extended intervals in the spectrum in which no eigenvalues are present, the eigenvalues bounding these gaps are the inner extreme eigenvalues.We will describe a procedure for detecting the extreme eigenvalues that relies on the relationship between the acceleration rate of polynomial acceleration iteration and the norm of the matrix via the spectral theorem, applicable to normal matrices. The strategy makes use of the fast growth rate of Chebyshev polynomials to distinguish ranges in the spectrum of the matrix which are devoid of eigenvalues.The method is numerically stable with regard to the dimension of the matrix problem and is thus capable of handling matrices of large dimension. The overall computational cost is quadratic in the size of a dense matrix; linear in the size of a sparse matrix. We verify computationally that the algorithm is accurate and efficient, even on large matrices.

We have identified environmental and demographic variables, available in January, that predict the relative magnitude and spatial distribution of West Nile virus (WNV) for the following summer. The yearly magnitude and spatial distribution for WNV incidence in humans in the United States (US) have varied wildly in the past decade. Mosquito control measures are expensive and having better estimates of the expected relative size of a future WNV outbreak can help in planning for the mitigation efforts and costs. West Nile virus is spread primarily between mosquitoes and birds; humans are an incidental host. Previous efforts have demonstrated a strong correlation between environmental factors and the incidence of WNV. A predictive model for human cases must include both the environmental factors for the mosquito-bird epidemic and an anthropological model for the risk of humans being bitten by a mosquito. Using weather data and demographic data available in January for every county in the US, we use logistic regression analysis to predict the probability that the county will have at least one WNV case the following summer. We validate our approach and the spatial and temporal WNV incidence in the US from 2005 to 2013. The methodology was applied to forecast the 2014 WNV incidence in late January 2014. We find the most significant predictors for a county to have a case of WNV to be the mean minimum temperature in January, the deviation of this minimum temperature from the expected minimum temperature, the total population of the county, publicly available samples of local bird populations, and if the county had a case of WNV the previous year.

We develop and analyse an ordinary differential equation model to investigate the transmission dynamics of releasing Wolbachia-infected mosquitoes to establish an endemic infection in a population of wild uninfected mosquitoes. Wolbachia is a genus of endosymbiotic bacteria that can infect mosquitoes and reduce their ability to transmit some viral mosquito-transmitted diseases, including dengue fever, chikungunya, and Zika. Although the bacterium is transmitted vertically from infected mothers to their offspring, it can be difficult to establish an endemic infection in a wild mosquito population. Our transmission model for the adult and aquatic-stage mosquitoes takes into account Wolbachia-induced fitness change and cytoplasmic incompatibility. We show that, for a wide range of realistic parameter values, the basic reproduction number, [Formula: see text], is less than one. Hence, the epidemic will die out if only a few Wolbachia-infected mosquitoes are introduced into the wild population. Even though the basic reproduction number is less than one, an endemic Wolbachia infection can be established if a sufficient number of infected mosquitoes are released. This threshold effect is created by a backward bifurcation with three coexisting equilibria: a stable zero-infection equilibrium, an intermediate-infection unstable endemic equilibrium, and a high-infection stable endemic equilibrium. We analyse the impact of reducing the wild mosquito population before introducing the infected mosquitoes and observed that the most effective approach to establish the infection in the wild is based on reducing mosquitoes in both the adult and aquatic stages.

Determining optimal surveillance networks for an emerging pathogen is difficult since it is not known beforehand what the characteristics of a pathogen will be or where it will emerge. The resources for surveillance of infectious diseases in animals and wildlife are often limited and mathematical modeling can play a supporting role in examining a wide range of scenarios of pathogen spread. We demonstrate how a hierarchy of mathematical and statistical tools can be used in surveillance planning help guide successful surveillance and mitigation policies for a wide range of zoonotic pathogens. The model forecasts can help clarify the complexities of potential scenarios, and optimize biosurveillance programs for rapidly detecting infectious diseases. Using the highly pathogenic zoonotic H5N1 avian influenza 2006-2007 epidemic in Nigeria as an example, we determined the risk for infection for localized areas in an outbreak and designed biosurveillance stations that are effective for different pathogen strains and a range of possible outbreak locations. We created a general multi-scale, multi-host stochastic SEIR epidemiological network model, with both short and long-range movement, to simulate the spread of an infectious disease through Nigerian human, poultry, backyard duck, and wild bird populations. We chose parameter ranges specific to avian influenza (but not to a particular strain) and used a Latin hypercube sample experimental design to investigate epidemic predictions in a thousand simulations. We ranked the risk of local regions by the number of times they became infected in the ensemble of simulations. These spatial statistics were then complied into a potential risk map of infection. Finally, we validated the results with a known outbreak, using spatial analysis of all the simulation runs to show the progression matched closely with the observed location of the farms infected in the 2006-2007 epidemic.

Recurrent outbreaks of the avian H5N1 influenza virus in Asia represent a constant global pandemic threat. We characterize and evaluate hypothetical public health measures during the 1918 influenza pandemic in the Canton of Geneva, Switzerland. The transmission rate, the recovery rate, the diagnostic rate, the relative infectiousness of asymptomatic cases, and the proportion of clinical cases are estimated through least-squares fitting of the model to epidemic curve data of the cumulative number of hospital notifications. The latent period and the case fatality proportion are taken from published literature. We determine the variance and identifiability of model parameters via a simulation study. Our epidemic model agrees well with the observed epidemic data. We estimate the basic reproductive number for the spring wave R1;=1.49 (95% CI: 1.45-1.53) and the reproductive number for the fall wave R2;=3.75 (95% CI: 3.57-3.93). In addition, we estimate the clinical reporting for these two waves to be 59.7% (95% CI: 55.7-63.7) and 83% (95% CI: 79-87). We surmise that the lower reporting in the first wave can be explained by a lack of initial awareness of the epidemic and the relative higher severity of the symptoms experienced during the fall wave. We found that effective isolation measures in hospital clinics at best would only ensure control with probability 0.87 while reducing the transmission rate by >76.5% guarantees stopping an epidemic.

We formulate differential susceptibility and differential infectivity models for disease transmission in this paper. The susceptibles are divided into n groups based on their susceptibilities, and the infectives are divided into m groups according to their infectivities. Both the standard incidence and the bilinear incidence are considered for different diseases. We obtain explicit formulas for the reproductive number. We define the reproductive number for each subgroup. Then the reproductive number for the entire population is a weighted average of those reproductive numbers for the subgroups. The formulas for the reproductive number are derived from the local stability of the infection-free equilibrium. We show that the infection-free equilibrium is globally stable as the reproductive number is less than one for the models with the bilinear incidence or with the standard incidence but no disease-induced death. We then show that if the reproductive number is greater than one, there exists a unique endemic equilibrium for these models. For the general cases of the models with the standard incidence and death, conditions are derived to ensure the uniqueness of the endemic equilibrium. We also provide numerical examples to demonstrate that the unique endemic equilibrium is asymptotically stable if it exists.

Objective—To evaluate the influence of individual spatial units (ie, counties) on the epidemic spread of foot-and-mouth disease (FMD) virus. Sample Population—163 counties in Uruguay where there was an outbreak of FMD between April 23 and July 11, 2001. Procedure—A geographically referenced database was created, and the distance between counties (13,203 county pairs), road density of counties (163 counties), and time when cases were reported in those counties (11 weeks of the epidemic) were considered to assess global spatial and spatial-temporal autocorrelation, determine the contribution of links connecting pairs of counties with infected animals, and allow us to hypothesize the influence for spread during the epidemic for counties with greater than the mean infective link contributions. Results—Case clusters were indicated by the Moran Iand Mantel tests during the first 6 weeks of the epidemic. Spatial lags between pairs of counties with infected animals revealed case clustering before and after vaccination was implemented. Temporal lags predicted autocorrelation for up to 3 weeks. Link indices identified counties expected to facilitate epidemic spread. If control measures had been implemented in counties with a high index link (identifiable as early as week 1 of the epidemic), they could have prevented (by week 11 of the epidemic) at least 2.5 times as many cases per square kilometer than the same measures implemented in counties with average link indices. Conclusions and Clinical Relevance—Analysis of spatial autocorrelation and infective link indices may identify network conditions that facilitate (or prevent) disease spread.

We present an ordinary differential equation mathematical model for the spread of malaria in human and mosquito populations. Susceptible humans can be infected when they are bitten by an infectious mosquito. They then progress through the exposed, infectious, and recovered classes, before reentering the susceptible class. Susceptible mosquitoes can become infected when they bite infectious or recovered humans, and once infected they move through the exposed and infectious classes. Both species follow a logistic population model, with humans having immigration and disease‐induced death. We define a reproductive number, $R_0$, for the number of secondary cases that one infected individual will cause through the duration of the infectious period. We find that the disease‐free equilibrium is locally asymptotically stable when $R_0 1$. We prove the existence of at least one endemic equilibrium point for all $R_0 > 1$. In the absence of disease‐induced death, we prove that the tran...

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.

Scorpionism is a public health problem in several regions of the world. The highest mortality, with over 1000 deaths per year, has been reported in Mexico. We analysed the significance of climatological variables to predict the incidence of scorpion stings in humans in the state of Colima (Mexico) for the years 2000-2001. The pluvial precipitation (mm), the evaporation (mm), and the mean, maximum, and minimum temperatures (degrees C) were obtained from local meteorological offices. There are approximately 3 stings/year per 1000 people in municipalities of Colima and Villa de Alvarez and about 18-30 stings/year per 1000 people in the rest of the municipalities. There is very little rain and there are few stings in the winter when the minimum temperature is below about 16 degrees C. The number of scorpion stings is independent of the actual rainfall when this is above 30 mm/month. Using multiple linear regression, we used a backward model selection procedure to estimate that the minimum temperature is correlated with scorpion sting incidence with a statistically significance of 95%. We briefly discuss the application of predictive models of scorpion sting incidence in the appropriate allocation of antivenom serum in hospital clinics.

We formulate an HIV epidemic model with differential infectivity and staged disease progression to account for variations in viral loads and in the rate of disease progression in infected individuals. The stability of the infection-free equilibrium determines the threshold conditions under which the modeled disease either dies out or persists in the population. This stability, expressed in terms of the epidemic reproductive number, can be determined by the spectral radius of the next generation operator, or from the eigenvalues of the Jacobian matrix for the model system linearized about the infection-free equilibrium. We derive an explicit formula for the reproductive number employing both of these techniques by investigating the spectral radius of the next generation operator, and by directly applying M-matrix theory with recursive forward and backward inductions to characterize the eigenvalues of the Jacobian matrix in terms of the reproductive number.

Both the hippocampus and the medial prefrontal cortex are essential for successful performance in learning- and memory-related tasks. Within the hippocampus the theta rhythm plays an integral role in the timing of action potentials of hippocampal neurons responding to elements of any given task. Medial prefrontal cortex (mPFC) neurons display firing rate changes to specific facets of behavioral tasks (Jung et al., 1998. Cereb Cortex 8:437--450). We recorded units in the mPFC and field potentials in the hippocampus to determine whether behaviorally correlated mPFC cells fired with phase relationships to the hippocampal theta rhythm. In two different behavioral tasks (running a linear track and foraging in two distinct environments) we found mPFC cells that alternated between theta entrained firing and nonphasic firing depending on the ongoing behavior, while other cells were modulated during all conditions in both tasks. The majority of the mPFC cells with a significant correlation of firing rate changes with behavior were entrained to hippocampal theta. Cells that fired to specific events during only one direction of running were predisposed to theta modulation only in that direction. mPFC neurons have the capability to respond to behaviorally relevant elements by dynamically alternating between hippocampal theta entrained and nonphasic firing.

We describe a pseudo-spectral numerical method to solve the systems of one-dimensional evolution equations for free surface waves in a homogeneous layer of an ideal fluid. We use the method to solve a system of one-dimensional integro-differential equations, first proposed by Ovsjannikov and later derived by Dyachenko, Zakharov, and Kuznetsov, to simulate the exact evolution of nonlinear free surface waves governed by the two-dimensional Euler equations. These equations are written in the transformed plane where the free surface is mapped onto a flat surface and do not require the common assumption that the waves have small amplitude used in deriving the weakly nonlinear Korteweg-de Vries and Boussinesq long-wave equations. We compare the solution of the exact reduced equations with these weakly nonlinear long-wave models and with the nonlinear long-wave equations of Su and Gardner that do not assume the waves have small amplitude. The Su and Gardner solutions are in remarkably close agreement with the exact Euler solutions for large amplitude solitary wave interactions while the interactions of low-amplitude solitary waves of all four models agree. The simulations demonstrate that our method is an efficient and accurate approach to integrate all of these equations and conserves the mass, momentum, and energy of the Euler equations over very long simulations.

The uncertainty in the variables and functions in computer simulations can be quantified by probability distributions and the correlations between the variables. We augment the standard computer arithmetic operations and the interval arithmetic approach to include probability distribution variable (PDV) as a basic data type. Probability distribution variable is a random variable that is usually characterized by generalized probabilistic discretization. The correlations or dependencies between PDVs that arise in a computation are automatically calculated and tracked. These correlations are used by the computer arithmetic rules to achieve the convergent approximation of the probability distribution function of a PDV and to guarantee that the derived bounds include the true solution. In many calculations, the calculated uncertainty bounds for PDVs are much tighter than they would have been had the dependencies been ignored. We describe the new PDV Arithmetic and verify the effectiveness of the approach to account for the creation and propagation of uncertainties in a computer program due to uncertainties in the initial data.

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.

We prove that the mimetic finite-difference discretizations of Laplace's equation converges on rough logically-rectangular grids with convex cells. Mimetic discretizations for the invariant operators' divergence, gradient, and curl satisfy exact discrete analogs of many of the important theorems of vector calculus. The mimetic discretization of the Laplacian is given by the composition of the discrete divergence and gradient. We first construct a mimetic discretization on a single cell by geometrically constructing inner products for discrete scalar and vector fields, then constructing a finite-volume discrete divergence, and then constructing a discrete gradient that is consistent with the discrete divergence theorem. This construction is then extended to the global grid. We demonstrate the convergence for the two-dimensional Laplace equation with Dirichlet boundary conditions on grids with a lower bound on the angles in the cell corners and an upper bound on the cell aspect ratios. The best convergence rate to be expected is first order, which is what we prove. The techniques developed apply to far more general initial boundary-value problems.

We formulate epidemiological models for the transmission of a pathogen that can mutate in the host to create a second infectious mutant strain. The models account for mutation rates that depend on how long the host has been infected. We derive explicit formulas for the reproductive number of the epidemic based on the local stability of the infection-free equilibrium. We analyze the existence and stability of the boundary equilibrium, whose infection components are zero and positive, respectively, and the endemic equilibrium, whose components are all positive. We establish the conditions for global stability of the infection-free and boundary equilibria and local stability of the endemic equilibrium for the case where there is no age structure for the pathogen in the infected population. We show that under certain circumstances, there is a Hopf bifurcation where the endemic equilibrium loses its stability, and periodic solutions appear. We provide examples and numerical simulations to illustrate the Hopf b...

Mathematical models of HIV-1 infection can help interpret drug treatment experiments and improve our understanding of the interplay between HIV-1 and the immune system. We develop and analyze an age-structured model of HIV-1 infection that allows for variations in the death rate of productively infected T cells and the production rate of viral particles as a function of the length of time a T cell has been infected. We show that this model is a generalization of the standard differential equation and of delay models previously used to describe HIV-1 infection, and provides a means for exploring fundamental issues of viral production and death. We show that the model has uninfected and infected steady states, linked by a transcritical bifurcation. We perform a local stability analysis of the nontrivial equilibrium solution and provide a general stability condition for models with age structure. We then use numerical methods to study solutions of our model focusing on the analysis of primary HIV infection. We show that the time to reach peak viral levels in the blood depends not only on initial conditions but also on the way in which viral production ramps up. If viral production ramps up slowly, we find that the time to peak viral load is delayed compared to results obtained using the standard (constant viral production) model of HIV infection. We find that data on viral load changing over time is insufficient to identify the functions specifying the dependence of the viral production rate or infected cell death rate on infected cell age. These functions must be determined through new quantitative experiments.

These experiments examine changes in theta power as measured by wavelet analysis in five rats performing a conditional visual discrimination task and a simple running task. In the conditional task, rats were trained to press one lever to initiate a trial and then to press one of two choice levers, each corresponding to one of two cue lights. Analysis of theta power in this operant task found a large decrease in theta power during the choice bar presses, in contrast to the increase in theta power during trial initiation bar presses. This result seems to stand counter to results that propose consistent relationships between motor actions and theta power (Vanderwolf, EEG Clin Neurophys 26:407-418, 1969), as well as studies suggesting that the lack of bar-press theta is the result of habituation. However, these data can be seen as being in broad agreement with the theoretical framework of sensorimotor integration (Bland and Oddie, Behav Brain Res 127:119-136, 2001). To investigate further the power of theta observed at the termination of type 1 motor activity, a runway task was devised in which rats ran back and forth between two ends of a linear track, one of which was always rewarded and the other never rewarded. Theta power decreased sharply 240 ms before movement ended at the rewarded end, but not at the unrewarded end of the track. These data extend the current scope of theory in demonstrating that hippocampal theta activity can end abruptly 200-400 ms prior to the end of type 1 motor movement when approaching the end of a motor sequence.

Experimental evidence suggests that the hippocampal theta rhythm plays a critical role in learning. Previous studies have shown long-term potentiation (LTP) to be preferentially induced with stimulation on the peak of local theta rhythm in region CA1 in anesthetized rats and with stimulation of the perforant path at the peak of theta in both anesthetized and behaving animals. We set out to determine the effects of tetanic burst stimulation in stratum radiatum of region CA1 in awake behaving animals, delivered during either the peak or the trough of the theta rhythm in the EEG. Bursts delivered to the peak resulted in an increase of 17.9 +/- 0.94% in potential slope. When identical stimulation bursts were delivered to the trough of local theta waves, the potential slope decreased 12.9 +/- 1.03%. This is the first report of LTP being preferentially induced at the peak of local theta rhythm in behaving animals in region CA1 and that LTD was found in response to tetanic stimulation at the trough of the local theta wave. The results are discussed within the framework of a recent theory that proposes that the theta rhythm sets the dynamics for alternating phases of encoding and retrieval (Hasselmo et al., 20021).

Adaptive mesh methods are valuable tools in improving the accuracy and efficiency of the numerical solution of evolutionary systems of partial differential equations. If the mesh moves to track fronts and large gradients in the solution, then larger time steps can be taken than if it were to remain stationary. We derive explicit differential equations for moving the mesh so that the time variation of the solution at the mesh points is minimized. Moving the mesh based on this approach allows for larger time steps but does not guarantee that the solution is well resolved in space. We maintain spatial accuracy when there are new emerging layers or wave fronts by adaptively rezoning the mesh points to equidistribute an error estimate. When using a multistep integration method, the past solution values are also interpolated so that the same multistep method can be used after rezoning. The resulting algorithm has very few problem-dependent numerical parameters and is appropriate for a large class of one-dimensional partial differential equations. We illustrate the performance of the algorithm by examples and demonstrate that the proposed algorithm is efficient and accurate when compared with other adaptive mesh strategies.

Mathematical models can help predict the effectiveness of control measures on the spread of HIV and other sexually transmitted diseases (STDs) by reducing the uncertainty in assessing the impact of intervention strategies such as random screening and contact tracing. Even though contact tracing is one of the most effective methods used for controlling treatable STDs, it is still a controversial strategy for controlling HIV because of cost and confidentiality issues. To help estimate the effectiveness of these control measures, we formulate two models with random screening and contact tracing based on the differential infectivity (DI) model and the staged-progression (SP) model. We derive formulas for the reproductive numbers and the endemic equilibria and compare the impact that random screening and contact tracing have in slowing the epidemic in the two models. In the DI model the infected population is divided into groups according to their infectiousness, and HIV is largely spread by a small, highly infectious, group of superspreaders. In this model contact tracing is an effective approach to identifying the superspreaders and has a large effect in slowing the epidemic. In the SP model every infected individual goes through a series of infection stages and the virus is primarily spread by individuals in an initial highly infectious stage or in the late stages of the disease. In this model random screening is more effective than for the DI model, and contact tracing is less effective. Thus the effectiveness of the intervention strategy strongly depends on the underlying etiology of the disease transmission.

We use the support operators method to derive discrete approximations for the gradient of a vector and divergence of a tensor on unstructured grids in two dimensions. These discrete operators satisfy discrete analogs of the integral identities of the differential operators on unstructured grids where vector functions are defined at the grid points, and tensor functions are defined as tangential projections to the zone edges, or as normal projections to the median mesh. We evaluate the accuracy of the discrete operators by determining the order of convergence of the truncation error on structured and unstructured grids, and show that the truncation error of the method is between first and second order depending on the smoothness of the grid. In a test problem on a highly nonuniform grid, we confirm that the convergence rate is between first and second order.

Summary The function of the anterior cingulate cortex (ACC) remains controversial, yet many theories suggest a role in behavioral adaptation, partly because a robust event-related potential, the feedback-related negativity (FN), is evoked over the ACC whenever expectations are violated. We recorded from the ACC as rats performed a task identical to one that reliably evokes an FN in humans. A subset of neurons was found that encoded expected outcomes as abstract outcome representations. The degree to which a reward/non-reward outcome representation emerged during a trial depended on the history of outcomes that preceded it. A prediction error was generated on incongruent trials as the ensembles shifted from representing the expected to the actual outcome, at the same time point we have previously reported an FN in the local field potential. The results describe a novel mode of prediction error signaling by ACC neurons that is associated with the generation of an FN.