Optimizing reactive responses to outbreaks of immunizing infections: balancing case management and vaccination

For vaccine-preventable infections, immunization generally needs to be supplemented by palliative care of individuals missed by the vaccination. Costs and availability of vaccine doses and palliative care vary by disease and by region. In many situations, resources for delivery of palliative care are independent of resources required for vaccination; however we also need to consider the conservative scenario where there is some trade-off between efforts, which is of potential relevance for resource-poor settings. We formulate an SEIR model that includes those two control strategies - vaccination and palliative care. We consider their relative merit and optimal allocation in the context of a highly efficacious vaccine, and under the assumption that palliative care may reduce transmission. We investigate the utility of a range of mixed or pure strategies that can be implemented after an epidemic has started, and look for rule-of-thumb principles of how best to reduce the burden of disease during an acute outbreak over a spectrum of vaccine-preventable infections. Intuitively, we expect the best strategy to initially focus on vaccination, and enhanced palliative care after the infection has peaked, but a number of plausible realistic constraints for control result in important qualifications on the intervention strategy. The time in the epidemic when one should switch strategy depends sensitively on the relative cost of vaccine to palliative care, the available budget, and [Formula: see text]. Crucially, outbreak response vaccination may be more effective in managing low-[Formula: see text] diseases, while high [Formula: see text] scenarios enhance the importance of routine vaccination and case management.     

Prevention and control of malaria epidemics

Malaria epidemics have recently occurred in many areas of the world, particularly in the irregular fringe, along the limits of distribution of malaria endemicity, whether the limiting factors are temperature (latitude or altitude) or relative humidity (deserts), which were the scene of the major epidemics of the past. A review is made of the current approaches to epidemic prevention and control in line with the global malaria control strategy, of which it constitutes an essential element. The different components are discussed, including the identification and study of epidemic prone areas, the search for indicators of epidemic risk, their monitoring, and the early detection and control of actual epidemics. The potential implementation of preventive and control activities depends, nevertheless, on the degree of preparedness of the health services to detect alarm signals, the real time left for action and their capacity of implementation within that time. Recent developments in geographical information systems (GIS) and satellite derived meteorological information offer most useful tools for precise and timely epidemic forecasting, although it should be recognised that such information is only useful if based on a real understanding of their local significance. There remains an urgent need to develop and support local capabilities for the ground truthing of satellite information and for translating it into preventive and control actions.     

Control of snakebite envenoming: A mathematical modeling study

A mathematical model is designed to assess the impact of some interventional strategies for curtailing the burden of snakebite envenoming in a community. The model is fitted with real data set. Numerical simulations have shown that public health awareness of the susceptible individuals on snakebite preventive measures could reduce the number of envenoming and prevent deaths and disabilities in the population. The simulations further revealed that if at least fifty percent of snakebite envenoming patients receive early treatment with antivenom a substantial number of deaths will be averted. Furthermore, it is shown using optimal control that combining public health awareness and antivenom treatment averts the highest number of snakebite induced deaths and disability adjusted life years in the study area. To choose the best strategy amidst limited resources in the study area, cost effectiveness analysis in terms of incremental cost effectiveness ratio is performed. It has been established that the control efforts of combining public health awareness of the susceptible individuals and antivenom treatment for victims of snakebite envenoming is the most cost effective strategy. Approximately the sum of US$72,548 is needed to avert 117 deaths or 2,739 disability adjusted life years that are recorded within 21 months in the study area. Thus, the combination of these two control strategies is recommended.     

Optimal control and cost effectiveness analysis for Newcastle disease eco-epidemiological model in Tanzania

In this paper, a deterministic compartmental eco- epidemiological model with optimal control of Newcastle disease (ND) in Tanzania is proposed and analysed. Necessary conditions of optimal control problem were rigorously analysed using Pontryagin's maximum principle and the numerical values of model parameters were estimated using maximum likelihood estimator. Three control strategies were incorporated such as chicken vaccination (preventive), human education campaign and treatment of infected human (curative) and its' impact were graphically observed. The incremental cost effectiveness analysis technique used to determine the most cost effectiveness strategy and we observe that combination of chicken vaccination and human education campaign strategy is the best strategy to implement in limited resources. Therefore, ND can be controlled if the farmers will apply chicken vaccination properly and well in time.     

Optimal surveillance and eradication of invasive species in heterogeneous landscapes

Cost-effective surveillance strategies are needed for efficient responses to biological invasions and must account for the trade-offs between surveillance effort and management costs. Less surveillance may allow greater population growth and spread prior to detection, thereby increasing the costs of damages and control. In addition, surveillance strategies are usually applied in environments under continual invasion pressure where the number, size and location of established populations are unknown prior to detection. We develop a novel modeling framework that accounts for these features of the decision and invasion environment and determines the long term sampling effort that minimises the total expected costs of new invasions. The optimal solution depends on population establishment and growth rates, sample sensitivity, and sample, eradication, and damage costs. We demonstrate how to optimise surveillance systems under budgetary constraints and find that accounting for spatial heterogeneity in sampling costs and establishment rates can greatly reduce management costs.     

Evaluating the combined effectiveness of influenza control strategies and human preventive behavior

Control strategies enforced by health agencies are a major type of practice to contain influenza outbreaks. Another type of practice is the voluntary preventive behavior of individuals, such as receiving vaccination, taking antiviral drugs, and wearing face masks. These two types of practices take effects concurrently in influenza containment, but little attention has been paid to their combined effectiveness. This article estimates this combined effectiveness using established simulation models in the urbanized area of Buffalo, NY, USA. Three control strategies are investigated, including: Targeted Antiviral Prophylaxis (TAP), workplace/school closure, community travel restriction, as well as the combination of the three. All control strategies are simulated with and without regard to individual preventive behavior, and the resulting effectiveness are compared. The simulation outcomes suggest that weaker control strategies could suffice to contain influenza epidemics, because individuals voluntarily adopt preventive behavior, rendering these weaker strategies more effective than would otherwise have been expected. The preventive behavior of individuals could save medical resources for control strategies and avoid unnecessary socio-economic interruptions. This research adds a human behavioral dimension into the simulation of control strategies and offers new insights into disease containment. Health policy makers are recommended to review current control strategies and comprehend preventive behavior patterns of local populations before making decisions on influenza containment.     

Trypanosoma evansi control and horse mortality in the Brazilian Pantanal

The impact of three treatment strategies for Trypanosoma evansi control on horse mortality in the Brazilian Pantanal based on four size categories of cattle ranches is explored. The region's 49,000 horses are indispensable to traditional extensive cattle ranching and T. evansi kills horses. About 13% of these horses would be lost, annually, due to T. evansi if no control were undertaken. One preventive and two curative treatment strategies are financially justifiable in the Pantanal. The best available technology for the treatment of T. evansi from a horse mortality perspective is the preventive strategy, which spares 6,462 horses, annually. The year-round cure spares 5,783 horses, and the seasonal cure saves 5,204 horses on a regional basis relative to no control strategy. Regardless of the strategy adopted, 39% of the costs or benefits fall to the largest ranches, while 18% fall to the smallest ranches.     

Supportive therapy of lung cancer patients

The effectiveness of cancer treatment given to lung cancer patients is indicated by the asymptomatic and non-toxic survival time. The goal is not to prolong the patients' suffering, but to lengthen the duration of the best quality of life lived (Time Without Symptoms and Toxicity-TWIST). Supportive care is the prevention and management of side effects which occur during therapy (chemotherapy, radiotherapy, surgery) given to patients suffering from cancer. Supportive care is the widespread activity of doctors, nurses and social workers, including psychosocial assistance and rehabilitation through the various stages of illness till death. Though palliative therapy is understood to be the high level and professional treatment of terminally ill patients in those cases where curative measures are not possible anymore, supportive and palliative treatment often overlap (e.g. pain control, cachexia, obstructive syndromes). Palliative care is part of supportive therapy. The goal of supportive care is to reduce the patients' subjective symptoms to the minimum ("well being") during therapy, follow up and consequently until death. The essence of supportive care is to keep the patients' quality of life on the highest possible level. This article summarizes the pathophysiology, prevention and therapy of the most frequently occuring side effects observed during the management of lung cancer patients.     

Optimal treatment of an SIR epidemic model with time delay

In this paper the optimal control strategies of an SIR (susceptible–infected–recovered) epidemic model with time delay are introduced. In order to do this, we consider an optimally controlled SIR epidemic model with time delay where a control means treatment for infectious hosts. We use optimal control approach to minimize the probability that the infected individuals spread and to maximize the total number of susceptible and recovered individuals. We first derive the basic reproduction number and investigate the dynamical behavior of the controlled SIR epidemic model. We also show the existence of an optimal control for the control system and present numerical simulations on real data regarding the course of Ebola virus in Congo. Our results indicate that a small contact rate(probability of infection) is suitable for eradication of the disease (Ebola virus) and this is one way of optimal treatment strategies for infectious hosts.     

Alignment with context dependent scoring function.

In the paper by Gambin et al. (2002) we introduced the model of contextual alignment of biological sequences. It is an extension of the classical alignment, in which the cost of a substitution depends on the surrounding symbols. Consequently, in this model the cost of transforming one sequence into another depends on the order of editing operations. In this paper, we strengthen some of our results which concern reconstructing (the representation of) all the orders of operations which yield this optimal cost. We also present a procedure to construct context-dependent substitution tables and discuss the distribution of scores of local contextual alignment, which is shown to follow the extreme value distribution in the gap-free, reduced context case. We also demonstrate a linear time algorithm to compute the optimal local and global alignment without gaps.     

Natal movement in juvenile Atlantic salmon: a body size-dependent strategy?

If competitive ability depends on body size, then the optimal natal movement from areas of high local population density can also be predicted to be size-dependent. Specifically, small, competitively-inferior individuals would be expected to benefit most from moving to areas of lower local density. Here we evaluate whether individual variation in natal movement following emergence from nests is consistent with such a size-dependent strategy in Atlantic salmon, and whether such a strategy is evident across a range of environmental conditions (principally predator presence and conspecific density). In stream channel experiments, those juveniles that stayed close to nests were larger than those that emigrated. This result was not sensitive to predator presence or conspecific density. These observations were mirrored in natural streams in which salmon eggs were planted in nests and the resulting offspring were sampled at high spatial resolution. A negative relationship was found between juvenile body size and distance from nests early in development whereas in those streams sampled later in ontogeny, individuals that had moved furthest were largest. Thus, movement away from nests appeared to result in a reduced competitive intensity and increased growth rate. The fact that there is ultimately a growth advantage associated with moving suggests that there is also a cost that selects against movement by the larger individuals. Thus, natal movement in juvenile Atlantic salmon appears to represent a body size-dependent strategy.     

Cost-effective control of chronic viral diseases: Finding the optimal level of screening and contact tracing

Chronic viral diseases such as human immunodeficiency virus (HIV) and hepatitis B virus (HBV) afflict millions of people worldwide. A key public health challenge in managing such diseases is identifying infected, asymptomatic individuals so that they can receive antiviral treatment. Such treatment can benefit both the treated individual (by improving quality and length of life) and the population as a whole (through reduced transmission). We develop a compartmental model of a chronic, treatable infectious disease and use it to evaluate the cost and effectiveness of different levels of screening and contact tracing. We show that: (1) the optimal strategy is to get infected individuals into treatment at the maximal rate until the incremental health benefits balance the incremental cost of controlling the disease; (2) as one reduces the disease prevalence by moving people into treatment (which decreases the chance that they will infect others), one should increase the level of contact tracing to compensate for the decreased effectiveness of screening; (3) as the disease becomes less prevalent, it is optimal to spend more per case identified; and (4) the relative mix of screening and contact tracing at any level of disease prevalence is such that the marginal efficiency of contact tracing (cost per infected person found) equals that of screening if possible (e.g., when capacity limitations are not binding). We also show how to determine the cost-effective equilibrium level of disease prevalence (among untreated individuals), and we develop an approximation of the path of the optimal prevalence over time. Using this, one can obtain a close approximation of the optimal solution without having to solve an optimal control problem. We apply our methods to an example of hepatitis B virus.     

Evolution of local adaptations in dispersal strategies

The optimal probability and distance of dispersal largely depend on the risk to end up in unsuitable habitat. This risk is highest close to the habitat's edge and consequently, optimal dispersal probability and distance should decline towards the habitat's border. This selection should lead to the emergence of spatial gradients in dispersal strategies. However, gene flow caused by dispersal itself is counteracting local adaptation. Using an individual based model we investigate the evolution of local adaptations of dispersal probability and distance within a single, circular, habitat patch. We compare evolved dispersal probabilities and distances for six different dispersal kernels (two negative exponential kernels, two skewed kernels, nearest neighbour dispersal and global dispersal) in patches of different size. For all kernels a positive correlation between patch size and dispersal probability emerges. However, a minimum patch size is necessary to allow for local adaptation of dispersal strategies within patches. Beyond this minimum patch area the difference in mean dispersal distance between center and edge increases linearly with patch radius, but the intensity of local adaptation depends on the dispersal kernel. Except for global and nearest neighbour dispersal, the evolved spatial pattern are qualitatively similar for both, mean dispersal probability and distance. We conclude, that inspite of the gene-flow originating from dispersal local adaptation of dispersal strategies is possible if a habitat is of sufficient size. This presumably holds for any realistic type of dispersal kernel.     

The role of folic acid in the prevention of cardiovascular disease

Coronary heart disease is the leading cause of death in the developed world. Current surgical and pharmacological interventions are essentially palliative and interest in preventive strategies, particularly through nutrition and avoidance of tobacco has increased in recent years. Basic scientific, clinical and epidemiological evidence indicates a positive association between the plasma level of the amino acid homocysteine and vascular disease. Homocysteine levels are inversely related to both intake and plasma levels of folate. Less strong evidence indicates an inverse relationship between folate intake and coronary heart disease risk. It is likely that current estimates of dietary folate requirements are lower than optimal. Folic acid supplementation reliably reduces homocysteine levels, and may also modify endothelial function independent of this effect on homocysteine. Such treatment is cheap and appears to be essentially free of risk. However, until present randomised control trials are complete, it will not be known definitively whether or not increasing folate intake reduces cardiovascular risk.     

Time Budgets and Territory Size: Some Simultaneous Optimization Models for Energy Maximizers

A set of optimization models in two variables of choice, territorysize and time spent patrolling for intruders, is presented forenergy maximizers. Models vary in the curvilinearity of therelationship between territory circumference and both intrusionrate and cost of expelling a single intruder. Models are analyzedboth with and without constraints; constraints are on processingrate and on the time spent patrolling, feeding and activelydefending. The models all include the concept of "intruder equilibrium,"an equilibrial density of intruders in a territory resultingfrom a balance between intrusion rate and expulsion by the defender.This equilibrial density can be considered a measure of territorialexclusiveness. The two-variable models predict effects on territory size andpatrol time of variation in food density, intrusion rate, costsof expelling a single intruder in energy and time, food-consumptionrate of an intruder, area of detection while patrolling, totaltime available for territorial and feeding activities, timeto eat a unit of food energy, energy cost of patrol per time,and processing-rate capacity. With increasing intruder rate,optimal territory size usually decreases, whereas optimal patroltime behaves much more irregularly. With increasing food density,optimal patrol time usually decreases, whereas optimal territorysize behaves irregularly. In particular, when intrusion rateand expulsion costs accelerate sufficiently with increasingterritory size and no constraints exist, the higher the fooddensity the smaller the optimal territory size. When food densityis large enough for a constraint to be effective, the oppositerelation can hold and will always hold for a processing constraint. When a particular parameter changes, optimal territory sizeand optimal patrol time may covary or one may increase whilethe other decreases, depending on the parameter and model. A new set of one-variable models is suggested by the two-variablemodels; models optimizing patrol time while holding territorysize constant could correspond to a tightly packed system ofterritories initially determined by settlement patterns. A unifiedonevariable analysis suggests that how food density affectsterritory size when patrol time is constant depends upon whethera constraint is operating: Provided that invasion rate doesnot vary with density of intruders on the territory, time minimizersand constrained energy maximizers decrease territory size withincreasing food density; unconstrained energy maximizers dothe opposite. The addition of a second optimization variable to a one-variablemodel can change qualitative predictions about variation inparticular parameters (e.g., food density) and can increasethe number of parameters predicted to affect optimal territorysize and patrol time.     

A test of the sequential assessment game: the effect of increased cost of sampling

The sequential assessment game describes a fight between twoconspecifics as a statistical sampling process, allowing forspecific predictions about fight duration and number of repetitionsof a behavioral element depending on relative fighting ability.Fight duration and number of repetitions of a behavioral elementcorrelate moderately to relative fighting ability. Variationin real contests depends on differences between the contestantsin the ability to incur cost and the value of the contestedresource. I hypothesized that an additional source of variationis differences between individuals in their perception of howdangerous it is to fight. To investigate this, I used the riskof predation to study the effect on the use of different agonisticbehaviors in fights between males of the cichlid fish Nannacaraanomala. In the group subjected to predation risk, the time untilthe most escalated behavior (mouth wrestling) was more variableand increased significantly on average. In addition, the durationof fights was significantly longer. In the predator treatmentthe use of visual assessment and tail beating varied more thanin the control, giving a significant positive relationship betweenthe use of low-intensity behaviors and time to mouth wrestlingacross the group. These relationships were less pronounced in thecontrol group. The effect of predation risk on optimal information transferis discussed based on the behavioral mechanism suggested bythe sequential assessment game.     

Isolation by Distance in a Quantitative Trait

Random genetic drift in a quantitative character is modeled for a population with a continuous spatial distribution in an infinite habitat of one or two dimensions. The analysis extends Wright's concept of neighborhood size to spatially autocorrelated sampling variation in the expected phenotype at different locations. Weak stabilizing selection is assumed to operate toward the same optimum phenotype in every locality, and the distribution of dispersal distances from parent to offspring is a (radially) symmetric function. The equilibrium pattern of geographic variation in the expected local phenotype depends on the neighborhood size, the genetic variance within neighborhoods, and the strength of selection, but is nearly independent of the form of the dispersal function. With all else equal, geographic variance is smaller in a two-dimensional habitat than in one dimension, and the covariance between expected local phenotypes decreases more rapidly with the distance separating them in two dimensions than in one. The equilibrium geographic variance is less than the phenotypic variance within localities, unless the neighborhood size is small and selection is extremely weak, especially in two dimensions. Nevertheless, dispersal of geographic variance created by random genetic drift is an important mechanism maintaining genetic variance within local populations. For a Gaussian dispersal function it is shown that, even with a small neighborhood size, a population in a two-dimensional habitat can maintain within neighborhoods most of the genetic variance that would occur in an infinite panmictic population.     

Modeling inhalational tularemia: deliberate release and public health response

Two epidemic modeling studies of inhalational tularemia were identified in the published literature, both demonstrating the high number of potential casualties that could result from a deliberate aerosolized release of the causative agent in an urban setting. However, neither study analyzed the natural history of inhalational tularemia nor modeled the relative merits of different mitigation strategies. We first analyzed publicly available human/primate experimental data and reports of naturally acquired inhalational tularemia cases to better understand the epidemiology of the disease. We then simulated an aerosolized release of the causative agent, using airborne dispersion modeling to demonstrate the potential number of casualties and the extent of their spatial distribution. Finally, we developed a public health intervention model that compares 2 mitigation strategies: targeting antibiotics at symptomatic individuals with or without mass distribution of antibiotics to potentially infected individuals. An antibiotic stockpile that is sufficient to capture all areas where symptomatic individuals were infected is likely to save more lives than treating symptomatic individuals alone, providing antibiotics can be distributed rapidly and their uptake is high. However, with smaller stockpiles, a strategy of treating symptomatic individuals alone is likely to save many more lives than additional mass distribution of antibiotics to potentially infected individuals. The spatial distribution of symptomatic individuals is unlikely to coincide exactly with the path of the dispersion cloud if such individuals are infected near their work locations but then seek treatment close to their homes. The optimal mitigation strategy will depend critically on the size of the release relative to the stockpile level and the effectiveness of treatment relative to the speed at which antibiotics can be distributed.     

Different reactions to adverse neighborhoods in games of cooperation

In social dilemmas, cooperation among randomly interacting individuals is often difficult to achieve. The situation changes if interactions take place in a network where the network structure jointly evolves with the behavioral strategies of the interacting individuals. In particular, cooperation can be stabilized if individuals tend to cut interaction links when facing adverse neighborhoods. Here we consider two different types of reaction to adverse neighborhoods, and all possible mixtures between these reactions. When faced with a gloomy outlook, players can either choose to cut and rewire some of their links to other individuals, or they can migrate to another location and establish new links in the new local neighborhood. We find that in general local rewiring is more favorable for the evolution of cooperation than emigration from adverse neighborhoods. Rewiring helps to maintain the diversity in the degree distribution of players and favors the spontaneous emergence of cooperative clusters. Both properties are known to favor the evolution of cooperation on networks. Interestingly, a mixture of migration and rewiring is even more favorable for the evolution of cooperation than rewiring on its own. While most models only consider a single type of reaction to adverse neighborhoods, the coexistence of several such reactions may actually be an optimal setting for the evolution of cooperation.     

Population subdivision and adaptation in asexual populations of Saccharomyces cerevisiae

Population subdivision limits competition between individuals, which can have a profound effect on adaptation. Subdivided populations maintain more genetic diversity at any given time compared to well-mixed populations, and thus "explore" larger parts of the genotype space. At the same time, beneficial mutations take longer to spread in such populations, and thus subdivided populations do not "exploit" discovered mutations as efficiently as well-mixed populations. Whether subdivision inhibits or promotes adaptation in a given environment depends on the relative importance of exploration versus exploitation, which in turn depends on the structure of epistasis among beneficial mutations. Here we investigate the relative importance of exploration versus exploitation for adaptation by evolving 976 independent asexual populations of budding yeast with several degrees of geographic subdivision. We find that subdivision systematically inhibits adaptation: even the luckiest demes in subdivided populations on average fail to discover genotypes that are fitter than those discovered by well-mixed populations. Thus, exploitation of discovered mutations is more important for adaptation in our system than a thorough exploration of the mutational neighborhood, and increasing subdivision slows adaptation.