Epidemic patch models applied to pandemic influenza: Contact matrix, stochasticity, robustness of predictions

Due to the recent emergence of H5N1 virus, the modelling of pandemic influenza has become a relevant issue. Here we present an SEIR model formulated to simulate a possible outbreak in Italy, analysing its structure and, more generally, the effect of including specific details into a model. These details regard population heterogeneities, such as age and spatial distribution, as well as stochasticity, that regulates the epidemic dynamics when the number of infectives is low. We discuss and motivate the specific modelling choices made when building the model and investigate how the model details influence the predicted dynamics. Our analysis may help in deciding which elements of complexity are worth including in the design of a deterministic model for pandemic influenza, in a balance between, on the one hand, keeping the model computationally efficient and the number of parameters low and, on the other hand, maintaining the necessary realistic features.     

Optimal control for pandemic influenza: The role of limited antiviral treatment and isolation

The implementation of optimal control strategies involving antiviral treatment and/or isolation measures can reduce significantly the number of clinical cases of influenza. Pandemic-level control measures must be carefully assessed specially in resource-limited situations. A model for the transmission dynamics of influenza is used to evaluate the impact of isolation and/or antiviral drug delivery measures during an influenza pandemic. Five pre-selected control strategies involving antiviral treatment and isolation are tested under the “unlimited” resource assumption followed by an exploration of the impact of these “optimal” policies when resources are limited in the context of a 1918-type influenza pandemic scenario. The implementation of antiviral treatment at the start of a pandemic tends to reduce the magnitude of epidemic peaks, spreading the maximal impact of an outbreak over an extended window in time. Hence, the controls’ timing and intensity can reduce the pressures placed on the health care infrastructure by a pandemic reducing the stress put on the system during epidemic peaks. The role of isolation strategies is highlighted in this study particularly when access to antiviral resources is limited.     

Emergence of drug resistance: implications for antiviral control of pandemic influenza

Given the danger of an unprecedented spread of the highly pathogenic avian influenza strain H5N1 in humans, and great challenges to the development of an effective influenza vaccine, antiviral drugs will probably play a pivotal role in combating a novel pandemic strain. A critical limitation to the use of these drugs is the evolution of highly transmissible drug-resistant viral mutants. Here, we develop a mathematical model to evaluate the potential impact of an antiviral treatment strategy on the emergence of drug resistance and containment of a pandemic. The results show that elimination of the wild-type strain depends crucially on both the early onset of treatment in indexed cases and population-level treatment. Given the probable delay of 0.5-1 day in seeking healthcare and therefore initiating therapy, the findings indicate that a single strategy of antiviral treatment will be unsuccessful at controlling the spread of disease if the reproduction number of the wild-type strain (R0s) exceeds 1.4. We demonstrate the possible occurrence of a self-sustaining epidemic of resistant strain, in terms of its transmission fitness relative to the wild-type, and the reproduction number R0s. Considering reproduction numbers estimated for the past three pandemics, the findings suggest that an uncontrollable pandemic is likely to occur if resistant viruses with relative transmission fitness above 0.4 emerge. While an antiviral strategy is crucial for containing a pandemic, its effectiveness depends critically on timely and strategic use of drugs.     

Coinfection and the evolution of drug resistance

Recent experimental work in the rodent malaria model has shown that when two or more strains share a host, there is competitive release of drug‐resistant strains upon treatment. In other words, the propagule output of a particular strain is repressed when competing with other strains and increases upon the removal of this competition. This within‐host effect is predicted to have an important impact on the evolution and growth of resistant strains. However, how this effect translates to epidemiological parameters at the between‐host level, the level at which disease and resistance spread, has yet to be determined. Here we present a general, between‐host epidemiological model that explicitly takes into account the effect of coinfection and competitive release. Although our model does show that when there is coinfection competitive release may contribute to the emergence of resistance, it also highlights an additional between‐host effect. It is the combination of these two effects, the between‐host effect and the within‐host effect, that determines the overall influence of coinfection on the emergence of resistance. Therefore, even when competitive release of drug‐resistant strains occurs, within an infected individual, it is not necessarily true that coinfection will result in the increased emergence of resistance. These results have important implications for the control of the emergence and spread of drug resistance.     

The role of health care workers and antiviral drugs in the control of pandemic influenza

Until a vaccine against the new strain becomes available, the response to newly emerged pandemic influenza will consist of the use of antiviral drugs and measures that limit exposure to infectious individuals. These first-line defence measures include isolating cases upon diagnosis, reducing close contacts, the use of personal protective equipment and hygiene, and using antiviral drugs for treatment and prophylaxis. There are significant 'costs' associated with control measures, so to justify such interventions it is important to assess their potential to reduce transmission. In this paper, we determine the effect that a number of different antiviral interventions have on the reproduction number of infectives and the probability that an imported infection fades out, and determine parameter scenarios for which these interventions are able to eliminate an emerging pandemic of influenza. We also assess the role that health care workers play in transmission and the extent to which providing them with antiviral prophylaxis and personal protective equipment modifies this role. Our results indicate that this class requires protection to avoid a greatly disproportionate contribution to early infective numbers, and for the maintenance of a stable health care system. Further, we show that the role children play in increasing transmission is moderate, in spite of closer mixing with other children.     

The structural simplification of an epidemiological compartment model

It is shown how a multicompartmental infectious disease model can be systematically examined for reduction of structural complexity. For steadystate situations, four basic rules are proposed for eliminating components of flow-lines, whole flow-lines, and compartments, plus combining compartments. An application to a typhoid fever model allows calculations to be done on a pocket calculator. The approach could be particularly important in developing countries.     

Neuraminidase inhibitors for treatment of human and avian strain influenza: A comparative modeling study

Treatment of seasonal influenza viral infections using antivirals such as neuraminidase inhibitors (NAIs) has been proven effective if administered within 48 h post-infection. However, there is growing evidence that antiviral treatment of infections with avian-derived strains even as late as 6 days post-infection (dpi) can significantly reduce infection severity and duration. Using a mathematical model of in-host influenza viral infections which can capture the kinetics of both a short-lived, typical, seasonal infection and a severe infection exhibiting sustained viral titer, we explore differences in the effects of NAI treatment on both types of influenza viral infections. Comparison of our model's behavior against experimental data from patients naturally infected with avian strains yields estimates for the times at which patients were infected that are consistent with those reported by the patients, and estimates of drug efficacies that are lower for patients who died than for those who recovered. In addition, our model suggests that the sustained, high, viral titers often seen in more severe influenza virus infections are the reason why antiviral treatment delayed by as much as 6 dpi will still lead to reduced viral titers and shortened illness. We conclude that NAIs may be an effective and beneficial treatment strategy against more severe strains of influenza virus characterized by high, sustained, viral titers. We believe that our mathematical model will be an effective tool in guiding treatment of severe influenza viral infections with antivirals.     

Optimal control strategy for prevention of avian influenza pandemic

The spread of H5N1 virus to Europe and continued human infection in Southeast Asia have heightened pandemic concern. Although, fortunately, sustained human-to-human transmissions have not been reported yet, it is said that a pandemic virus which can be easily transmitted among humans certainly emerges in the future. In this study, we extended the previous studies for the prevention of the pandemic influenza to evaluate the time-dependent optimal prevention policies, which are associated with elimination policy and quarantine policy, considering its execution cost. Actually, the execution cost affects the optimal strategy of prevention policies and the prevention of the disease spread. We found that the quarantine policy is very important rather than the elimination policy during the disease spread, even if the unit execution cost of the quarantine policy is more expensive than that of the elimination policy. And also, the change of the unit execution cost does affect the total cumulative cost of the optimal prevention policies but does not affect the relative frequency of each cumulative execution cost. Furthermore, interestingly, we revealed that an optimal strategy to reduce the number of total infected humans might increase a chance of invadability of the mutant influenza.     

A susceptible-infected model of early detection of respiratory infection outbreaks on a background of influenza

The threat of biological warfare and the emergence of new infectious agents spreading at a global scale have highlighted the need for major enhancements to the public health infrastructure. Early detection of epidemics of infectious diseases requires both real-time data and real-time interpretation of data. Despite moderate advancements in data acquisition, the state of the practice for real-time analysis of data remains inadequate. We present a nonlinear mathematical framework for modeling the transient dynamics of influenza, applied to historical data sets of patients with influenza-like illness. We estimate the vital time-varying epidemiological parameters of infections from historical data, representing normal epidemiological trends. We then introduce simulated outbreaks of different shapes and magnitudes into the historical data, and estimate the parameters representing the infection rates of anomalous deviations from normal trends. Finally, a dynamic threshold-based detection algorithm is devised to assess the timeliness and sensitivity of detecting the irregularities in the data, under a fixed low false-positive rate. We find that the detection algorithm can identify such designated abnormalities in the data with high sensitivity with specificity held at 97%, but more importantly, early during an outbreak. The proposed methodology can be applied to a broad range of influenza-like infectious diseases, whether naturally occurring or a result of bioterrorism, and thus can be an integral component of a real-time surveillance system.     

A dynamic model for tuberculosis transmission and optimal treatment strategies in South Korea

We have developed a dynamic model for tuberculosis (TB) transmission in South Korea using a SEIR model with the time-dependent parameters. South Korea ranked the highest TB incidence among members of the Organization for Economic Cooperation and Development (OECD) in 2005 yr. The observed data from the Korea Center for Disease Control and Prevention (KCDC) shows a certain rise of active-TB incidence individuals after 2001 yr. Because of this sudden jump, we have considered two different periods for best fitting the model: prior to 2001 yr and posterior to 2001 yr. The least-squares fitting has been used for estimating model parameters to the observed data of active-TB incidence. Our model agrees well with the observed data. In this work, we also propose optimal treatment strategies of TB model in South Korea for the future. We have considered three control mechanisms representing distancing, case finding and case holding efforts. Optimal control programs have been proposed in various scenarios, in order to minimize the number of exposed and infectious individuals and the cost of implementing the control treatment.     

Modelling selection for resistance to methods of insect pest control in combination

The development of resistance to insecticides is now widespread among insects. Other methods of pest control are also potentially at risk of encountering resistance. A modelling approach is presented here to evaluate the effects of combining methods of insect pest control on the selection for resistance to the control methods. This analysis is based on partitioning the total mortality acting on a population into its constituent components from all known sources, and these are related to selection for resistance. When two control methods are used in combination, selection for resistance against the two is a linear function if the two don't interact, otherwise it may be sublinear or supralinear. A specific example is presented using a model of the Olive fruit fly (Dacus oleae Gmel.) and employing food-baited and pheromone-baited traps for control. The control methods that appear least likely to encounter resistance are natural enemies and the use of pheromone traps for male annihilation. These should be integrated into a control program where possible to minimize the development of resistance to other control methods being used.     

Evaluation of the roles of passive and active control of balance using a balance control model

At present there is a lack of consensus regarding the relative roles of passive and active control of quiet upright stance. In the current work, this issue was investigated using two simulation models based on contemporary theories. Specifically, the two models, both of which assumed active control torques to be generated from an optimal neural controller, differed with respect to whether or not passive control torques (stiffness and damping) were included. Model parameters were specified using experimental center-of-pressure (COP) time series obtained during upright stance, and comparisons then made between simulated and actual COP-based measures. Including both active and passive joint torques in the control model did not appear to lead to any improvement in the ability to simulate COP compared with only including active joint torque. Further, simulated passive control torques were typically less than 10% of the active control torques, though some exceptions were found. These results, along with existing empirical evidence, suggest that active control torque is dominant in maintaining balance during upright stance.     

Source-sink dynamics shape the evolution of antibiotic resistance and its pleiotropic fitness cost

Understanding the conditions that favour the evolution and maintenance of antibiotic resistance is the central goal of epidemiology. A crucial feature explaining the adaptation to harsh, or 'sink', environments is the supply of beneficial mutations via migration from a 'source' population. Given that antibiotic resistance is frequently associated with antagonistic pleiotropic fitness costs, increased migration rate is predicted not only to increase the rate of resistance evolution but also to increase the probability of fixation of resistance mutations with minimal fitness costs. Here we report in vitro experiments using the nosocomial pathogenic bacterium Pseudomonas aeruginosa that support these predictions: increasing rate of migration into environments containing antibiotics increased the rate of resistance evolution and decreased the associated costs of resistance. Consistent with previous theoretical work, we found that resistance evolution arose more rapidly in the presence of a single antibiotic than two. Evolution of resistance was also more rapid when bacteria were subjected to sequential exposure with two antibiotics (cycling therapy) compared with simultaneous exposure (bi-therapy). Furthermore, pleiotropic fitness costs of resistance to two antibiotics were higher than for one antibiotic, and were also higher under bi-therapy than cycling therapy, although the cost of resistance depended on the order of the antibiotics through time. These results may be relevant to the clinical setting where immigration is known to be important between chemotherapeutically treated patients, and demonstrate the importance of ecological and evolutionary dynamics in the control of antibiotic resistance.     

Specific resistance prevents the evolution of general resistance and facilitates disease emergence

Host-shifts, where pathogens jump from an ancestral host to a novel host, can be facilitated or impeded by standing variation in disease resistance, but only if resistance provides broad-spectrum general resistance against multiple pathogen species. Host resistance comes in many forms and includes both general resistance, as well as specific resistance, which may only be effective against a single pathogen species or even genotype. However, most evolutionary models consider only one of these forms of resistance, and we have less understanding of how these two forms of resistance evolve in tandem. Here, we develop a model that allows for the joint evolution of specific and general resistance and asks if the evolution of specific resistance drives a decrease in the evolution of general resistance. We also explore how these evolutionary outcomes affect the risk of foreign pathogen invasion and persistence. We show that in the presence of a single endemic pathogen, the two forms of resistance are strongly exclusionary. Critically, we find that specific resistance polymorphisms can prevent the evolution of general resistance, facilitating the invasion of foreign pathogens. We also show that specific resistance polymorphisms are a necessary condition for the successful establishment of foreign pathogens following invasion, as they prevent the exclusion of the foreign pathogen by the more transmissible endemic pathogen. Our results demonstrate the importance of considering the joint evolution of multiple forms of resistance when evaluating a population's susceptibility to foreign pathogens.     

Kin selection and evolution of infectious disease resistance

Discoveries of mutations conferring resistance to infectious diseases have led to increased interest in the evolutionary dynamics of disease resistance. Several recent papers have estimated the historical strength of selection for mutations conferring disease resistance. These studies are based on simple population genetic models that do not take account of factors such as spatial and family structure. Such factors may have a substantial impact on the strength of natural selection through inclusive fitness effects. That is, people have a strong tendency to live with relatives and therefore have a high probability of transmitting infectious diseases to them. Thus, an allele that protects an individual against disease infection also protects that individual's family members. Because some of these family members are likely to also be carrying the allele, selection for that allele is magnified by family structure. In this paper, I use mathematical modeling techniques to explore the impact of such kin selection on the strength of selection for infectious disease resistance alleles. I show that if the resistance allele has the same proportional effect on both within- and between-family transmission, then the impact of kin selection is relatively minor. Selection coefficients are increased by 5-35%, with a greater benefit for weaker alleles. The reason is that an individual with a strong resistance allele does not need much protection from infection by family members and thus does not benefit much from their alleles. The effect of kin selection can be dramatic, however, if the resistance allele has a larger effect on between-family transmission than within-family transmission (which can occur if between-family infection rates are much smaller than within-family rates), increasing selection coefficients by as much as two- to threefold. These results show conditions when it is important to consider family structure in estimates of the strength of selection for infectious disease resistance alleles.     

Genetics and evolution of resistance to insecticides

The evolution of resistance to insecticides has become a serious problem world-wide. It is important to identify patterns of insecticide use whereby insecticides can be used in integrated pest management programmes to help control insect numbers, but in such a manner that the evolution of resistance to insecticides will be retarded. The principal mechanisms of insecticide action and of resistance to these are reviewed. Some generalizations that can be made about the evolution of resistance are examined. In general, to control resistance it appears better to use an intense dose of non-persistent pesticides over a circumscribed area. Some features of the problem where population genetics and evolutionary theory might contribute to controlling resistance are discussed.     

Insecticide resistance in the horn fly: alternative control strategies

Abstract.  The horn fly, Haematobia irritans (Linnaeus 1758) (Diptera: Muscidae) is one of the most widespread and economically important pests of cattle. Although insecticides have been used for fly control, success has been limited because of the development of insecticide resistance in all countries where the horn fly is found. This problem, along with public pressure for insecticide-free food and the prohibitive cost of developing new classes of compounds, has driven the investigation of alternative control methods that minimize or avoid the use of insecticides. This review provides details of the economic impact of horn flies, existing insecticides used for horn fly control and resistance mechanisms. Current research on new methods of horn fly control based on resistant cattle selection, semiochemicals, biological control and vaccines is also discussed.     

The onion model, a simple neutral model for the evolution of diversity in bacterial biofilms

Bacterial biofilms are particularly resistant to a wide variety of antimicrobial compounds. Their persistence in the face of antibiotic therapies causes significant problems in the treatment of infectious diseases. Seldom have evolutionary processes like genetic drift and mutation been invoked to explain how resistance to antibiotics emerges in biofilms, and we lack a simple and tractable model for the genetic and phenotypic diversification that occurs in bacterial biofilms. Here, we introduce the 'onion model', a simple neutral evolutionary model for phenotypic diversification in biofilms. We explore its properties and show that the model produces patterns of diversity that are qualitatively similar to observed patterns of phenotypic diversity in biofilms. We suggest that models like our onion model, which explicitly invoke evolutionary process, are key to understanding biofilm resistance to bactericidal and bacteriostatic agents. Elevated phenotypic variance provides an insurance effect that increases the likelihood that some proportion of the population will be resistant to imposed selective agents and may thus enhance persistence of the biofilm. Accounting for evolutionary change in biofilms will improve our ability to understand and counter diseases that are caused by biofilm persistence.