Optimal mix of screening and contact tracing for endemic diseases

Two common means of controlling infectious diseases are screening and contact tracing. Which should be used, and when? We consider the problem of determining the cheapest mix of screening and contact tracing necessary to achieve a desired endemic prevalence of a disease or to identify a specified number of cases. We perform a partial equilibrium analysis of small-scale interventions, assuming that prevalence is unaffected by the intervention; we develop a full equilibrium analysis where we compare the long-term cost of various combinations of screening and contact tracing needed to achieve a given equilibrium prevalence; and we solve the problem of minimizing the total costs of identifying and treating disease cases plus the cost of untreated disease cases. Our analysis provides several insights. First, contact tracing is only cost effective when prevalence is below a threshold value. This threshold depends on the relative cost per case found by screening versus contact tracing. Second, for a given contact tracing policy, the screening rate needed to achieve a given prevalence or identify a specified number of cases is a decreasing function of disease prevalence. As prevalence increases above the threshold (and contact tracing is discontinued), the screening rate jumps discontinuously to a higher level. Third, these qualitative results hold when we consider unchanged or changed prevalence, and short-term or long-term costs.     

Modeling the impact of random screening and contact tracing in reducing the spread of HIV

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.     

Parameter-dependent transitions and the optimal control of dynamical diseases

Many theoretical studies in biological and physical sciences consider the dynamical behavior of ann-dimensional ordinary differential equation that contains a large number of independent parameters. A frequently asked question is, are there permissible parameter sets that result in periodic or chaotic behavior? The large number of distinct parameters often limits the feasibility of trial and error calculations. The large dimension and nonlinearity of the system make application of analytic methods at best difficult and at worst effectively impossible. It is shown here that a computational search for parameter-dependent transitions of attractor topology can be effected by constrained optimization of quantitative measures of dynamical behavior (Hurwitz polynomials, Floquet coefficients, Lyapunov exponents and correlation dimension). As an example, we examine a three-dimensional nonlinear ordinary differential equation containing seven parameters that was constructed by Goldbeter and Segel to model periodic synthesis of cyclic AMP inDictyostelium. A search for bifurcations to periodic solutions is made by minimizing Hurwitz coefficients subject to parameter constraints. By comparing four optimization algorithms, the defects and advantages of the procedure are identified. It is also argued that it may be possible to use this characterization of dynamics to construct optimal responses to dynamical diseases (those disorders that result from parameter-dependent bifurcations in physiological control systems).     

Word construction: tracing an optimal path through the lexicon

Optimal Construction Morphology (OCM) is a new construction-based theory of morphology that selects the optimal combination of lexical constructions to best achieve a target meaning. OCM combines elements of realizational and item-based morphological theories. It is realizational, in that words are constructed in response to a given meaning target. It is incremental in that words are built from lexical structures, one layer at a time. It is optimizing in that, in response to a meaning target, the morphological grammar dips into the lexicon, building and assessing morphological constituents incrementally until the word being built optimally matches the target meaning. In this paper OCM is shown to illuminate a vexing optimization puzzle confronted by all theories of morphology: why is redundancy in morphology rejected as ungrammatical in some situations (“blocking”), but absolutely required in others (“multiple/extended exponence”)? The OCM analysis incorporates two notions of morphological strength that have been proposed in the literature: stem type, on a scale from root (weakest) to word (strongest), and exponence strength, related to productivity and parsability.     

Prediction of optimal folding routes of proteins that satisfy the principle of lowest entropy loss: dynamic contact maps and optimal control

An optimization model is introduced in which proteins try to evade high energy regions of the folding landscape, and prefer low entropy loss routes during folding. We make use of the framework of optimal control whose convenient solution provides practical and useful insight into the sequence of events during folding. We assume that the native state is available. As the protein folds, it makes different set of contacts at different folding steps. The dynamic contact map is constructed from these contacts. The topology of the dynamic contact map changes during the course of folding and this information is utilized in the dynamic optimization model. The solution is obtained using the optimal control theory. We show that the optimal solution can be cast into the form of a Gaussian Network that governs the optimal folding dynamics. Simulation results on three examples (CI2, Sso7d and Villin) show that folding starts by the formation of local clusters. Non-local clusters generally require the formation of several local clusters. Non-local clusters form cooperatively and not sequentially. We also observe that the optimal controller prefers "zipping" or small loop closure steps during folding. The folding routes predicted by the proposed method bear strong resemblance to the results in the literature.     

Finding the one: optimal choosiness under sequential mate choice

When mates are encountered sequentially, each encounter involves a decision whether to reject the current suitor and risk not finding a better mate, or to accept them despite their flaws. I provide a flexible framework for modelling optimal choosiness when mate encounters occur unpredictably in time. The model allows for temporal variation in the fitness benefits of mating, including seasonal breeding conditions, accrual of mate search costs, survival of the choosing individual or senescence of gametes. The basic optimality framework can be applied iteratively to obtain mate choice equilibria in dynamically evolving populations. My model predicts that individuals should be choosier when the average rate of mate encounters is high, but that choosiness should decline over time as the likelihood of future mate encounters decreases. When mate encounters are uncertain, there is a trade‐off between reproductive timing and mate choice (the ‘when’ and the ‘who’). Mate choice may be selected against when reproductive timing is highly important (e.g. when breeding conditions show a narrow peak in time). This can even lead to step‐shaped mate choice functions, where individuals abruptly switch from rejecting to accepting all suitors as peak breeding conditions approach. The model contributes to our understanding of why individuals may not express mate preferences, even when there is substantial variation in mate quality.     

Social contact patterns in Vietnam and implications for the control of infectious diseases

Background

The spread of infectious diseases from person to person is determined by the frequency and nature of contacts between infected and susceptible members of the population. Although there is a long history of using mathematical models to understand these transmission dynamics, there are still remarkably little empirical data on contact behaviors with which to parameterize these models. Even starker is the almost complete absence of data from developing countries. We sought to address this knowledge gap by conducting a household based social contact diary in rural Vietnam.

Methods and Findings

A diary based survey of social contact patterns was conducted in a household-structured community cohort in North Vietnam in 2007. We used generalized estimating equations to model the number of contacts while taking into account the household sampling design, and used weighting to balance the household size and age distribution towards the Vietnamese population. We recorded 6675 contacts from 865 participants in 264 different households and found that mixing patterns were assortative by age but were more homogenous than observed in a recent European study. We also observed that physical contacts were more concentrated in the home setting in Vietnam than in Europe but the overall level of physical contact was lower. A model of individual versus household vaccination strategies revealed no difference between strategies in the impact on R ₀.

Conclusions and Significance

This work is the first to estimate contact patterns relevant to the spread of infections transmitted from person to person by non-sexual routes in a developing country setting. The results show interesting similarities and differences from European data and demonstrate the importance of context specific data.     

Timely identification of optimal control strategies for emerging infectious diseases

Background

Health authorities must rely on quarantine, isolation, and other non-pharmaceutical interventions to contain outbreaks of newly emerging human diseases.

Methods

We modeled a generic disease caused by a pathogen apparently transmitted by close interpersonal contact, but about which little else is known. In our model, people may be infectious while incubating or during their prodrome or acute illness. We derived an expression for ℜ, the reproduction number, took its partial derivatives with respect to control parameters, and encoded these analytical results in a user-friendly Mathematica™ notebook. With biological parameters for SARS estimated from the initial case series in Hong Kong and infection rates from hospitalizations in Singapore, we determined ℜ's sensitivity to control parameters.

Results

Stage-specific infection rate estimates from cases hospitalized before quarantine began exceed those from the entire outbreak, but are qualitatively similar: infectiousness was negligible until symptom onset, and increased 10-fold from prodrome to acute illness. Given such information, authorities might instead have emphasized a strategy whose efficiency more than compensates for any possible reduction in efficacy.

Conclusions

In future outbreaks of new human diseases transmitted via close interpersonal contact, it should be possible to identify the optimal intervention early enough to facilitate effective decision-making.     

Genomic signatures: tracing the origin of retroelements at the nucleotide level

We investigate the nucleotide sequences of 23 retroelements (4 mammalian retroviruses, 1 human, 3 yeast, 2 plant, and 13 invertebrate retrotransposons) in terms of their oligonucleotide composition in order to address the problem of relationship between retrotransposons and retroviruses, and the coadaptation of these retroelements to their host genomes. We have identified by computer analysis over-represented 3- through 6-mers in each sequence. Our results indicate retrotransposons are heterogeneous in contrast to retroviruses, suggesting different modes of evolution by slippage-like mechanisms. Moreover, we have calculated the Observed/Expected number ratio for each of the 256 tetramers and analysed the data using a multivariate approach. The tetramer composition of retroelement sequences appears to be influenced by host genomic factors like methylase activity. This revised version was published online in August 2006 with corrections to the Cover Date.     

Manipulation of TGF-beta to control autoimmune and chronic inflammatory diseases

Defining the mechanisms whereby transforming growth factor-beta (TGF-beta) controls physiologic inflammation and the immune response and how it contributes to pathology when it is dysregulated is critical to our ability to manipulate the levels and activity of this potent cytokine for therapeutic benefit. In keeping with its dichotomous nature, recent evidence suggests that overproduction and/or activation contribute to persistent inflammation and that antagonists of TGF-beta delivered locally can break the cycle of leukocyte recruitment and fibrotic sequelae. On the other hand, systemic routing of TGF-beta can also inhibit inflammatory pathogenesis by multiple mechanisms as exemplified by systemic injections of the protein and by recent gene transfer studies. In addition, enhanced levels of circulating endogenous TGF-beta appear to be an instrument of suppression during the development of oral tolerance, cyclosporin treatment, and following administration of retinoic acid. Although treatment of autoimmune and chronic inflammatory diseases is an important goal, the multiplicity of actions of TGF-beta and the nearly ubiquitous expression of TGF-beta and its receptors dictate a cautious approach to the use of this powerful cytokine as a therapeutic agent.     

React or wait: which optimal culling strategy to control infectious diseases in wildlife

We applied optimal control theory to an SI epidemic model to identify optimal culling strategies for diseases management in wildlife. We focused on different forms of the objective function, including linear control, quadratic control, and control with limited amount of resources. Moreover, we identified optimal solutions under different assumptions on disease-free host dynamics, namely: self-regulating logistic growth, Malthusian growth, and the case of negligible demography. We showed that the correct characterization of the disease-free host growth is crucial for defining optimal disease control strategies. By analytical investigations of the model with negligible demography, we demonstrated that the optimal strategy for the linear control can be either to cull at the maximum rate at the very beginning of the epidemic (reactive culling) when the culling cost is low, or never to cull, when culling cost is high. On the other hand, in the cases of quadratic control or limited resources, we demonstrated that the optimal strategy is always reactive. Numerical analyses for hosts with logistic growth showed that, in the case of linear control, the optimal strategy is always reactive when culling cost is low. In contrast, if the culling cost is high, the optimal strategy is to delay control, i.e. not to cull at the onset of the epidemic. Finally, we showed that for diseases with the same basic reproduction number delayed control can be optimal for acute infections, i.e. characterized by high disease-induced mortality and fast dynamics, while reactive control can be optimal for chronic ones.