Epidemiological and economic impact of pandemic influenza in Chicago: Priorities for vaccine interventions.

The study objective is to estimate the epidemiological and economic impact of vaccine interventions during influenza pandemics in Chicago, and assist in vaccine intervention priorities. Scenarios of delay in vaccine introduction with limited vaccine efficacy and limited supplies are not unlikely in future influenza pandemics, as in the 2009 H1N1 influenza pandemic. We simulated influenza pandemics in Chicago using agent-based transmission dynamic modeling. Population was distributed among high-risk and non-high risk among 0-19, 20-64 and 65+ years subpopulations. Different attack rate scenarios for catastrophic (30.15%), strong (21.96%), and moderate (11.73%) influenza pandemics were compared against vaccine intervention scenarios, at 40% coverage, 40% efficacy, and unit cost of $28.62. Sensitivity analysis for vaccine compliance, vaccine efficacy and vaccine start date was also conducted. Vaccine prioritization criteria include risk of death, total deaths, net benefits, and return on investment. The risk of death is the highest among the high-risk 65+ years subpopulation in the catastrophic influenza pandemic, and highest among the high-risk 0-19 years subpopulation in the strong and moderate influenza pandemics. The proportion of total deaths and net benefits are the highest among the high-risk 20-64 years subpopulation in the catastrophic, strong and moderate influenza pandemics. The return on investment is the highest in the high-risk 0-19 years subpopulation in the catastrophic, strong and moderate influenza pandemics. Based on risk of death and return on investment, high-risk groups of the three age group subpopulations can be prioritized for vaccination, and the vaccine interventions are cost saving for all age and risk groups. The attack rates among the children are higher than among the adults and seniors in the catastrophic, strong, and moderate influenza pandemic scenarios, due to their larger social contact network and homophilous interactions in school. Based on return on investment and higher attack rates among children, we recommend prioritizing children (0-19 years) and seniors (65+ years) after high-risk groups for influenza vaccination during times of limited vaccine supplies. Based on risk of death, we recommend prioritizing seniors (65+ years) after high-risk groups for influenza vaccination during times of limited vaccine supplies

Multi-scale immunoepidemiological modeling of within-host and between-host HIV dynamics: systematic review of mathematical models.

OBJECTIVE: The objective of this study is to conduct a systematic review of multi-scale HIV immunoepidemiological models to improve our understanding of the synergistic impact between the HIV viral-immune dynamics at the individual level and HIV transmission dynamics at the population level. BACKGROUND: While within-host and between-host models of HIV dynamics have been well studied at a single scale, connecting the immunological and epidemiological scales through multi-scale models is an emerging method to infer the synergistic dynamics of HIV at the individual and population levels. METHODS: We reviewed nine articles using the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) framework that focused on the synergistic dynamics of HIV immunoepidemiological models at the individual and population levels. RESULTS: HIV immunoepidemiological models simulate viral immune dynamics at the within-host scale and the epidemiological transmission dynamics at the between-host scale. They account for longitudinal changes in the immune viral dynamics of HIV+ individuals, and their corresponding impact on the transmission dynamics in the population. They are useful to analyze the dynamics of HIV super-infection, co-infection, drug resistance, evolution, and treatment in HIV+ individuals, and their impact on the epidemic pathways in the population. We illustrate the coupling mechanisms of the within-host and between-host scales, their mathematical implementation, and the clinical and public health problems that are appropriate for analysis using HIV immunoepidemiological models. CONCLUSION: HIV immunoepidemiological models connect the within-host immune dynamics at the individual level and the epidemiological transmission dynamics at the population level. While multi-scale models add complexity over a single-scale model, they account for the time varying immune viral response of HIV+ individuals, and the corresponding impact on the time-varying risk of transmission of HIV+ individuals to other susceptibles in the population

Don't bleach chaotic data

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ``bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.Comment: 12 dense pages (82K) of ordinary LaTeX; uses macro psfig.tex for inclusion of figures in text; figures are uufile'd into a single file of size 306K; the final dvips'd postscript file is about 1.3mb Replaced 9/30/93 to incorporate final changes in the proofs and to make the LaTeX more portable; the paper will appear in CHAOS 4 (Dec, 1993

Synthetic social network of Chicago.

<p>Synthetic population of Chicago is generated and a social contact network is estimated through the following four steps.</p

Decision tree of health outcomes for influenza cases and related costs.

<p>For each influenza case, the probability of the different health outcomes and related costs depend on the age and risk group of the patient. Patients with pre-existing medical condition have a high risk of experiencing severe influenza related health outcomes. The probability of each health outcome is assigned an uniform or triangular distribution [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005521#pcbi.1005521.ref004" target="_blank">4</a>]. For the uniform distribution, the lower and upper rate are presented; for triangular distribution, the lower, most probably, and higher rates are presented.</p

Sensitivity analysis of vaccine compliance, vaccine efficacy and vaccine start date, and impact on attack rate.

<p>Univariate sensitivity analysis for vaccine compliance rates of 10%, 40%, 60% and 80% (Fig 7A), vaccine efficacy rates of 10%, 20%, 30%, 40%, 50% and 60% (Fig 7B) and vaccine start dates after epidemic onset of day 15, day 30, day 60 and day 90 (Fig 7C), and their impact on attack rates for catastrophic, strong, and moderate influenza pandemic scenarios with no vaccine intervention (base case) and vaccine intervention (static and dynamic models). </p

Prioritization of influenza vaccine intervention.

<p>Prioritization of influenza vaccine intervention among different age and risk groups based on different criteria: <i>risk of death</i>, <i>total deaths</i>, <i>net benefits</i>, and <i>return on investment</i>. <b>Fig 6A:</b> Risk of death is estimated based on the number of influenza related deaths per 100,000 subpopulation for the specific age and risk groups. Risk of death is the highest among the high risk 65+ years subpopulation in the catastrophic influenza and it is the highest among high risk 0–19 years old among strong, and moderate influenza pandemic scenarios. <b>Fig 6B:</b> Total deaths is estimated based on the proportion of influenza related deaths for the specific age and risk groups among total influenza related deaths. The proportion of influenza related deaths is the highest among the high risk 20–64 years subpopulation in the catastrophic, strong, and moderate influenza pandemic scenarios. <b>Fig 6C:</b> Net benefits are the difference in cost due to improved health outcomes from vaccination and the vaccination cost. Net benefits are the highest among the high risk 20–64 years subpopulation in the catastrophic, strong, and moderate influenza pandemic scenarios. <b>Fig 6D:</b> Return on investment is the gain in net benefits relative to the vaccination cost, that is, dollars saved per $1 investment in vaccine intervention. Return on investment is highest among the high risk 0–19 years subpopulation in the catastrophic, strong and moderate influenza pandemic scenarios.</p

Computation of pandemic cost, pandemic cost per capita, net benefits and return on investment.

<p>The formulations to compute <i>pandemic cost</i>, <i>pandemic cost per capita</i>, <i>net benefits</i> and <i>return on investment</i> are presented below for the scenarios of without and with vaccine intervention. <i>Pandemic cost</i> is the total cost associated with the health outcomes of influenza cases and the cost of vaccination, and <i>pandemic cost per capita</i> is the average pandemic cost per person. The <i>net benefits</i> is the difference in cost due to improved health outcomes from vaccination and the vaccination cost. <i>Return on investment</i> is the gain in net benefits relative to the vaccination cost.</p

Risk of death, total deaths, net benefits and return on investment for different age and risk groups in the catastrophic, strong, and moderate influenza pandemic scenarios.

<p><i>Risk of death</i> is estimated based on the number of influenza related deaths per 100,000 subpopulation for the specific age and risk groups. <i>Total deaths</i> is estimated based on the proportion of influenza related deaths for the specific age and risk groups among total influenza related deaths. <i>Net benefits</i> are the difference in cost due to improved health outcomes from vaccination and the vaccination cost. <i>Return on investment</i> is the gain in net benefits relative to the vaccination cost, that is, dollars saved per $1 investment in vaccine intervention.</p