What is the best control strategy for multiple infectious disease outbreaks?

Effective control of infectious disease outbreaks is an important public health goal. In a number of recent studies, it has been shown how different intervention measures like travel restrictions, school closures, treatment and prophylaxis might allow us to control outbreaks of diseases, such as SARS, pandemic influenza and others. In these studies, control of a single outbreak is considered. It is, however, not clear how one should handle a situation where multiple outbreaks are likely to occur. Here, we identify the best control strategy for such a situation. We further discuss ways in which such a strategy can be implemented to achieve additional public health objectives.     

Epidemiology, transmission dynamics and control of SARS: the 2002-2003 epidemic

This paper reviews current understanding of the epidemiology, transmission dynamics and control of the aetiological agent of severe acute respiratory syndrome (SARS). We present analyses of data on key parameters and distributions and discuss the processes of data capture, analysis and public health policy formulation during the SARS epidemic are discussed. The low transmissibility of the virus, combined with the onset of peak infectiousness following the onset of clinical symptoms of disease, transpired to make simple public health measures, such as isolating patients and quarantining their contacts, very effective in the control of the SARS epidemic. We conclude that we were lucky this time round, but may not be so with the next epidemic outbreak of a novel aetiological agent. We present analyses that help to further understanding of what intervention measures are likely to work best with infectious agents of defined biological and epidemiological properties. These lessons learnt from the SARS experience are presented in an epidemiological and public health context.     

Steady state analysis of influx and transbilayer distribution of ergosterol in the yeast plasma membrane

Mathematical modeling is now frequently used in outbreak investigations to understand underlying mechanisms of infectious disease dynamics, assess patterns in epidemiological data, and forecast the trajectory of epidemics. However, the successful application of mathematical models to guide public health interventions lies in the ability to reliably estimate model parameters and their corresponding uncertainty. Here, we present and illustrate a simple computational method for assessing parameter identifiability in compartmental epidemic models. We describe a parametric bootstrap approach to generate simulated data from dynamical systems to quantify parameter uncertainty and identifiability. We calculate confidence intervals and mean squared error of estimated parameter distributions to assess parameter identifiability. To demonstrate this approach, we begin with a low-complexity SEIR model and work through examples of increasingly more complex compartmental models that correspond with applications to pandemic influenza, Ebola, and Zika. Overall, parameter identifiability issues are more likely to arise with more complex models (based on number of equations/states and parameters). As the number of parameters being jointly estimated increases, the uncertainty surrounding estimated parameters tends to increase, on average, as well. We found that, in most cases, R0 is often robust to parameter identifiability issues affecting individual parameters in the model. Despite large confidence intervals and higher mean squared error of other individual model parameters, R0 can still be estimated with precision and accuracy. Because public health policies can be influenced by results of mathematical modeling studies, it is important to conduct parameter identifiability analyses prior to fitting the models to available data and to report parameter estimates with quantified uncertainty. The method described is helpful in these regards and enhances the essential toolkit for conducting model-based inferences using compartmental dynamic models.     

Early real-time estimation of the basic reproduction number of emerging or reemerging infectious diseases in a community with heterogeneous contact pattern: Using data from Hong Kong 2009 H1N1 Pandemic Influenza as an illustrative example

Emerging and re-emerging infections such as SARS (2003) and pandemic H1N1 (2009) have caused concern for public health researchers and policy makers due to the increased burden of these diseases on health care systems. This concern has prompted the use of mathematical models to evaluate strategies to control disease spread, making these models invaluable tools to identify optimal intervention strategies. A particularly important quantity in infectious disease epidemiology is the basic reproduction number, R_0. Estimation of this quantity is crucial for effective control responses in the early phase of an epidemic. In our previous study, an approach for estimating the basic reproduction number in real time was developed. This approach uses case notification data and the structure of potential transmission contacts to accurately estimate R₀ from the limited amount of information available at the early stage of an outbreak. Based on this approach, we extend the existing methodology; the most recent method features intra- and inter-age groups contact heterogeneity. Given the number of newly reported cases at the early stage of the outbreak, with parsimony assumptions on removal distribution and infectivity profile of the diseases, experiments to estimate real time R₀ under different levels of intra- and inter-group contact heterogeneity using two age groups are presented. We show that the new method converges more quickly to the actual value of R₀ than the previous one, in particular when there is high-level intra-group and inter-group contact heterogeneity. With the age specific contact patterns, number of newly reported cases, removal distribution, and information about the natural history of the 2009 pandemic influenza in Hong Kong, we also use the extended model to estimate R₀ and age-specific R₀.     

The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda

Despite improved control measures, Ebola remains a serious public health risk in African regions where recurrent outbreaks have been observed since the initial epidemic in 1976. Using epidemic modeling and data from two well-documented Ebola outbreaks (Congo 1995 and Uganda 2000), we estimate the number of secondary cases generated by an index case in the absence of control interventions R0. Our estimate of R0 is 1.83 (SD 0.06) for Congo (1995) and 1.34 (SD 0.03) for Uganda (2000). We model the course of the outbreaks via an SEIR (susceptible-exposed-infectious-removed) epidemic model that includes a smooth transition in the transmission rate after control interventions are put in place. We perform an uncertainty analysis of the basic reproductive number R0 to quantify its sensitivity to other disease-related parameters. We also analyse the sensitivity of the final epidemic size to the time interventions begin and provide a distribution for the final epidemic size. The control measures implemented during these two outbreaks (including education and contact tracing followed by quarantine) reduce the final epidemic size by a factor of 2 relative the final size with a 2-week delay in their implementation.     

A graph-theoretic method for the basic reproduction number in continuous time epidemiological models

In epidemiological models of infectious diseases the basic reproduction number is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for can be obtained from the digraphs in the reduction process.     

Anti-severe acute respiratory syndrome coronavirus spike antibodies trigger infection of human immune cells via a pH- and cysteine protease-independent FcγR pathway

Public health measures successfully contained outbreaks of the severe acute respiratory syndrome coronavirus (SARS-CoV) infection. However, the precursor of the SARS-CoV remains in its natural bat reservoir, and reemergence of a human-adapted SARS-like coronavirus remains a plausible public health concern. Vaccination is a major strategy for containing resurgence of SARS in humans, and a number of vaccine candidates have been tested in experimental animal models. We previously reported that antibody elicited by a SARS-CoV vaccine candidate based on recombinant full-length Spike-protein trimers potentiated infection of human B cell lines despite eliciting in vivo a neutralizing and protective immune response in rodents. These observations prompted us to investigate the mechanisms underlying antibody-dependent enhancement (ADE) of SARS-CoV infection in vitro. We demonstrate here that anti-Spike immune serum, while inhibiting viral entry in a permissive cell line, potentiated infection of immune cells by SARS-CoV Spike-pseudotyped lentiviral particles, as well as replication-competent SARS coronavirus. Antibody-mediated infection was dependent on Fcγ receptor II but did not use the endosomal/lysosomal pathway utilized by angiotensin I converting enzyme 2 (ACE2), the accepted receptor for SARS-CoV. This suggests that ADE of SARS-CoV utilizes a novel cell entry mechanism into immune cells. Different SARS vaccine candidates elicit sera that differ in their capacity to induce ADE in immune cells despite their comparable potency to neutralize infection in ACE2-bearing cells. Our results suggest a novel mechanism by which SARS-CoV can enter target cells and illustrate the potential pitfalls associated with immunization against it. These findings should prompt further investigations into SARS pathogenesis.     

Avian influenza H5N1 transmission in households, Indonesia

Background

Disease transmission patterns are needed to inform public health interventions, but remain largely unknown for avian influenza H5N1 virus infections. A recent study on the 139 outbreaks detected in Indonesia between 2005 and 2009 found that the type of exposure to sources of H5N1 virus for both the index case and their household members impacted the risk of additional cases in the household. This study describes the disease transmission patterns in those outbreak households.

Methodology/Principal Findings

We compared cases (n = 177) and contacts (n = 496) in the 113 sporadic and 26 cluster outbreaks detected between July 2005 and July 2009 to estimate attack rates and disease intervals. We used final size household models to fit transmission parameters to data on household size, cases and blood-related household contacts to assess the relative contribution of zoonotic and human-to-human transmission of the virus, as well as the reproduction number for human virus transmission. The overall household attack rate was 18.3% and secondary attack rate was 5.5%. Secondary attack rate remained stable as household size increased. The mean interval between onset of subsequent cases in outbreaks was 5.6 days. The transmission model found that human transmission was very rare, with a reproduction number between 0.1 and 0.25, and the upper confidence bounds below 0.4. Transmission model fit was best when the denominator population was restricted to blood-related household contacts of index cases.

Conclusions/Significance

The study only found strong support for human transmission of the virus when a single large cluster was included in the transmission model. The reproduction number was well below the threshold for sustained transmission. This study provides baseline information on the transmission dynamics for the current zoonotic virus and can be used to detect and define signatures of a virus with increasing capacity for human-to-human transmission.     

The More the Better? A Comparison of the Information Sources Used by the Public during Two Infectious Disease Outbreaks

Recent infectious disease outbreaks have resulted in renewed recognition of the importance of risk communication planning and execution to public health control strategies. Key to these efforts is public access to information that is understandable, reliable and meets their needs for informed decision-making on protective health behaviours. Learning from the trends in sources used in previous outbreaks will enable improvements in information access in future outbreaks. Two separate random-digit dialled telephone surveys were conducted in Alberta, Canada, to explore information sources used by the public, together with their perceived usefulness and credibility, during the 2003 Severe Acute Respiratory Syndrome (SARS) epidemic (n = 1209) and 2009–2010 H1N1 pandemic (n = 1206). Traditional mass media were the most used information sources in both surveys. Although use of the Internet increased from 25% during SARS to 56% during H1N1, overall use of social media was not as high as anticipated. Friends and relatives were commonly used as an information source, but were not deemed very useful or credible. Conversely, doctors and health professionals were considered credible, but not consulted as frequently. The use of five or more information sources increased by almost 60% between the SARS and H1N1 surveys. There was a shift to older, more educated and more affluent respondents between the surveys, most likely caused by a decrease in the use of landlines amongst younger Canadians. It was concluded that people are increasingly using multiple sources of health risk information, presumably in a complementary manner. Subsequently, although using online media is important, this should be used to augment rather than replace more traditional information channels. Efforts should be made to improve knowledge transfer to health care professionals and doctors and provide them with opportunities to be more accessible as information sources. Finally, the future use of telephone surveys needs to account for the changing demographics of the respondents accessed through such surveys.     

Using models to identify routes of nosocomial infection: a large hospital outbreak of SARS in Hong Kong

Two factors dominated the epidemiology of severe acute respiratory syndrome (SARS) during the 2002-2003 global outbreak, namely super-spreading events (SSE) and hospital infections. Although both factors were important during the first and the largest hospital outbreak in Hong Kong, the relative importance of different routes of infection has not yet been quantified. We estimated the parameters of a novel mathematical model of hospital infection using SARS episode data. These estimates described levels of transmission between the index super-spreader, staff and patients, and were used to compare three plausible hypotheses. The broadest of the supported hypotheses ascribes the initial surge in cases to a single super-spreading individual and suggests that the per capita risk of infection to patients increased approximately one month after the start of the outbreak. Our estimate for the number of cases caused by the SSE is substantially lower than the previously reported values, which were mostly based on self-reported exposure information. This discrepancy suggests that the early identification of the index case as a super-spreader might have led to biased contact tracing, resulting in too few cases being attributed to staff-to-staff transmission. We propose that in future outbreaks of SARS or other directly transmissible respiratory pathogens, simple mathematical models could be used to validate preliminary conclusions concerning the relative importance of different routes of transmission with important implications for infection control.     

Predicting epidemics on directed contact networks

Contact network epidemiology is an approach to modeling the spread of infectious diseases that explicitly considers patterns of person-to-person contacts within a community. Contacts can be asymmetric, with a person more likely to infect one of their contacts than to become infected by that contact. This is true for some sexually transmitted diseases that are more easily caught by women than men during heterosexual encounters; and for severe infectious diseases that cause an average person to seek medical attention and thereby potentially infect health care workers (HCWs) who would not, in turn, have an opportunity to infect that average person. Here we use methods from percolation theory to develop a mathematical framework for predicting disease transmission through semi-directed contact networks in which some contacts are undirected-the probability of transmission is symmetric between individuals-and others are directed-transmission is possible only in one direction. We find that the probability of an epidemic and the expected fraction of a population infected during an epidemic can be different in semi-directed networks, in contrast to the routine assumption that these two quantities are equal. We furthermore demonstrate that these methods more accurately predict the vulnerability of HCWs and the efficacy of various hospital-based containment strategies during outbreaks of severe respiratory diseases.     

Get the News Out Loudly and Quickly: The Influence of the Media on Limiting Emerging Infectious Disease Outbreaks

During outbreaks of infectious diseases with high morbidity and mortality, individuals closely follow media reports of the outbreak. Many will attempt to minimize contacts with other individuals in order to protect themselves from infection and possibly death. This process is called social distancing. Social distancing strategies include restricting socializing and travel, and using barrier protections. We use modeling to show that for short-term outbreaks, social distancing can have a large influence on reducing outbreak morbidity and mortality. In particular, public health agencies working together with the media can significantly reduce the severity of an outbreak by providing timely accounts of new infections and deaths. Our models show that the most effective strategy to reduce infections is to provide this information as early as possible, though providing it well into the course of the outbreak can still have a significant effect. However, our models for long-term outbreaks indicate that reporting historic infection data can result in more infections than with no reporting at all. We examine three types of media influence and we illustrate the media influence with a simulated outbreak of a generic emerging infectious disease in a small city. Social distancing can never be complete; however, for a spectrum of outbreaks, we show that leaving isolation (stopping applying social distancing measures) for up to 4 hours each day has modest effect on the overall morbidity and mortality.     

Preparedness for SARS in the UK in 2003

Severe acute respiratory syndrome (SARS) has been described as the first major emerging infectious disease of the twenty-first century. Having initially emerged, almost unnoticed, in southern China, it rapidly spread across the globe. It severely tested national public health and health systems. However, it also resulted in rapid, intensive international collaboration, led by the World Health Organization, to elucidate its characteristics and cause and to contain its spread. The UK mounted a vigorous public health response. Some particular issues concerned: the practicalities of implementing exit screening had this been required; the likely efficacy of this and other control measures; the legal base for public health action; and the surge capacity in all systems should the disease have taken hold in the UK. We have used this experience of 2003 to inform our preparation of a framework for an integrated, escalating response to a future re-emergence of SARS according to the levels of disease activity worldwide. Recent cases confirm that SARS has not "gone away". We cannot be complacent about our contingency planning.     

Characterization of an outbreak of hand, foot, and mouth disease in Nanchang, China in 2010

Recent outbreaks of human enterovirus 71 (EV71) infection and EV71-associated hand, foot, and mouth disease (HFMD) in China have affected millions and potentially lead to life-threatening complications in newborns. Furthermore, these outbreaks represent a significant global public health issue in the world. Understanding the epidemiology of HFMD and EV71 infection and their transmission patterns in China is essential for controlling outbreaks. However, no studies on the outbreaks of HFMD and EV71 infection in China during 2010 have been reported. In this report, we carried out an epidemiological analysis to study an outbreak of HFMD and EV71 infection in 2010 in the city of Nanchang in the Jiangxi province of People's Republic of China. From April 7 to May 11, 2010, a total of 109 HFMD cases were reported, and in this report the HFMD cases were studied by both epidemiological and laboratory analyses. The epidemiological study indicates that children aged younger than 8 years old represented more than 90% of the reported cases, with the age group of 1-3 years containing the highest number of cases. Laboratory studies detected a high prevalence of EV71 amongst the cases in our study, suggesting EV71 as a common enterovirus found in HFMD cases in Nanchang. Phylogenetic analysis of the sequence of the VP1 region of four EV71 isolates indicated that the Nanchang strains belong to the C4 subgenotype commonly found in China during outbreaks in 2008 but contain distinct variations from these strains. Our study for the first time characterizes the epidemiology of HFMD and EV71 infection in China in 2010 and furthermore, provides the first direct evidence of the genotype of EV71 circulating in Nanchang, China. Our study should facilitate the development of public health measures for the control and prevention of HFMD and EV71 infection in at-risk individuals in China.     

Heterogeneities in transmission rates and the epidemiology of schistosome infection.

Previous theoretical studies have suggested that heterogeneities in transmission rates can have significant effects on the epidemiology of parasite infections. However, the magnitude of these effects in practice remains uncertain because of the difficulty of quantifying such heterogeneities under natural conditions. In this paper we consider the effects of heterogeneous rates of contact with infective water bodies on the basic reproductive rate, R0, of human schistosomes. In particular, we examine the theoretical effects of differences in the distribution of contacts among individuals and among sites. We find that an individual's contribution to R0 depends not only on the net contact rate but also on how these contacts are distributed among sites--the contact pattern. Our analysis of field data suggests a substantial impact of heterogeneous contact rates on R0 in practice. Significant reductions in R0 may be possible if schistosomiasis control efforts are targeted at certain sites and, especially, certain individuals.     

Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE)

One goal of this paper is to give an algorithm for computing a threshold condition for epidemiological systems arising from compartmental deterministic modeling. We calculate a threshold condition T(0) of the parameters of the system such that if T(0)<1 the disease-free equilibrium (DFE) is locally asymptotically stable (LAS), and if T(0)>1, the DFE is unstable. The second objective, by adding some reasonable assumptions, is to give, depending on the model, necessary and sufficient conditions for global asymptotic stability (GAS) of the DFE. In many cases, we can prove that a necessary and sufficient condition for the global asymptotic stability of the DFE is R(0)< or =1, where R(0) is the basic reproduction number [O. Diekmann, J.A. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley, New York, 2000]. To illustrate our results, we apply our techniques to examples taken from the literature. In these examples we improve the results already obtained for the GAS of the DFE. We show that our algorithm is relevant for high dimensional epidemiological models.     

Candidate Genes Associated with Susceptibility for SARS-Coronavirus

Assuming that no human had any previously acquired immunoprotection against severe acute respiratory syndrome coronavirus (SARS-CoV) during the 2003 SARS outbreak, the biological bases for possible difference in individual susceptibility are intriguing. However, this issue has never been fully elucidated. Based on the premise that SARS patients belonging to a given genotype group having a significantly higher SARS infection rate than others would imply that genotype group being more susceptible, we make use of a compartmental model describing disease transmission dynamics and clinical and gene data of 100 laboratory confirmed SARS patients from Chinese Han population in Taiwan to estimate the infection rates of distinct candidate genotype groups among these SARS-infected individuals. The results show that CXCL10(−938AA) is always protective whenever it appears, but appears rarely and only jointly with either Fgl2(+158T/*) or HO-1(−497A/*), while (Fgl2)(+158T/*) is associated with higher susceptibility unless combined with CXCL10/IP-10(−938AA), when jointly is associated with lower susceptibility. The novel modeling approach proposed, which does not require sizable case and control gene datasets, could have important future public health implications in swiftly identifying potential high-risk groups associated with being highly susceptible to a particular infectious disease.     

Theory versus data: how to calculate R0?

To predict the potential severity of outbreaks of infectious diseases such as SARS, HIV, TB and smallpox, a summary parameter, the basic reproduction number R(0), is generally calculated from a population-level model. R(0) specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. R(0) is used to assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control. Conventionally, it is assumed that if R(0)>1 the outbreak generates an epidemic, and if R(0)<1 the outbreak becomes extinct. Here, we use computational and analytical methods to calculate the average number of secondary infections and to show that it does not necessarily represent an epidemic threshold parameter (as it has been generally assumed). Previously we have constructed a new type of individual-level model (ILM) and linked it with a population-level model. Our ILM generates the same temporal incidence and prevalence patterns as the population-level model; we use our ILM to directly calculate the average number of secondary infections (i.e., R(0)). Surprisingly, we find that this value of R(0) calculated from the ILM is very different from the epidemic threshold calculated from the population-level model. This occurs because many different individual-level processes can generate the same incidence and prevalence patterns. We show that obtaining R(0) from empirical contact tracing data collected by epidemiologists and using this R(0) as a threshold parameter for a population-level model could produce extremely misleading estimates of the infectiousness of the pathogen, the severity of an outbreak, and the strength of the medical and/or behavioral interventions necessary for control.     

An IDEA for Short Term Outbreak Projection: Nearcasting Using the Basic Reproduction Number

Background

Communicable disease outbreaks of novel or existing pathogens threaten human health around the globe. It would be desirable to rapidly characterize such outbreaks and develop accurate projections of their duration and cumulative size even when limited preliminary data are available. Here we develop a mathematical model to aid public health authorities in tracking the expansion and contraction of outbreaks with explicit representation of factors (other than population immunity) that may slow epidemic growth.

Methodology

The Incidence Decay and Exponential Adjustment (IDEA) model is a parsimonious function that uses the basic reproduction number R₀, along with a discounting factor to project the growth of outbreaks using only basic epidemiological information (e.g., daily incidence counts).

Principal Findings

Compared to simulated data, IDEA provides highly accurate estimates of total size and duration for a given outbreak when R₀ is low or moderate, and also identifies turning points or new waves. When tested with an outbreak of pandemic influenza A (H1N1), the model generates estimated incidence at the i+1^th serial interval using data from the i^th serial interval within an average of 20% of actual incidence.

Conclusions and Significance

This model for communicable disease outbreaks provides rapid assessments of outbreak growth and public health interventions. Further evaluation in the context of real-world outbreaks will establish the utility of IDEA as a tool for front-line epidemiologists.