How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space.

We extend a previously published model for the dynamics of a single strain of an influenza-like infection. The model incorporates a waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of coupled integral equations within a season and a discrete map between seasons. The long term behaviour of the model is demonstrated by examples where immunity to infection depends on the time since a host was last infected, and where immunity depends on the number of times that a host has been infected. The first scenario leads to complicated dynamics in some regions of parameter space, and to regions of parameter space with more than one attractor. The second scenario leads to a stable fixed point, corresponding to an identical epidemic each season. We also examine the model with both paradigms in combination, almost always but not exclusively observing a stable fixed point or periodic solution. Adding stochastic perturbations to the between season map fails to destroy the model's qualitative dynamics. Our results suggest that if the level of host immunity depends on the elapsed time since the last infection then the epidemiological dynamics may be unpredictable.

A simple influenza model with complicated dynamics.

We propose and analyse a model for the dynamics of a single strain of an influenza-like infection. The model incorporates waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of differential equations within a season and a discrete map between seasons. We show that the between-season map displays a variety of qualitatively different dynamics: fixed points, periodic solutions, or more complicated behaviour suggestive of chaos. For some example parameters we demonstrate the existence of two distinct basins of attraction, that is the initial conditions determine the long term dynamics. Our results suggest that there is no reason to expect influenza dynamics to be regular, or to expect past epidemics to give a clear indication of future seasons' behaviour.

Characterization of Influenza B Virus Variants with Reduced Neuraminidase Inhibitor Susceptibility.

Treatment options for influenza B virus infections are limited to neuraminidase inhibitors (NAIs), which block the neuraminidase (NA) glycoprotein on the virion surface. The development of NAI resistance would therefore result in a loss of antiviral treatment options for influenza B virus infections. This study characterized two contemporary influenza B viruses with known resistance-conferring NA amino acid substitutions, D197N and H273Y, detected during routine surveillance. The D197N and H273Y variants were characterized in vitro by assessing NA enzyme activity and affinity, as well as replication in cell culture compared to those of NAI-sensitive wild-type viruses. In vivo studies were also performed in ferrets to assess the replication and transmissibility of each variant. Mathematical models were used to analyze within-host and between-host fitness of variants relative to wild-type viruses. The data revealed that the H273Y variant had NA enzyme function similar to that of its wild type but had slightly reduced replication and transmission efficiency in vivo The D197N variant had impaired NA enzyme function, but there was no evidence of reduction in replication or transmission efficiency in ferrets. Our data suggest that the influenza B virus variant with the H273Y NA substitution had a more notable reduction in fitness compared to wild-type viruses than the influenza B variant with the D197N NA substitution. Although a D197N variant is yet to become widespread, it is the most commonly detected NAI-resistant influenza B virus in surveillance studies. Our results highlight the need to carefully monitor circulating viruses for the spread of influenza B viruses with the D197N NA substitution.

Calculation of the age of the first infection for skin sores and scabies in five remote communities in northern Australia.

Prevalence of skin sores and scabies in remote Australian Aboriginal communities remains unacceptably high, with Group A Streptococcus (GAS) the dominant pathogen. We aim to better understand the drivers of GAS transmission using mathematical models. To estimate the force of infection, we quantified the age of first skin sores and scabies infection by pooling historical data from three studies conducted across five remote Aboriginal communities for children born between 2001 and 2005. We estimated the age of the first infection using the Kaplan-Meier estimator; parametric exponential mixture model; and Cox proportional hazards. For skin sores, the mean age of the first infection was approximately 10 months and the median was 7 months, with some heterogeneity in median observed by the community. For scabies, the mean age of the first infection was approximately 9 months and the median was 8 months, with significant heterogeneity by the community and an enhanced risk for children born between October and December. The young age of the first infection with skin sores and scabies reflects the high disease burden in these communities.

Retrospective forecasting of the 2010-2014 Melbourne influenza seasons using multiple surveillance systems.

Accurate forecasting of seasonal influenza epidemics is of great concern to healthcare providers in temperate climates, since these epidemics vary substantially in their size, timing and duration from year to year, making it a challenge to deliver timely and proportionate responses. Previous studies have shown that Bayesian estimation techniques can accurately predict when an influenza epidemic will peak many weeks in advance, and we have previously tailored these methods for metropolitan Melbourne (Australia) and Google Flu Trends data. Here we extend these methods to clinical observation and laboratory-confirmation data for Melbourne, on the grounds that these data sources provide more accurate characterizations of influenza activity. We show that from each of these data sources we can accurately predict the timing of the epidemic peak 4-6 weeks in advance. We also show that making simultaneous use of multiple surveillance systems to improve forecast skill remains a fundamental challenge. Disparate systems provide complementary characterizations of disease activity, which may or may not be comparable, and it is unclear how a 'ground truth' for evaluating forecasts against these multiple characterizations might be defined. These findings are a significant step towards making optimal use of routine surveillance data for outbreak forecasting.

Influenza as a trigger for cardiovascular disease: An investigation of serotype, subtype and geographic location.

BACKGROUND: Seasonal peaks of influenza and cardiovascular disease tend to coincide. Many excess deaths may be triggered by influenza, and the severity of this effect may vary with the virulence of the circulating influenza strain and host susceptibility. We aimed to explore the association between hospital admissions for influenza and/or pneumonia (IP) and acute myocardial infarction (AMI) or ischaemic heart disease (IHD) in Queensland, Australia, taking into account temporal and spatial variation of influenza virus type and subtype in 2007, 2008 and 2009. METHODS: This ecological study at Statistical Subdivision level (SSD, n=38) used linked patient-level data. For each study year, Standardized Morbidity Ratios (SMRs) were calculated for hospital admissions with diagnoses of IP, AMI and IHD. We investigated the associations between IP and AMI or IHD using spatial autoregressive modelling, adjusting for socio-demographic factors. RESULTS: Spatial autocorrelation was detected in SMRs, possibly reflecting underlying social and behavioural risk factors, but consistent with infectious disease spread. SMRs for IP were consistently predictive of SMRs for AMI and IHD when adjusted for socioeconomic status, population density and per cent Indigenous population (coefficient: 0.707, 95% confidence interval (CI): 0.318 - 1.096; 0.553, 0.222 - 0.884; 0.598, 0.307 - 0.888 and 1.017, 0.711 - 1.323; 0.650, 0.342 - 0.958; 1.031, 0.827 - 1.236) in 2007, 2008 and 2009, respectively. CONCLUSIONS: This ecological study provides further evidence that severe respiratory infections may trigger the onset of cardiovascular events, implicating the influenza virus as a contributing factor.

Quantifying differences in the epidemic curves from three influenza surveillance systems: a nonlinear regression analysis.

Influenza surveillance enables systematic collection of data on spatially and demographically heterogeneous epidemics. Different data collection mechanisms record different aspects of the underlying epidemic with varying bias and noise. We aimed to characterize key differences in weekly incidence data from three influenza surveillance systems in Melbourne, Australia, from 2009 to 2012: laboratory-confirmed influenza notified to the Victorian Department of Health, influenza-like illness (ILI) reported through the Victorian General Practice Sentinel Surveillance scheme, and ILI cases presenting to the Melbourne Medical Deputising Service. Using nonlinear regression, we found that after adjusting for the effects of geographical region and age group, characteristics of the epidemic curve (including season length, timing of peak incidence and constant baseline activity) varied across the systems. We conclude that unmeasured factors endogenous to each surveillance system cause differences in the disease patterns recorded. Future research, particularly data synthesis studies, could benefit from accounting for these differences.

Pandemic controllability: a concept to guide a proportionate and flexible operational response to future influenza pandemics.

The 2009 H1N1 influenza pandemic posed challenges for governments worldwide. Strategies designed to limit community transmission, such as antiviral deployment, were largely ineffective due to both feasibility constraints and the generally mild nature of disease, resulting in incomplete case ascertainment. Reviews of national pandemic plans have identified pandemic impact, primarily linked to measures of transmissibility and severity, as a key concept to incorporate into the next generation of plans. While an assessment of impact provides the rationale under which interventions may be warranted, it does not directly provide an assessment on whether particular interventions may be effective. Such considerations motivate our introduction of the concept of pandemic controllability. For case-targeted interventions, such as antiviral treatment and post-exposure prophylaxis, we identify the visibility and transmissibility of a pandemic as the key drivers of controllability. Taking a case-study approach, we suggest that high-impact pandemics, for which control is most desirable, are likely uncontrollable with case-targeted interventions. Strategies that do not rely on the identification of cases may prove relatively more effective. By introducing a pragmatic framework for relating the assessment of impact to the ability to mitigate an epidemic (controllability), we hope to address a present omission identified in pandemic response plans.

A model for malaria treatment evaluation in the presence of multiple species.

Plasmodium falciparum and P. vivax are the two most common causes of malaria. While the majority of deaths and severe morbidity are due to P. falciparum, P. vivax poses a greater challenge to eliminating malaria outside of Africa due to its ability to form latent liver stage parasites (hypnozoites), which can cause relapsing episodes within an individual patient. In areas where P. falciparum and P. vivax are co-endemic, individuals can carry parasites of both species simultaneously. These mixed infections complicate dynamics in several ways: treatment of mixed infections will simultaneously affect both species, P. falciparum can mask the detection of P. vivax, and it has been hypothesised that clearing P. falciparum may trigger a relapse of dormant P. vivax. When mixed infections are treated for only blood-stage parasites, patients are at risk of relapse infections due to P. vivax hypnozoites. We present a stochastic mathematical model that captures interactions between P. falciparum and P. vivax, and incorporates both standard schizonticidal treatment (which targets blood-stage parasites) and radical cure treatment (which additionally targets liver-stage parasites). We apply this model via a hypothetical simulation study to assess the implications of different treatment coverages of radical cure for mixed and P. vivax infections and a "unified radical cure" treatment strategy where P. falciparum, P. vivax, and mixed infections all receive radical cure after screening glucose-6-phosphate dehydrogenase (G6PD) normal. In addition, we investigated the impact of mass drug administration (MDA) of blood-stage treatment. We find that a unified radical cure strategy leads to a substantially lower incidence of malaria cases and deaths overall. MDA with schizonticidal treatment was found to decrease P. falciparum with little effect on P. vivax. We perform a univariate sensitivity analysis to highlight important model parameters.

Likely effectiveness of pharmaceutical and non-pharmaceutical interventions for mitigating influenza virus transmission in Mongolia.

OBJECTIVE: To assess the likely benefit of the interventions under consideration for use in Mongolia during future influenza pandemics. METHODS: A stochastic, compartmental patch model of susceptibility, exposure, infection and recovery was constructed to capture the key effects of several interventions--travel restrictions, school closure, generalized social distancing, quarantining of close contacts, treatment of cases with antivirals and prophylaxis of contacts--on the dynamics of influenza epidemics. The likely benefit and optimal timing and duration of each of these interventions were assessed using Latin-hypercube sampling techniques, averaging across many possible transmission and social mixing parameters. FINDINGS: Timely interventions could substantially alter the time-course and reduce the severity of pandemic influenza in Mongolia. In a moderate pandemic scenario, early social distancing measures decreased the mean attack rate from around 10% to 7-8%. Similarly, in a severe pandemic scenario such measures cut the mean attack rate from approximately 23% to 21%. In both moderate and severe pandemic scenarios, a suite of non-pharmaceutical interventions proved as effective as the targeted use of antivirals. Targeted antiviral campaigns generally appeared more effective in severe pandemic scenarios than in moderate pandemic scenarios. CONCLUSION: A mathematical model of pandemic influenza transmission in Mongolia indicated that, to be successful, interventions to prevent transmission must be triggered when the first cases are detected in border regions. If social distancing measures are introduced at this stage and implemented over several weeks, they may have a notable mitigating impact. In low-income regions such as Mongolia, social distancing may be more effective than the large-scale use of antivirals.

Constructing an ethical framework for priority allocation of pandemic vaccines.

BACKGROUND: Allocation of scarce resources during a pandemic extends to the allocation of vaccines when they eventually become available. We describe a framework for priority vaccine allocation that employed a cross-disciplinary approach, guided by ethical considerations and informed by local risk assessment. METHODS: Published and grey literature was reviewed, and augmented by consultation with key informants, to collate past experience, existing guidelines and emerging strategies for pandemic vaccine deployment. Identified ethical issues and decision-making processes were also included. Concurrently, simulation modelling studies estimated the likely impacts of alternative vaccine allocation approaches. Assembled evidence was presented to a workshop of national experts in pandemic preparedness, vaccine strategy, implementation and ethics. All of this evidence was then used to generate a proposed ethical framework for vaccine priorities best suited to the Australian context. FINDINGS: Published and emerging guidance for priority pandemic vaccine distribution differed widely with respect to strategic objectives, specification of target groups, and explicit discussion of ethical considerations and decision-making processes. Flexibility in response was universally emphasised, informed by real-time assessment of the pandemic impact level, and identification of disproportionately affected groups. Model outputs aided identification of vaccine approaches most likely to achieve overarching goals in pandemics of varying transmissibility and severity. Pandemic response aims deemed most relevant for an Australian framework were: creating and maintaining trust, promoting equity, and reducing harmful outcomes. INTERPRETATION: Defining clear and ethically-defendable objectives for pandemic response in context aids development of flexible and adaptive decision support frameworks and facilitates clear communication and engagement activities.

A biological model of scabies infection dynamics and treatment informs mass drug administration strategies to increase the likelihood of elimination.

Infections with Sarcoptes scabiei, or scabies, remain common in many disadvantaged populations. Mass drug administration (MDA) has been used in such settings to achieve a rapid reduction in infection and transmission, with the goal of eliminating the public health burden of scabies. While prevalence has been observed to fall substantially following such an intervention, in some instances resurgence of infection to baseline levels has occurred over several years. To explore the biology underpinning this phenomenon, we have developed a theoretical model of scabies life-cycle and transmission dynamics in a homogeneously mixing population, and simulate the impact of mass drug treatment strategies acting on egg and mite life cycle stages (ovicidal) or mites alone (non-ovicidal). In order to investigate the dynamics of the system, we first define and calculate the optimal interval between treatment doses. We calculate the probability of eradication as a function of the number of optimally-timed successive treatment doses and the number of years over which a program is run. For the non-ovicidal intervention, we first show that at least two optimally-timed doses are required to achieve eradication. We then demonstrate that while more doses over a small number of years provides the highest chance of eradication, a similar outcome can be achieved with fewer doses delivered annually over a longer period of time. For the ovicidal intervention, we find that doses should be delivered as close together as possible. This work provides a platform for further research into optimal treatment strategies which may incorporate heterogeneity of transmission, and the interplay between MDA and enhancement of continuing scabies surveillance and treatment strategies.

Turnover of Village Chickens Undermines Vaccine Coverage to Control HPAI H5N1.

Highly pathogenic avian influenza (HPAI) subtype H5N1 remains an enzootic disease of village chickens in Indonesia, posing ongoing risk at the animal-human interface. Previous modelling showed that the fast natural turnover of chicken populations might undermine herd immunity after vaccination, although actual details of how this effect applies to Indonesia's village chicken population have not been determined. We explored the turnover effect in Indonesia's scavenging and mixed populations of village chickens using an extended Leslie matrix model parameterized with data collected from village chicken flocks in Java region, Indonesia. Population dynamics were simulated for 208 weeks; the turnover effect was simulated for 16 weeks after vaccination in two 'best case' scenarios, where the whole population (scenario 1), or birds aged over 14 days (scenario 2), were vaccinated. We found that the scavenging and mixed populations have different productive traits. When steady-state dynamics are reached, both populations are dominated by females (54.5%), and 'growers' and 'chicks' represent the most abundant age stages with 39% and 38% in the scavenging, and 60% and 25% in the mixed population, respectively. Simulations showed that the population turnover might reduce the herd immunity below the critical threshold that prevents the re-emergence of HPAI H5N1 4-8 weeks (scavenging) and 6-9 weeks (mixed population) after vaccination in scenario 1, and 2-6 weeks (scavenging) and 4-7 weeks (mixed population) after vaccination in scenario 2. In conclusion, we found that Indonesia's village chicken population does not have a unique underlying population dynamic and therefore, different turnover effects on herd immunity may be expected after vaccination; nonetheless, our simulations carried out in best case scenarios highlight the limitations of current vaccine technologies to control HPAI H5N1. This suggests that the improvements and complementary strategies are necessary and must be explored.

The influence of changing host immunity on 1918-19 pandemic dynamics.

The sociological and biological factors which gave rise to the three pandemic waves of Spanish influenza in England during 1918-19 are still poorly understood. Symptom reporting data available for a limited set of locations in England indicates that reinfection in multiple waves occurred, suggesting a role for loss of infection-acquired immunity. Here we explore the role that changes in host immunity, driven by a combination of within-host factors and viral evolution, may play in explaining weekly mortality data and wave-by-wave symptomatic attack-rates available for a subset of English cities. Our results indicate that changes in the phenotype of the pandemic virus are likely required to explain the closely spaced waves of infection, but distinguishing between the detailed contributions of viral evolution and changing adaptive immune responses to transmission rates is difficult given the dearth of sero-epidemiological and virological data available even for more contemporary pandemics. We find that a dynamical model in which pre-pandemic protection in older "influenza-experienced" cohorts is lost rapidly prior to the second wave provides the best fit to the mortality and symptom reporting data. Best fitting parameter estimates for such a model indicate that post-infection protection lasted of order months, while other statistical analyses indicate that population-age was inversely correlated with overall mortality during the herald wave. Our results suggest that severe secondary waves of pandemic influenza may be triggered by viral escape from pre-pandemic immunity, and thus that understanding the role of heterosubtypic or cross-protective immune responses to pandemic influenza may be key to controlling the severity of future influenza pandemics.

Population pharmacokinetics of intravenous artesunate: a pooled analysis of individual data from patients with severe malaria.

There are ~660,000 deaths from severe malaria each year. Intravenous artesunate (i.v. ARS) is the first-line treatment in adults and children. To optimize the dosing regimen of i.v. ARS, the largest pooled population pharmacokinetic study to date of the active metabolite dihydroartemisinin (DHA) was performed. The pooled dataset consisted of 71 adults and 195 children with severe malaria, with a mixture of sparse and rich sampling within the first 12 h after drug administration. A one-compartment model described the population pharmacokinetics of DHA adequately. Body weight had the greatest impact on DHA pharmacokinetics, resulting in lower DHA exposure for smaller children (6-10 kg) than adults. Post hoc estimates of DHA exposure were not significantly associated with parasitological outcomes. Comparable DHA exposure in smaller children and adults after i.v. ARS was achieved under a dose modification for intramuscular ARS proposed in a separate analysis of children.

Incorporating population dynamics into household models of infectious disease transmission.

Most household models of disease transmission assume static household distributions. Although this is a reasonable simplification for assessing vaccination strategies at a single point in time or over the course of an outbreak, it has considerable drawbacks for assessing long term vaccination policies or for predicting future changes in immunity. We demonstrate that household models that include births, deaths and movement between households can show dramatically different patterns of infection and immunity to static population models. When immunity is assumed to be life-long, the pattern of births by household size is the key driver of infection, suggesting that the influx of susceptibles has most impact on infection risk in the household. In a comparison of 12 countries, we show that both the crude birth rate and the mean household size affect the risk of infection in households.