Impact of emerging antiviral drug resistance on influenza containment and spread: influence of subclinical infection and strategic use of a stockpile containing one or two drugs

Development of an influenza pandemic decision support tool linking situational analytics to national response policy

National influenza pandemic plans have evolved substantially over recent decades, as has the scientific research that underpins the advice contained within them. While the knowledge generated by many research activities has been directly incorporated into the current generation of pandemic plans, scientists and policymakers are yet to capitalise fully on the potential for near real-time analytics to formally contribute to epidemic decision-making. Theoretical studies demonstrate that it is now possible to make robust estimates of pandemic impact in the earliest stages of a pandemic using first few hundred household cohort (FFX) studies and algorithms designed specifically for analysing FFX data. Pandemic plans already recognise the importance of both situational awareness i.e., knowing pandemic impact and its key drivers, and the need for pandemic special studies and related analytic methods for estimating these drivers. An important next step is considering how information from these situational assessment activities can be integrated into the decision-making processes articulated in pandemic planning documents. Here we introduce a decision support tool that directly uses outputs from FFX algorithms to present recommendations on response options, including a quantification of uncertainty, to decision makers. We illustrate this approach using response information from within the Australian influenza pandemic plan.

On the Transmission Dynamics of SARS-CoV-2 in a Temperate Climate

An epidemiological model, which describes the transmission dynamics of SARS-CoV-2 under specific consideration of the incubation period including the population with subclinical infections and being infective is presented. The COVID-19 epidemic in Greece was explored through a Monte Carlo uncertainty analysis framework, and the optimal values for the parameters that determined the transmission dynamics could be obtained before, during, and after the interventions to control the epidemic. The dynamic change of the fraction of asymptomatic individuals was shown. The analysis of the modelling results at the intra-annual climatic scale allowed for in depth investigation of the transmission dynamics of SARS-CoV-2 and the significance and relative importance of the model parameters. Moreover, the analysis at this scale incorporated the exploration of the forecast horizon and its variability. Three discrete peaks were found in the transmission rates throughout the investigated period (15 February–15 December 2020). Two of them corresponded to the timing of the spring and autumn epidemic waves while the third one occurred in mid-summer, implying that relaxation of social distancing and increased mobility may have a strong effect on rekindling the epidemic dynamics offsetting positive effects from factors such as decreased household crowding and increased environmental ultraviolet radiation. In addition, the epidemiological state was found to constitute a significant indicator of the forecast reliability horizon, spanning from as low as few days to more than four weeks. Embedding the model in an ensemble framework may extend the predictability horizon. Therefore, it may contribute to the accuracy of health risk assessment and inform public health decision making of more efficient control measures.

Infectious disease pandemic planning and response: Incorporating decision analysis

Freya Shearer and co-authors discuss the use of decision analysis in planning for infectious disease pandemics.

Modelling and analysing the coexistence of dual dilemmas in the proactive vaccination game and retroactive treatment game in epidemic viral dynamics

The dynamics of a spreadable disease are largely governed by four factors: proactive vaccination, retroactive treatment, individual decisions, and the prescribing behaviour of physicians. Under the imposed vaccination policy and antiviral treatment in society, complex factors (costs and expected effects of the vaccines and treatments, and fear of being infected) trigger an emulous situation in which individuals avoid infection by the pre-emptive or ex post provision. Aside from the established voluntary vaccination game, we propose a treatment game model associated with the resistance evolution of antiviral/antibiotic overuse. Moreover, the imperfectness of vaccinations has inevitably led to anti-vaccine behaviour, necessitating a proactive treatment policy. However, under the excessively heavy implementation of treatments such as antiviral medicine, resistant strains emerge. The model explicitly exhibits a dual social dilemma situation, in which the treatment behaviour changes on a local time scale, and the vaccination uptake later evolves on a global time scale. The impact of resistance evolution and the coexistence of dual dilemmas are investigated by the control reproduction number and the social efficiency deficit, respectively. Our investigation might elucidate the substantial impacts of both vaccination and treatment in the framework of epidemic dynamics, and hence suggest the appropriate use of antiviral treatment.

Behavioral incentives in a vaccination-dilemma setting with optional treatment

Social dilemmas are situations wherein individuals choose between selfish interest and common good. One example of this is the vaccination dilemma, in which an individual who vaccinates at a cost protects not only himself but also others by helping maintain a common good called herd immunity. There is, however, a strong incentive to forgo vaccination, thus avoiding the associated cost, all the while enjoying the protection of herd immunity. To analyze behavioral incentives in a vaccination-dilemma setting in which an optional treatment is available to infected individuals, we combined epidemiological and game-theoretic methodologies by coupling a disease-spreading model with treatment and an evolutionary decision-making model. Extensive numerical simulations show that vaccine characteristics are more important in controlling the treatment adoption than the cost of treatment itself. The main effect of the latter is that expensive treatment incentivizes vaccination, which somewhat surprisingly comes at a little cost to society. More surprising is that the margin for a true synergy between vaccine and treatment in reducing the final epidemic size is very small. We furthermore find that society-centered decision making helps protect herd immunity relative to individual-centered decision making, but the latter may be better in establishing a novel vaccine. These results point to useful policy recommendations as well as to intriguing future research directions.

Dynamics of Drug Resistance: Optimal Control of an Infectious Disease

Antimicrobial resistance is a significant public health threat. In the U.S. alone, 2 million people are infected and 23,000 die each year from antibiotic resistant bacterial infections. In many cases, infections are resistant to all but a few remaining drugs. We examine the case where a single drug remains and solve for the optimal treatment policy for an SIS infectious disease model incorporating the effects of drug resistance. The problem is formulated as an optimal control problem with two continuous state variables, the disease prevalence and drug's "quality" (the fraction of infections that are drug-susceptible). The decision maker's objective is to minimize the discounted cost of the disease to society over an infinite horizon. We provide a new generalizable solution approach that allows us to thoroughly characterize the optimal treatment policy analytically. We prove that the optimal treatment policy is a bang-bang policy with a single switching time. The action/inaction regions can be described by a single boundary that is strictly increasing when viewed as a function of drug quality, indicating that when the disease transmission rate is constant, the policy of withholding treatment to preserve the drug for a potentially more serious future outbreak is not optimal. We show that the optimal value function and/or its derivatives are neither C ¹ nor Lipschitz continuous suggesting that numerical approaches to this family of dynamic infectious disease models may not be computationally stable. Furthermore, we demonstrate that relaxing the standard assumption of constant disease transmission rate can fundamentally change the shape of the action region, add a singular arc to the optimal control, and make preserving the drug for a serious outbreak optimal. In addition, we apply our framework to the case of antibiotic resistant gonorrhea.

Population-level mathematical modeling of antimicrobial resistance: a systematic review

BACKGROUND

Mathematical transmission models are increasingly used to guide public health interventions for infectious diseases, particularly in the context of emerging pathogens; however, the contribution of modeling to the growing issue of antimicrobial resistance (AMR) remains unclear. Here, we systematically evaluate publications on population-level transmission models of AMR over a recent period (2006-2016) to gauge the state of research and identify gaps warranting further work.

METHODS

We performed a systematic literature search of relevant databases to identify transmission studies of AMR in viral, bacterial, and parasitic disease systems. We analyzed the temporal, geographic, and subject matter trends, described the predominant medical and behavioral interventions studied, and identified central findings relating to key pathogens.

RESULTS

We identified 273 modeling studies; the majority of which (> 70%) focused on 5 infectious diseases (human immunodeficiency virus (HIV), influenza virus, Plasmodium falciparum (malaria), Mycobacterium tuberculosis (TB), and methicillin-resistant Staphylococcus aureus (MRSA)). AMR studies of influenza and nosocomial pathogens were mainly set in industrialized nations, while HIV, TB, and malaria studies were heavily skewed towards developing countries. The majority of articles focused on AMR exclusively in humans (89%), either in community (58%) or healthcare (27%) settings. Model systems were largely compartmental (76%) and deterministic (66%). Only 43% of models were calibrated against epidemiological data, and few were validated against out-of-sample datasets (14%). The interventions considered were primarily the impact of different drug regimens, hygiene and infection control measures, screening, and diagnostics, while few studies addressed de novo resistance, vaccination strategies, economic, or behavioral changes to reduce antibiotic use in humans and animals.

CONCLUSIONS

The AMR modeling literature concentrates on disease systems where resistance has been long-established, while few studies pro-actively address recent rise in resistance in new pathogens or explore upstream strategies to reduce overall antibiotic consumption. Notable gaps include research on emerging resistance in Enterobacteriaceae and Neisseria gonorrhoeae; AMR transmission at the animal-human interface, particularly in agricultural and veterinary settings; transmission between hospitals and the community; the role of environmental factors in AMR transmission; and the potential of vaccines to combat AMR.

Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number, Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lower Rc to a critical value Rc∗ for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

The Mechanisms for Within-Host Influenza Virus Control Affect Model-Based Assessment and Prediction of Antiviral Treatment

Models of within-host influenza viral dynamics have contributed to an improved understanding of viral dynamics and antiviral effects over the past decade. Existing models can be classified into two broad types based on the mechanism of viral control: models utilising target cell depletion to limit the progress of infection and models which rely on timely activation of innate and adaptive immune responses to control the infection. In this paper, we compare how two exemplar models based on these different mechanisms behave and investigate how the mechanistic difference affects the assessment and prediction of antiviral treatment. We find that the assumed mechanism for viral control strongly influences the predicted outcomes of treatment. Furthermore, we observe that for the target cell-limited model the assumed drug efficacy strongly influences the predicted treatment outcomes. The area under the viral load curve is identified as the most reliable predictor of drug efficacy, and is robust to model selection. Moreover, with support from previous clinical studies, we suggest that the target cell-limited model is more suitable for modelling in vitro assays or infection in some immunocompromised/immunosuppressed patients while the immune response model is preferred for predicting the infection/antiviral effect in immunocompetent animals/patients.

Monitoring the fitness of antiviral-resistant influenza strains during an epidemic: a mathematical modelling study

BACKGROUND

Antivirals (eg, oseltamivir) are important for mitigating influenza epidemics. In 2007, an oseltamivir-resistant influenza seasonal A H1N1 strain emerged and spread to global fixation within 1 year. This event showed that antiviral-resistant (AVR) strains can be intrinsically more transmissible than their contemporaneous antiviral-sensitive (AVS) counterpart. Surveillance of AVR fitness is therefore essential. Our objective was to develop a simple method for estimating AVR fitness from surveillance data.

METHODS

We defined the fitness of AVR strains as their reproductive number relative to their co-circulating AVS counterparts. We developed a simple method for real-time estimation of AVR fitness from surveillance data. This method requires only information on generation time without other specific details regarding transmission dynamics. We first used simulations to validate this method by showing that it yields unbiased and robust fitness estimates in most epidemic scenarios. We then applied this method to two retrospective case studies and one hypothetical case study.

FINDINGS

We estimated that the oseltamivir-resistant A H1N1 strain that emerged in 2007 was 4% (95% credible interval [CrI] 3-5) more transmissible than its oseltamivir-sensitive predecessor and the oseltamivir-resistant pandemic A H1N1 strain that emerged and circulated in Japan during 2013-14 was 24% (95% CrI 17-30) less transmissible than its oseltamivir-sensitive counterpart. We show that in the event of large-scale antiviral interventions during a pandemic with co-circulation of AVS and AVR strains, our method can be used to inform optimal use of antivirals by monitoring intrinsic AVR fitness and drug pressure on the AVS strain.

INTERPRETATION

We developed a simple method that can be easily integrated into contemporary influenza surveillance systems to provide reliable estimates of AVR fitness in real time.

FUNDING

Research Fund for the Control of Infectious Disease (09080792) and a commissioned grant from the Health and Medical Research Fund from the Government of the Hong Kong Special Administrative Region, Harvard Center for Communicable Disease Dynamics from the National Institute of General Medical Sciences (grant number U54 GM088558), Area of Excellence Scheme of the Hong Kong University Grants Committee (grant number AoE/M-12/06).

14-Deoxy-11,12-dehydroandrographolide exerts anti-influenza A virus activity and inhibits replication of H5N1 virus by restraining nuclear export of viral ribonucleoprotein complexes

The highly pathogenic avian influenza H5N1 virus has become a worldwide public health threat, and current antiviral therapies have limited activity against the emerging, resistant influenza viruses. Therefore, effective drugs with novel targets against influenza A viruses, H5N1 strains in particular, should be developed. In the present study, 14-deoxy-11,12-dehydroandrographolide (DAP), a major component of the traditional Chinese medicine Andrographis paniculata, exerted potent anti-influenza A virus activity against A/chicken/Hubei/327/2004 (H5N1), A/duck/Hubei/XN/2007 (H5N1), A/PR/8/34 (H1N1), A/NanChang/08/2010 (H1N1) and A/HuNan/01/2014 (H3N2) in vitro. To elucidate the underlying mechanisms, a series of experiments was conducted using A/chicken/Hubei/327/2004 (H5N1) as an example. Our results demonstrated that DAP strongly inhibited H5N1 replication by reducing the production of viral nucleoprotein (NP) mRNA, NP and NS1proteins, whereas DAP had no effect on the absorption and release of H5N1 towards/from A549 cells. DAP also effectively restrained the nuclear export of viral ribonucleoprotein (vRNP) complexes. This inhibitory effect ought to be an important anti-H5N1 mechanism of DAP. Meanwhile, DAP significantly reduced the upregulated expression of all the tested proinflammatory cytokines (TNF-α, IL-6, IL-8, IFN-α, IL-1β and IFN-β) and chemokines (CXCL-10 and CCL-2) stimulated by H5N1. Overall results suggest that DAP impairs H5N1 replication at least in part by restraining nuclear export of vRNP complexes, and the inhibition of viral replication leads to a subsequent decrease of the intense proinflammatory cytokine/chemokine expression. In turn, the effect of modification of the host excessive immune response may contribute to overcoming H5N1. To our knowledge, this study is the first to reveal the antiviral and anti-inflammatory activities of DAP in vitro against H5N1 influenza A virus infection.

Timing of antimicrobial use influences the evolution of antimicrobial resistance during disease epidemics

How can antimicrobial drugs be deployed optimally during infectious disease epidemics? Our mathematical models show it is optimal to delay treatment to maximize successful treatments. In formulating policy, however, this must be balanced against the risk of incorrectly predicting the peak of an epidemic.

Background: Although the emergence and spread of antibiotic resistance have been well studied for endemic infections, comparably little is understood for epidemic infections such as influenza. The availability of antimicrobial treatments for epidemic diseases raises the urgent question of how to deploy treatments to achieve maximum benefit despite resistance evolution. Recent simulation studies have shown that the number of cases prevented by antimicrobials can be maximized by delaying the use of treatments during an epidemic. Those studies focus on indirect effects of antimicrobial use: preventing disease among untreated individuals. Here, we identify and examine direct effects of antimicrobial use: the number of successfully treated cases.

Methodology: We develop mathematical models to study how the schedule of antiviral use influences the success or failure of subsequent use due to the spread of resistant strains.

Results: Direct effects are maximized by postponing drug use, even with unlimited stockpiles of drugs. This occurs because the early use of antimicrobials disproportionately drives emergence and spread of antibiotic resistance, leading to subsequent treatment failure. However, for antimicrobials with low effect on transmission, the relative benefit of delaying antimicrobial deployment is greatly reduced and can only be reaped if the trajectory of the epidemic can be accurately estimated early.

Conclusions and implications: Health planners face uncertainties during epidemics, including the possibility of early containment. Hence, despite the optimal deployment time near the epidemic peak, it will often be preferable to initiate widespread antimicrobial use as early as possible, particularly if the drug is ineffective in reducing transmission.

Dynamical crises, multistability and the influence of the duration of immunity in a seasonally-forced model of disease transmission

BACKGROUND

Highly successful strategies to make populations more resilient to infectious diseases, such as childhood vaccinations programs, may nonetheless lead to unpredictable outcomes due to the interplay between seasonal variations in transmission and a population's immune status.

METHODS

Motivated by the study of diseases such as pertussis we introduce a seasonally-forced susceptible-infectious-recovered model of disease transmission with waning and boosting of immunity. We study the system's dynamical properties using a combination of numerical simulations and bifurcation techniques, paying particular attention to the properties of the initial condition space.

RESULTS

We find that highly unpredictable behaviour can be triggered by changes in biologically relevant model parameters such as the duration of immunity. In the particular system we analyse--used in the literature to study pertussis dynamics--we identify the presence of an initial-condition landscape containing three coexisting attractors. The system's response to interventions which perturb population immunity (e.g. vaccination "catch-up" campaigns) is therefore difficult to predict.

CONCLUSION

Given the increasing use of models to inform policy decisions regarding vaccine introduction and scheduling and infectious diseases intervention policy more generally, our findings highlight the importance of thoroughly investigating the dynamical properties of those models to identify key areas of uncertainty. Our findings suggest that the often stated tension between capturing biological complexity and utilising mathematically simple models is perhaps more nuanced than generally suggested. Simple dynamical models, particularly those which include forcing terms, can give rise to incredibly complex behaviour.

Modelling strategic use of the national antiviral stockpile during the CONTAIN and SUSTAIN phases of an Australian pandemic influenza response

OBJECTIVE

To define optimum use of the national antiviral stockpile during the early phases of the response to pandemic influenza in Australia, to inform the 2008 revision of the Australian Health Management Plan for Pandemic Influenza.

METHODS

A mathematical model was used to compare strategic uses of antiviral agents for treatment and post-exposure prophylaxis to limit transmission until availability of a strain-specific vaccine. The impact of provision of pre-exposure prophylaxis to healthcare workers (HCWs) on the ability to control the epidemic was also assessed.

RESULTS

Optimal constraint of epidemic growth was achieved by intensive ascertainment of contacts of cases for post-exposure prophylaxis for as long as feasible. While pre-exposure prophylaxis of healthcare workers utilised a substantial proportion of the stockpile, this did not impede disease control or the ability to treat cases. Absolute delays to outbreak depended on both the intervention strategy and the growth rate of the epidemic. As vaccination was only effective when introduced before explosive growth, this timing was critical to success.

CONCLUSIONS AND IMPLICATIONS

Liberal distribution of antiviral drugs to limit disease spread for as long as is feasible represents optimal use of these agents to constrain epidemic growth. In reality, additional non-pharmaceutical control measures are likely to be required to control transmission until vaccines can definitively contain pandemic influenza outbreaks.

Systematic review of strategies to manage and allocate scarce resources during mass casualty events

STUDY OBJECTIVE

Efficient management and allocation of scarce medical resources can improve outcomes for victims of mass casualty events. However, the effectiveness of specific strategies has never been systematically reviewed. We analyze published evidence on strategies to optimize the management and allocation of scarce resources across a wide range of mass casualty event contexts and study designs.

METHODS

Our literature search included MEDLINE, Scopus, EMBASE, Cumulative Index to Nursing and Allied Health Literature, Global Health, Web of Science, and the Cochrane Database of Systematic Reviews, from 1990 through late 2011. We also searched the gray literature, using the New York Academy of Medicine's Grey Literature Report and key Web sites. We included both English- and foreign-language articles. We included studies that evaluated strategies used in actual mass casualty events or tested through drills, exercises, or computer simulations. We excluded studies that lacked a comparison group or did not report quantitative outcomes. Data extraction, quality assessment, and strength of evidence ratings were conducted by a single researcher and reviewed by a second; discrepancies were reconciled by the 2 reviewers. Because of heterogeneity in outcome measures, we qualitatively synthesized findings within categories of strategies.

RESULTS

From 5,716 potentially relevant citations, 74 studies met inclusion criteria. Strategies included reducing demand for health care services (18 studies), optimizing use of existing resources (50), augmenting existing resources (5), implementing crisis standards of care (5), and multiple categories (4). The evidence was sufficient to form conclusions on 2 strategies, although the strength of evidence was rated as low. First, as a strategy to reduce demand for health care services, points of dispensing can be used to efficiently distribute biological countermeasures after a bioterrorism attack or influenza pandemic, and their organization influences speed of distribution. Second, as a strategy to optimize use of existing resources, commonly used field triage systems do not perform consistently during actual mass casualty events. The number of high-quality studies addressing other strategies was insufficient to support conclusions about their effectiveness because of differences in study context, comparison groups, and outcome measures. Our literature search may have missed key resource management and allocation strategies because of their extreme heterogeneity. Interrater reliability was not assessed for quality assessments or strength of evidence ratings. Publication bias is likely, given the large number of studies reporting positive findings.

CONCLUSION

The current evidence base is inadequate to inform providers and policymakers about the most effective strategies for managing or allocating scarce resources during mass casualty events. Consensus on methodological standards that encompass a range of study designs is needed to guide future research and strengthen the evidence base. Evidentiary standards should be developed to promote consensus interpretations of the evidence supporting individual strategies.

A model for the emergence of drug resistance in the presence of asymptomatic infections

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We model the emergence of drug resistance in the presence of asymptomatic cases.

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The absence of a preclinical state leads to an overestimation of peak incidence.

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Two reproduction numbers, for drug sensitive or resistant strains, are identified.

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Drug resistant and sensitive strains can coexist in the population.

An analysis of a mathematical model, which describes the dynamics of an aerially transmitted disease, and the effects of the emergence of drug resistance after the introduction of treatment as an intervention strategy is presented. Under explicit consideration of asymptomatic and symptomatic infective individuals for the basic model without intervention the analysis shows that the dynamics of the epidemic is determined by a basic reproduction number R0. A disease-free and an endemic equilibrium exist and are locally asymptotically stable when R0<1 and R0>1 respectively. When treatment is included the system has a basic reproduction number, which is the largest of the two reproduction numbers that characterise the drug-sensitive (R1) or resistant (R2) strains of the infectious agent. The system has a disease-free equilibrium, which is stable when both R1 and R2 are less than unity. Two endemic equilibria also exist and are associated with treatment and the development of drug resistance. An endemic equilibrium where only the drug-resistant strain persists exists and is stable when R2>1 and R1<R2. A second endemic equilibrium exists when R1>1 and R1>R2 and both drug-sensitive and drug-resistant strains are present. The analysis of the system provides insights about the conditions under which the infection will persist and whether sensitive and resistant strains will coexist or not.

Drivers and consequences of influenza antiviral resistant-strain emergence in a capacity-constrained pandemic response

Antiviral agents remain a key component of most pandemic influenza preparedness plans, but there is considerable uncertainty regarding their optimal use. In particular, concerns exist regarding the likelihood of wide-scale distribution to select for drug-resistant variants. We used a model that considers the influence of logistical constraints on diagnosis and drug delivery to consider achievable 'reach' of alternative antiviral intervention strategies targeted at cases of varying severity, with or without pre-exposure prophylaxis of contacts. To identify key drivers of epidemic mitigation and resistance emergence, we used Latin hypercube sampling to explore plausible ranges of parameters describing characteristics of wild type and resistant viruses, along with intervention efficacy, target coverage and distribution capacity. Within our model framework, 'real world' constraints substantially reduced achievable drug coverage below stated targets as the epidemic progressed. In consequence, predictions of both intervention impact and selection for resistance were more modest than earlier work that did not consider such limitations. Definitive containment of transmission was unlikely but, where observed, achieved through early liberal post-exposure prophylaxis of known contacts of treated cases. Predictors of resistant strain dominance were high intrinsic fitness relative to the wild type virus, and early emergence in the course of the epidemic into a largely susceptible population, even when drug use was restricted to severe case treatment. Our work demonstrates the importance of consideration of 'real world' constraints in scenario analysis modeling, and highlights the utility of models to guide surveillance activities in preparedness and response.

A SEASONALLY FORCED EPIDEMIC MODEL WITH TARGETED ANTIVIRAL PROPHYLAXIS

In this paper, we propose a mathematical model to describe the transmission dynamics of infectious diseases with targeted antiviral prophylaxis strategy. Our model incorporates seasonal driving force since seasonal force has a great effect on the spread of infectious diseases. Based on the local stability of disease free equilibrium we derive the control reproduction number [Formula: see text]. Sufficient conditions for the global stability of the disease free equilibrium are obtained. Using the persistence theory for discrete dynamical system, we prove that the infectious disease will remain endemic if [Formula: see text]. Simulation results are also provided to study the effect of targeted antiviral prophylaxis on transmission dynamics of infectious disease and investigate the influence of seasonality on the efficiency of targeted antiviral prophylaxis strategy.

Using experimental human influenza infections to validate a viral dynamic model and the implications for prediction

The aim of this work was to use experimental infection data of human influenza to assess a simple viral dynamics model in epithelial cells and better understand the underlying complex factors governing the infection process. The developed study model expands on previous reports of a target cell-limited model with delayed virus production. Data from 10 published experimental infection studies of human influenza was used to validate the model. Our results elucidate, mechanistically, the associations between epithelial cells, human immune responses, and viral titres and were supported by the experimental infection data. We report that the maximum total number of free virions following infection is 10(3)-fold higher than the initial introduced titre. Our results indicated that the infection rates of unprotected epithelial cells probably play an important role in affecting viral dynamics. By simulating an advanced model of viral dynamics and applying it to experimental infection data of human influenza, we obtained important estimates of the infection rate. This work provides epidemiologically meaningful results, meriting further efforts to understand the causes and consequences of influenza A infection.

Strategies for the use of oseltamivir and zanamivir during pandemic outbreaks

BACKGROUND

The use of neuraminidase inhibitors (oseltamivir and zanamivir) for the treatment of ill individuals has been an important intervention during the 2009 H1N1 pandemic. However, the emergence and spread of drug resistance remains a major concern and, therefore, optimizing antiviral strategies is crucial to retain the long-term effectiveness of these pharmaceutical interventions.

METHODS

A dynamic model of disease transmission was developed to investigate optimal scenarios for the use of a secondary drug (eg, zanamivir). Considering both small and large stockpiles, attack rates were projected by simulating the model to identify 'tipping points' for switching to zanamivir as resistance to oseltamivir develops.

RESULTS

The use of a limited stockpile of zanamivir can substantially reduce the overall attack rate during pandemic outbreaks. For a reasonably large stockpile of zanamivir, it is optimal to delay the use of this drug for a certain amount of time during which oseltamivir is used as the primary drug. For smaller stockpiles, however, earlier use of zanamivir will be most effective in reducing the overall attack rate. Given a limited stockpile of zanamivir (1.8% in the Canadian plan) without replenishment, and assuming that the fraction of ill individuals being treated is maintained below 60%, the results suggest that zanamivir should be dispensed as the primary drug for thresholds of the cumulative number of oseltamivir resistance below 20%.

INTERPRETATION

Strategic use of a secondary drug becomes crucial for pandemic mitigation if vaccination and other interventions fail to sufficiently reduce disease transmission in the community. These findings highlight the importance of enhanced surveillance and clinical monitoring for rapid identification of resistance emergence and its population incidence, so that optimal timing for adaptation to the use of drugs can be achieved.

The use of mathematical models to inform influenza pandemic preparedness and response

Influenza pandemics have occurred throughout history and were associated with substantial excess mortality and morbidity. Mathematical models of infectious diseases permit quantitative description of epidemic processes based on the underlying biological mechanisms. Mathematical models have been widely used in the past decade to aid pandemic planning by allowing detailed predictions of the speed of spread of an influenza pandemic and the likely effectiveness of alternative control strategies. During the initial waves of the 2009 influenza pandemic, mathematical models were used to track the spread of the virus, predict the time course of the pandemic and assess the likely impact of large-scale vaccination. While mathematical modeling has made substantial contributions to influenza pandemic preparedness, its use as a realtime tool for pandemic control is currently limited by the lack of essential surveillance information such as serological data. Mathematical modeling provided a useful framework for analyzing and interpreting surveillance data during the 2009 influenza pandemic, for highlighting limitations in existing pandemic surveillance systems, and for guiding how these systems should be strengthened in order to cope with future epidemics of influenza or other emerging infectious diseases.

A mathematical framework for estimating pathogen transmission fitness and inoculum size using data from a competitive mixtures animal model

We present a method to measure the relative transmissibility (“transmission fitness”) of one strain of a pathogen compared to another. The model is applied to data from “competitive mixtures” experiments in which animals are co-infected with a mixture of two strains. We observe the mixture in each animal over time and over multiple generations of transmission. We use data from influenza experiments in ferrets to demonstrate the approach. Assessment of the relative transmissibility between two strains of influenza is important in at least three contexts: 1) Within the human population antigenically novel strains of influenza arise and compete for susceptible hosts. 2) During a pandemic event, a novel sub-type of influenza competes with the existing seasonal strain(s). The unfolding epidemiological dynamics are dependent upon both the population's susceptibility profile and the inherent transmissibility of the novel strain compared to the existing strain(s). 3) Neuraminidase inhibitors (NAIs), while providing significant potential to reduce transmission of influenza, exert selective pressure on the virus and so promote the emergence of drug-resistant strains. Any adverse outcome due to selection and subsequent spread of an NAI-resistant strain is exquisitely dependent upon the transmission fitness of that strain. Measurement of the transmission fitness of two competing strains of influenza is thus of critical importance in determining the likely time-course and epidemiology of an influenza outbreak, or the potential impact of an intervention measure such as NAI distribution. The mathematical framework introduced here also provides an estimate for the size of the transmitted inoculum. We demonstrate the framework's behaviour using data from ferret transmission studies, and through simulation suggest how to optimise experimental design for assessment of transmissibility. The method introduced here for assessment of mixed transmission events has applicability beyond influenza, to other viral and bacterial pathogens.

Determining which of two related viruses will spread from human to human more efficiently – e. g. an influenza virus that is treatable with drugs and one that is resistant to them – is important when forecasting the potential impact of an emergent novel virus or developing public health intervention strategies. However, making such measurements of relative transmissibility directly through observation, even using an animal model, is difficult. We have recently developed and published an experimental technique in which an animal is infected with both viruses of interest at once, and then allowed to mix with other animals and so transmit the infection. These experiments provide the necessary data for analysis using the novel mathematical framework that we introduce here. Our mathematical and computational results exploit the power of the experimental system, and allow us to make a quantitative estimate of the relative transmissibility of a drug-resistant influenza virus compared to its drug-sensitive counterpart. Through computer simulation, we demonstrate the wider application of our mathematical technique, and suggest design criteria for future experiments designed to measure the transmissibility of one virus (or other type of pathogen) compared to another.

Diagnosis and antiviral intervention strategies for mitigating an influenza epidemic

BACKGROUND

Many countries have amassed antiviral stockpiles for pandemic preparedness. Despite extensive trial data and modelling studies, it remains unclear how to make optimal use of antiviral stockpiles within the constraints of healthcare infrastructure. Modelling studies informed recommendations for liberal antiviral distribution in the pandemic phase, primarily to prevent infection, but failed to account for logistical constraints clearly evident during the 2009 H1N1 outbreaks. Here we identify optimal delivery strategies for antiviral interventions accounting for logistical constraints, and so determine how to improve a strategy's impact.

METHODS AND FINDINGS

We extend an existing SEIR model to incorporate finite diagnostic and antiviral distribution capacities. We evaluate the impact of using different diagnostic strategies to decide to whom antivirals are delivered. We then determine what additional capacity is required to achieve optimal impact. We identify the importance of sensitive and specific case ascertainment in the early phase of a pandemic response, when the proportion of false-positive presentations may be high. Once a substantial percentage of ILI presentations are caused by the pandemic strain, identification of cases for treatment on syndromic grounds alone results in a greater potential impact than a laboratory-dependent strategy. Our findings reinforce the need for a decentralised system capable of providing timely prophylaxis.

CONCLUSIONS

We address specific real-world issues that must be considered in order to improve pandemic preparedness policy in a practical and methodologically sound way. Provision of antivirals on the scale proposed for an effective response is infeasible using traditional public health outbreak management and contact tracing approaches. The results indicate to change the transmission dynamics of an influenza epidemic with an antiviral intervention, a decentralised system is required for contact identification and prophylaxis delivery, utilising a range of existing services and infrastructure in a "whole of society" response.

Optimal antiviral treatment strategies and the effects of resistance

Recent pandemic planning has highlighted the importance of understanding the effect that widespread antiviral use will have on the emergence and spread of resistance. A number of recent studies have determined that if resistance to antiviral medication can evolve, then deploying treatment at a less than maximum rate often minimizes the outbreak size. This finding, however, involves the assumption that treatment levels remain constant during the entire outbreak. Using optimal control theory, we address the question of optimal antiviral use by considering a large class of time-varying treatment strategies. We prove that, contrary to previous results, it is always optimal to treat at the maximum rate provided that this treatment occurs at the right time. In general the optimal strategy is to wait some fixed amount of time and then to deploy treatment at the maximum rate for the remainder of the outbreak. We derive analytical conditions that characterize this optimal amount of delay. Our results show that it is optimal to start treatment immediately when one of the following conditions holds: (i) immediate treatment can prevent an outbreak, (ii) the initial pool of susceptibles is small, or (iii) when the maximum possible rate of treatment is low, such that there is little de novo emergence of resistant strains. Finally, we use numerical simulations to verify that the results also hold under more general conditions.

The dynamics of an epidemic model with targeted antiviral prophylaxis

Due to the increasing risk of drug resistance and side effects with large-scale antiviral use, it has been suggested to provide antiviral drugs only to susceptibles who have had contacts with infectives. This antiviral distribution strategy is referred to as 'targeted antiviral prophylaxis'. The question of how effective this strategy is in infection control is of great public heath interest. In this paper, we formulate an ordinary differential equation model to describe the transmission dynamics of infectious disease with targeted antiviral prophylaxis, and provide the analysis of dynamical behaviours of the model. The control reproduction number R(c) is derived and shown to govern the disease dynamics, and the stability analysis is carried out. The local bifurcation theory is applied to explore the variety of dynamics of the model. Our theoretical results show that the system undergoes two Hopf bifurcations due to the existence of multiple endemic equilibria and the switch of their stability. Numerical results demonstrate that the system may have more complex dynamical behaviours including multiple periodic solutions and a homoclinic orbit. The results of this study suggest that the possibility of complex disease dynamics can be driven by the use of targeted antiviral prophylaxis, and the critical level of prophylaxis which achieves ℛ(c)=1 is not enough to control the prevalence of a disease.

Assessing the viral fitness of oseltamivir-resistant influenza viruses in ferrets, using a competitive-mixtures model

To determine the relative fitness of oseltamivir-resistant strains compared to susceptible wild-type viruses, we combined mathematical modeling and statistical techniques with a novel in vivo "competitive-mixtures" experimental model. Ferrets were coinfected with either pure populations (100% susceptible wild-type or 100% oseltamivir-resistant mutant virus) or mixed populations of wild-type and oseltamivir-resistant influenza viruses (80%:20%, 50%:50%, and 20%:80%) at equivalent infectivity titers, and the changes in the relative proportions of those two viruses were monitored over the course of the infection during within-host and over host-to-host transmission events in a ferret contact model. Coinfection of ferrets with mixtures of an oseltamivir-resistant R292K mutant A(H3N2) virus and a R292 oseltamivir-susceptible wild-type virus demonstrated that the R292K mutant virus was rapidly outgrown by the R292 wild-type virus in artificially infected donor ferrets and did not transmit to any of the recipient ferrets. The competitive-mixtures model was also used to investigate the fitness of the seasonal A(H1N1) oseltamivir-resistant H274Y mutant and showed that within infected ferrets the H274Y mutant virus was marginally outgrown by the wild-type strain but demonstrated equivalent transmissibility between ferrets. This novel in vivo experimental method and accompanying mathematical analysis provide greater insight into the relative fitness, both within the host and between hosts, of two different influenza virus strains compared to more traditional methods that infect ferrets with only pure populations of viruses. Our statistical inferences are essential for the development of the next generation of mathematical models of the emergence and spread of oseltamivir-resistant influenza in human populations.

Cost-effectiveness of pharmaceutical-based pandemic influenza mitigation strategies

We used a hybrid transmission and economic model to evaluate the relative merits of stockpiling antiviral drugs and vaccine for pandemic influenza mitigation. In the absence of any intervention, our base-case assumptions generated a population clinical attack rate of 31.1%. For at least some parameter values, population prepandemic vaccination strategies were effective at containing an outbreak of pandemic influenza until the arrival of a matched vaccine. Because of the uncertain nature of many parameters, we used a probabilistic approach to determine the most cost-effective strategies. At a willingness to pay of >A$24,000 per life-year saved, more than half the simulations showed that a prepandemic vaccination program combined with antiviral treatment was cost-effective in Australia.

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.

Transmissibility of the 1918 pandemic influenza in Montreal and Winnipeg of Canada

Background  The threat of 2009 pandemic influenza A (H1N1) is still causing widespread public concern. A comprehensive understanding of the epidemiology of 1918 pandemic influenza commonly referred to as the Spanish flu may be helpful in offering insight into control strategies for the new pandemic.

Objective  We explore how the preparedness for a pandemic at the community and individual level impacts the spread of the virus by comparing the transmissibility of the 1918 Spanish flu in two Canadian cities: Montreal and Winnipeg, bearing in mind that each pandemic is unique and the current one may not follow the pattern of the 1918 outbreak.

Methods  The historical epidemiological data obtained for Montreal and Winnipeg in Canada is analyzed to estimate the basic reproduction number which is the most important summary measure of transmission potential of the pandemic.

Results  The transmissibility of the 1918 pandemic influenza virus in Winnipeg in the fall of 1918 was found to be much lower than in Montreal based on the estimated reproduction number obtained assuming different serial intervals which are the time between onsets of symptoms in an index case and a secondary case.

Conclusion  The early preparedness and public health control measures could suggest an explanation for the fact that the number of secondary cases generated by a primary case was significantly reduced in Winnipeg comparing to it in Montreal.

Post-exposure prophylaxis during pandemic outbreaks

BACKGROUND

With the rise of the second pandemic wave of the novel influenza A (H1N1) virus in the current season in the Northern Hemisphere, pandemic plans are being carefully re-evaluated, particularly for the strategic use of antiviral drugs. The recent emergence of oseltamivir-resistant in treated H1N1 patients has raised concerns about the prudent use of neuraminidase inhibitors for both treatment of ill individuals and post-exposure prophylaxis of close contacts.

METHODS

We extended an established population dynamical model of pandemic influenza with treatment to include post-exposure prophylaxis of close contacts. Using parameter estimates published in the literature, we simulated the model to evaluate the combined effect of treatment and prophylaxis in minimizing morbidity and mortality of pandemic infections in the context of transmissible drug resistance.

RESULTS

We demonstrated that, when transmissible resistant strains are present, post-exposure prophylaxis can promote the spread of resistance, especially when combined with aggressive treatment. For a given treatment level, there is an optimal coverage of prophylaxis that minimizes the total number of infections (final size) and this coverage decreases as a higher proportion of infected individuals are treated. We found that, when treatment is maintained at intermediate levels, limited post-exposure prophylaxis provides an optimal strategy for reducing the final size of the pandemic while minimizing the total number of deaths. We tested our results by performing a sensitivity analysis over a range of key model parameters and observed that the incidence of infection depends strongly on the transmission fitness of resistant strains.

CONCLUSION

Our findings suggest that, in the presence of transmissible drug resistance, strategies that prioritize the treatment of only ill individuals, rather than the prophylaxis of those suspected of being exposed, are most effective in reducing the morbidity and mortality of the pandemic. The impact of post-exposure prophylaxis depends critically on the treatment level and the transmissibility of resistant strains and, therefore, enhanced surveillance and clinical monitoring for resistant mutants constitutes a key component of any comprehensive plan for antiviral drug use during an influenza pandemic.

Understanding Australia's influenza pandemic policy on the strategic use of the antiviral drug stockpile

Targeted post-exposure prophylaxis represents a more efficient use of the stockpile than treatment alone.

Transmission dynamics of an influenza model with vaccination and antiviral treatment

Vaccination and antiviral treatment are two important prevention and control measures for the spread of influenza. However, the benefit of antiviral use can be compromised if drug-resistant strains arise. In this paper, we develop a mathematical model to explore the impact of vaccination and antiviral treatment on the transmission dynamics of influenza. The model includes both drug-sensitive and resistant strains. Analytical results of the model show that the quantities R(SC) and R(RC), which represent the control reproduction numbers of the sensitive and resistant strains, respectively, provide threshold conditions that determine the competitive outcomes of the two strains. These threshold conditions can be used to gain important insights into the effect of vaccination and treatment on the prevention and control of influenza. Numerical simulations are also conducted to confirm and extend the analytic results. The findings imply that higher levels of treatment may lead to an increase of epidemic size, and the extent to which this occurs depends on other factors such as the rates of vaccination and resistance development. This suggests that antiviral treatment should be implemented appropriately.

Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1)

Here we present a review of the literature of influenza modeling studies, and discuss how these models can provide insights into the future of the currently circulating novel strain of influenza A (H1N1), formerly known as swine flu. We discuss how the feasibility of controlling an epidemic critically depends on the value of the Basic Reproduction Number (R0). The R0 for novel influenza A (H1N1) has recently been estimated to be between 1.4 and 1.6. This value is below values of R0 estimated for the 1918-1919 pandemic strain (mean R0 approximately 2: range 1.4 to 2.8) and is comparable to R0 values estimated for seasonal strains of influenza (mean R0 1.3: range 0.9 to 2.1). By reviewing results from previous modeling studies we conclude it is theoretically possible that a pandemic of H1N1 could be contained. However it may not be feasible, even in resource-rich countries, to achieve the necessary levels of vaccination and treatment for control. As a recent modeling study has shown, a global cooperative strategy will be essential in order to control a pandemic. This strategy will require resource-rich countries to share their vaccines and antivirals with resource-constrained and resource-poor countries. We conclude our review by discussing the necessity of developing new biologically complex models. We suggest that these models should simultaneously track the transmission dynamics of multiple strains of influenza in bird, pig and human populations. Such models could be critical for identifying effective new interventions, and informing pandemic preparedness planning. Finally, we show that by modeling cross-species transmission it may be possible to predict the emergence of pandemic strains of influenza.

Paradox of vaccination: is vaccination really effective against avian flu epidemics?

Background

Although vaccination can be a useful tool for control of avian influenza epidemics, it might engender emergence of a vaccine-resistant strain. Field and experimental studies show that some avian influenza strains acquire resistance ability against vaccination. We investigated, in the context of the emergence of a vaccine-resistant strain, whether a vaccination program can prevent the spread of infectious disease. We also investigated how losses from immunization by vaccination imposed by the resistant strain affect the spread of the disease.

Methods and Findings

We designed and analyzed a deterministic compartment model illustrating transmission of vaccine-sensitive and vaccine-resistant strains during a vaccination program. We investigated how the loss of protection effectiveness impacts the program. Results show that a vaccination to prevent the spread of disease can instead spread the disease when the resistant strain is less virulent than the sensitive strain. If the loss is high, the program does not prevent the spread of the resistant strain despite a large prevalence rate of the program. The epidemic's final size can be larger than that before the vaccination program. We propose how to use poor vaccines, which have a large loss, to maximize program effects and describe various program risks, which can be estimated using available epidemiological data.

Conclusions

We presented clear and simple concepts to elucidate vaccination program guidelines to avoid negative program effects. Using our theory, monitoring the virulence of the resistant strain and investigating the loss caused by the resistant strain better development of vaccination strategies is possible.

Antiviral resistance during pandemic influenza: implications for stockpiling and drug use

Background

The anticipated extent of antiviral use during an influenza pandemic can have adverse consequences for the development of drug resistance and rationing of limited stockpiles. The strategic use of drugs is therefore a major public health concern in planning for effective pandemic responses.

Methods

We employed a mathematical model that includes both sensitive and resistant strains of a virus with pandemic potential, and applies antiviral drugs for treatment of clinical infections. Using estimated parameters in the published literature, the model was simulated for various sizes of stockpiles to evaluate the outcome of different antiviral strategies.

Results

We demonstrated that the emergence of highly transmissible resistant strains has no significant impact on the use of available stockpiles if treatment is maintained at low levels or the reproduction number of the sensitive strain is sufficiently high. However, moderate to high treatment levels can result in a more rapid depletion of stockpiles, leading to run-out, by promoting wide-spread drug resistance. We applied an antiviral strategy that delays the onset of aggressive treatment for a certain amount of time after the onset of the outbreak. Our results show that if high treatment levels are enforced too early during the outbreak, a second wave of infections can potentially occur with a substantially larger magnitude. However, a timely implementation of wide-scale treatment can prevent resistance spread in the population, and minimize the final size of the pandemic.

Conclusion

Our results reveal that conservative treatment levels during the early stages of the outbreak, followed by a timely increase in the scale of drug-use, will offer an effective strategy to manage drug resistance in the population and avoid run-out. For a 1918-like strain, the findings suggest that pandemic plans should consider stockpiling antiviral drugs to cover at least 20% of the population.

Antiviral prophylaxis during pandemic influenza may increase drug resistance

BACKGROUND

Neuraminidase inhibitors (NI) and social distancing play a major role in plans to mitigate future influenza pandemics.

METHODS

Using the freely available program InfluSim, the authors examine to what extent NI-treatment and prophylaxis promote the occurrence and transmission of a NI resistant strain.

RESULTS

Under a basic reproduction number of R0 = 2.5, a NI resistant strain can only spread if its transmissibility (fitness) is at least 40% of the fitness of the drug-sensitive strain. Although NI drug resistance may emerge in treated patients in such a late state of their disease that passing on the newly developed resistant viruses is unlikely, resistant strains quickly become highly prevalent in the population if their fitness is high. Antiviral prophylaxis further increases the pressure on the drug-sensitive strain and favors the spread of resistant infections. The authors show scenarios where pre-exposure antiviral prophylaxis even increases the number of influenza cases and deaths.

CONCLUSION

If the fitness of a NI resistant pandemic strain is high, any use of prophylaxis may increase the number of hospitalizations and deaths in the population. The use of neuraminidase inhibitors should be restricted to the treatment of cases whereas prophylaxis should be reduced to an absolute minimum in that case.

Antiviral Resistance in Influenza Viruses: Clinical and Epidemiological Aspects

Two classes of anti-viral agents, the M2 ion channel inhibitors (amantadine, rimantadine) and neuraminidase (NA) inhibitors (oseltamivir, zanamivir) are available for treatment and prevention of infl uenza in most countries of the world. The principle concerns about emergence of antiviral resistance in infl uenza viruses are loss of drug effi cacy, transmission of resistant variants, and possible increased virulence or transmissibility of resistant variants (1). Because seasonal infl uenza is usually an acute, self-limited illness in which viral clearance occurs rapidly due to innate and adaptive host immune responses, the emergence of drug-resistant variants would be anticipated to have modest effects on clinical recovery, except perhaps in immunocompromised or immunologically naïve hosts, such as young infants or during the appearance of a novel strain. In contrast to the limited impact of resistance emergence in the treated immunocompetent individual, the epidemiologic impact of resistance emergence and transmission could be considerable, including loss of both prophylactic and therapeutic activity for a particular drug, at the household, community, or perhaps global level. Infl uenza epidemiology in temperate climates is expected to provide some protection against widespread circulation of resistant variants, as viruses do not persist between epidemics but rather are re-introduced each season and new variants appear often (2, 3).