Are Staphylococcus aureus Carrier Types Evidence of Population Heterogeneity?

Asymptomatic colonization by Staphylococcus aureus is a precursor for infection, so identifying the mode and source of transmission which leads to colonization could help in targeting interventions. Longitudinal studies have shown that some people are persistently colonized for years, while others seem to carry S. aureus for weeks or less, and conventional wisdom attributes this disparity to an underlying risk factor in the persistently colonized. We analyze published data with mathematical models of acquisition and carriage to compare this hypothesis with alternatives. The null model assumed a homogeneous population and still produced highly variable colonization durations (mean = 101.7 weeks; 5th percentile, 5.2 weeks; 95th percentile, 304.7 weeks). Simulations showed that this inherent variability, combined with censoring in longitudinal cohort studies, is sufficient to produce the appearance of "persistent carriers," "intermittent carriers," and "noncarriers" in data. Our estimates for colonization duration exhibited sensitivity to the assumption that false-positive test results can occur despite being rare, but our model-based approach simultaneously estimates specificity and sensitivity along with epidemiologic parameters. Our results show it is plausible that S. aureus colonizes people indiscriminately, and improved understanding of the types of exposures which result in colonization is essential.

Economic Evaluations of New Antibiotics: The High Potential Value of Reducing Healthcare Transmission Through Decolonization.

BACKGROUND: Antibiotics designed to decolonize carriers of drug-resistant organisms could offer substantial population health benefits, particularly if they can help avert outbreaks by interrupting person-to-person transmission chains. However, cost effectiveness of an antibiotic is typically evaluated only according to its benefits to recipients, which can be difficult to demonstrate for carriers of an organism that may not pose an immediate health threat to the carrier. METHODS: We developed a mathematical transmission model to quantify the effects of 2 hypothetical antibiotics targeting carbapenem-resistant Enterobacteriaceae (CRE) among long-term acute care hospital inpatients: one assumed to decrease the death rate of patients with CRE bloodstream infections (BSIs) and the other assumed to decolonize CRE carriers after clinical detection. We quantified the effect of each antibiotic on the number of BSIs and deaths among patients receiving the drug (direct effect) and among all patients (direct and indirect effect) compared to usual care. We applied these results to a cost-effectiveness analysis with effectiveness outcome of life-years gained and assumed costs for antibiotic doses and for CRE BSI. RESULTS: The decolonizing antibiotic, once indirect effects were included, produced increased relative effectiveness and decreased relative costs compared to both usual care and the BSI treatment antibiotic. In fact, in most scenarios, the decolonizing drug was the dominant treatment strategy (ie, less costly and more effective). CONCLUSIONS: Antibiotics that decolonize carriers of drug-resistant organisms can be highly cost-effective when considering indirect benefits within populations vulnerable to outbreaks. Public health could benefit from finding ways to incentivize development of decolonizing antibiotics in the US, where drugs with unclear direct benefits to recipients would pose difficulties in achieving FDA approval and financial benefit to the developer.

Model-based Assessment of the Effect of Contact Precautions Applied to Surveillance-detected Carriers of Carbapenemase-producing Enterobacteriaceae in Long-term Acute Care Hospitals.

BACKGROUND: An intervention that successfully reduced colonization and infection with carbapenemase-producing Enterobacteriaceae (CPE) in Chicago-area long-term acute-care hospitals included active surveillance and contact precautions. However, the specific effects of contact precautions applied to surveillance-detected carriers on patient-to-patient transmission are unknown, as other, concurrent intervention components or changes in facility patient dynamics also could have affected the observed outcomes. METHODS: Using previously published data from before and after the CPE intervention, we designed a mathematical model with an explicit representation of postintervention surveillance. We estimated preintervention to postintervention changes of 3 parameters: ß, the baseline transmission rate excluding contact precaution effects; δb, the rate of a CPE carrier progressing to bacteremia; and δc, the progression rate to nonbacteremia clinical detection. RESULTS: Assuming that CPE carriers under contact precautions transmit carriage to other patients at half the rate of undetected carriers, the model produced no convincing evidence for a postintervention change in the baseline transmission rate ß (+2.1% [95% confidence interval {CI}, -18% to +28%]). The model did find evidence of a postintervention decrease for δb (-41% [95% CI, -60% to -18%]), but not for δc (-7% [95% CI, -28% to +19%]). CONCLUSIONS: Our results suggest that contact precautions for surveillance-detected CPE carriers could potentially explain the observed decrease in colonization by itself, even under conservative assumptions for the effectiveness of those precautions for reducing cross-transmission. Other intervention components such as daily chlorhexidine gluconate bathing of all patients and hand-hygiene education and adherence monitoring may have contributed primarily to reducing rates of colonized patients progressing to bacteremia.

The Potential for Interventions in a Long-term Acute Care Hospital to Reduce Transmission of Carbapenem-Resistant Enterobacteriaceae in Affiliated Healthcare Facilities.

BACKGROUND: Carbapenem-resistant Enterobacteriaceae (CRE) are high-priority bacterial pathogens targeted for efforts to decrease transmissions and infections in healthcare facilities. Some regions have experienced CRE outbreaks that were likely amplified by frequent transmission in long-term acute care hospitals (LTACHs). Planning and funding of intervention efforts focused on LTACHs is one proposed strategy to contain outbreaks; however, the potential regional benefits of such efforts are unclear. METHODS: We designed an agent-based simulation model of patients in a regional network of 10 healthcare facilities including 1 LTACH, 3 short-stay acute care hospitals (ACHs), and 6 nursing homes (NHs). The model was calibrated to achieve realistic patient flow and CRE transmission and detection rates. We then simulated the initiation of an entirely LTACH-focused intervention in a previously CRE-free region, including active surveillance for CRE carriers and enhanced isolation of identified carriers. RESULTS: When initiating the intervention at the first clinical CRE detection in the LTACH, cumulative CRE transmissions over 5 years across all 10 facilities were reduced by 79%-93% compared to no-intervention simulations. This result was robust to changing assumptions for transmission within non-LTACH facilities and flow of patients from the LTACH. Delaying the intervention until the 20th CRE detection resulted in substantial delays in achieving optimal regional prevalence, while still reducing transmissions by 60%-79% over 5 years. CONCLUSIONS: Focusing intervention efforts on LTACHs is potentially a highly efficient strategy for reducing CRE transmissions across an entire region, particularly when implemented as early as possible in an emerging outbreak.

Using network projections to explore co-incidence and context in large clinical datasets: Application to homelessness among U.S. Veterans.

INTRODUCTION: Network projections of data can provide an efficient format for data exploration of co-incidence in large clinical datasets. We present and explore the utility of a network projection approach to finding patterns in health care data that could be exploited to prevent homelessness among U.S. Veterans. METHOD: We divided Veteran ICD-9-CM (ICD9) data into two time periods (0-59 and 60-364days prior to the first evidence of homelessness) and then used Pajek social network analysis software to visualize these data as three different networks. A multi-relational network simultaneously displayed the magnitude of ties between the most frequent ICD9 pairings. A new association network visualized ICD9 pairings that greatly increased or decreased. A signed, subtraction network visualized the presence, absence, and magnitude difference between ICD9 associations by time period. RESULT: A cohort of 9468 U.S. Veterans was identified as having administrative evidence of homelessness and visits in both time periods. They were seen in 222,599 outpatient visits that generated 484,339 ICD9 codes (average of 11.4 (range 1-23) visits and 2.2 (range 1-60) ICD9 codes per visit). Using the three network projection methods, we were able to show distinct differences in the pattern of co-morbidities in the two time periods. In the more distant time period preceding homelessness, the network was dominated by routine health maintenance visits and physical ailment diagnoses. In the 59days immediately prior to the homelessness identification, alcohol related diagnoses along with economic circumstances such as unemployment, legal circumstances, along with housing instability were noted. CONCLUSION: Network visualizations of large clinical datasets traditionally treated as tabular and difficult to manipulate reveal rich, previously hidden connections between data variables related to homelessness. A key feature is the ability to visualize changes in variables with temporality and in proximity to the event of interest. These visualizations lend support to cognitive tasks such as exploration of large clinical datasets as a prelude to hypothesis generation.

Harnessing Intra-Host Strain Competition to Limit Antibiotic Resistance: Mathematical Model Results.

Antibiotic overuse has promoted the spread of antibiotic resistance. To compound the issue, treating individuals dually infected with antibiotic-resistant and antibiotic-vulnerable strains can make their infections completely resistant through competitive release. We formulate mathematical models of transmission dynamics accounting for dual infections and extensions accounting for lag times between infection and treatment or between cure and ending treatment. Analysis using the Next-Generation Matrix reveals how competition within hosts and the costs of resistance determine whether vulnerable and resistant strains persist, coexist, or drive each other to extinction. Invasion analysis predicts that treatment of dually infected cases will promote resistance. By varying antibiotic strength, the models suggest that physicians have two ways to achieve a particular resistance target: prescribe relatively weak antibiotics to everyone infected with an antibiotic-vulnerable strain or give more potent prescriptions to only those patients singly infected with the vulnerable strain after ruling out the possibility of them being dually infected with resistance. Through selectivity and moderation in antibiotic prescription, resistance might be limited.

Estimates of Outbreak Risk from New Introductions of Ebola with Immediate and Delayed Transmission Control.

While the ongoing Ebola outbreak continues in the West Africa countries of Guinea, Sierra Leone, and Liberia, health officials elsewhere prepare for new introductions of Ebola from infected evacuees or travelers. We analyzed transmission data from patients (i.e., evacuees, international travelers, and those with locally acquired illness) in countries other than the 3 with continuing Ebola epidemics and quantitatively assessed the outbreak risk from new introductions by using different assumptions for transmission control (i.e., immediate and delayed). Results showed that, even in countries that can quickly limit expected number of transmissions per case to <1, the probability that a single introduction will lead to a substantial number of transmissions is not negligible, particularly if transmission variability is high. Identifying incoming infected travelers before symptom onset can decrease worst-case outbreak sizes more than reducing transmissions from patients with locally acquired cases, but performing both actions can have a synergistic effect.

Quantitative models of the dose-response and time course of inhalational anthrax in humans.

Anthrax poses a community health risk due to accidental or intentional aerosol release. Reliable quantitative dose-response analyses are required to estimate the magnitude and timeline of potential consequences and the effect of public health intervention strategies under specific scenarios. Analyses of available data from exposures and infections of humans and non-human primates are often contradictory. We review existing quantitative inhalational anthrax dose-response models in light of criteria we propose for a model to be useful and defensible. To satisfy these criteria, we extend an existing mechanistic competing-risks model to create a novel Exposure-Infection-Symptomatic illness-Death (EISD) model and use experimental non-human primate data and human epidemiological data to optimize parameter values. The best fit to these data leads to estimates of a dose leading to infection in 50% of susceptible humans (ID50) of 11,000 spores (95% confidence interval 7,200-17,000), ID10 of 1,700 (1,100-2,600), and ID1 of 160 (100-250). These estimates suggest that use of a threshold to human infection of 600 spores (as suggested in the literature) underestimates the infectivity of low doses, while an existing estimate of a 1% infection rate for a single spore overestimates low dose infectivity. We estimate the median time from exposure to onset of symptoms (incubation period) among untreated cases to be 9.9 days (7.7-13.1) for exposure to ID50, 11.8 days (9.5-15.0) for ID10, and 12.1 days (9.9-15.3) for ID1. Our model is the first to provide incubation period estimates that are independently consistent with data from the largest known human outbreak. This model refines previous estimates of the distribution of early onset cases after a release and provides support for the recommended 60-day course of prophylactic antibiotic treatment for individuals exposed to low doses.

Vital Signs: Estimated Effects of a Coordinated Approach for Action to Reduce Antibiotic-Resistant Infections in Health Care Facilities - United States.

BACKGROUND: Treatments for health care-associated infections (HAIs) caused by antibiotic-resistant bacteria and Clostridium difficile are limited, and some patients have developed untreatable infections. Evidence-supported interventions are available, but coordinated approaches to interrupt the spread of HAIs could have a greater impact on reversing the increasing incidence of these infections than independent facility-based program efforts. METHODS: Data from CDC's National Healthcare Safety Network and Emerging Infections Program were analyzed to project the number of health care-associated infections from antibiotic-resistant bacteria or C. difficile both with and without a large scale national intervention that would include interrupting transmission and improved antibiotic stewardship. As an example, the impact of reducing transmission of one antibiotic-resistant infection (carbapenem-resistant Enterobacteriaceae [CRE]) on cumulative prevalence and number of HAI transmission events within interconnected groups of health care facilities was modeled using two distinct approaches, a large scale and a smaller scale health care network. RESULTS: Immediate nationwide infection control and antibiotic stewardship interventions, over 5 years, could avert an estimated 619,000 HAIs resulting from CRE, multidrug-resistant Pseudomonas aeruginosa, invasive methicillin-resistant Staphylococcus aureus (MRSA), or C. difficile. Compared with independent efforts, a coordinated response to prevent CRE spread across a group of inter-connected health care facilities resulted in a cumulative 74% reduction in acquisitions over 5 years in a 10-facility network model, and 55% reduction over 15 years in a 102-facility network model. CONCLUSIONS: With effective action now, more than half a million antibiotic-resistant health care-associated infections could be prevented over 5 years. Models representing both large and small groups of interconnected health care facilities illustrate that a coordinated approach to interrupting transmission is more effective than historical independent facilitybased efforts. IMPLICATIONS FOR PUBLIC HEALTH: Public health-led coordinated prevention approaches have the potential to more completely address the emergence and dissemination of these antibiotic-resistant organisms and C. difficile than independent facility-based efforts.

Incorporating social determinants of health into transmission modeling of COVID-19 vaccine in the US: a scoping review.

During COVID-19 in the US, social determinants of health (SDH) have driven health disparities. However, the use of SDH in COVID-19 vaccine modeling is unclear. This review aimed to summarize the current landscape of incorporating SDH into COVID-19 vaccine transmission modeling in the US. Medline and Embase were searched up to October 2022. We included studies that used transmission modeling to assess the effects of COVID-19 vaccine strategies in the US. Studies' characteristics, factors incorporated into models, and approaches to incorporate these factors were extracted. Ninety-two studies were included. Of these, 11 studies incorporated SDH factors (alone or combined with demographic factors). Various sets of SDH factors were integrated, with occupation being the most common (8 studies), followed by geographical location (5 studies). The results show that few studies incorporate SDHs into their models, highlighting the need for research on SDH impact and approaches to incorporating SDH into modeling. Funding: This research was funded by the Centers for Disease Control and Prevention (CDC).

Scoping review of modelling studies assessing the impact of disruptions to essential health services during COVID-19.

BACKGROUND: Studies assessing the indirect impact of COVID-19 using mathematical models have increased in recent years. This scoping review aims to identify modelling studies assessing the potential impact of disruptions to essential health services caused by COVID-19 and to summarise the characteristics of disruption and the models used to assess the disruptions. METHODS: Eligible studies were included if they used any models to assess the impact of COVID-19 disruptions on any health services. Articles published from January 2020 to December 2022 were identified from PubMed, Embase and CINAHL, using detailed searches with key concepts including COVID-19, modelling and healthcare disruptions. Two reviewers independently extracted the data in four domains. A descriptive analysis of the included studies was performed under the format of a narrative report. RESULTS: This scoping review has identified a total of 52 modelling studies that employed several models (n=116) to assess the potential impact of disruptions to essential health services. The majority of the models were simulation models (n=86; 74.1%). Studies covered a wide range of health conditions from infectious diseases to non-communicable diseases. COVID-19 has been reported to disrupt supply of health services, demand for health services and social change affecting factors that influence health. The most common outcomes reported in the studies were clinical outcomes such as mortality and morbidity. Twenty-five studies modelled various mitigation strategies; maintaining critical services by ensuring resources and access to services are found to be a priority for reducing the overall impact. CONCLUSION: A number of models were used to assess the potential impact of disruptions to essential health services on various outcomes. There is a need for collaboration among stakeholders to enhance the usefulness of any modelling. Future studies should consider disparity issues for more comprehensive findings that could ultimately facilitate policy decision-making to maximise benefits to all.

Comparison of antigen- and RT-PCR-based testing strategies for detection of SARS-CoV-2 in two high-exposure settings.

Surveillance testing for infectious disease is an important tool to combat disease transmission at the population level. During the SARS-CoV-2 pandemic, RT-PCR tests have been considered the gold standard due to their high sensitivity and specificity. However, RT-PCR tests for SARS-CoV-2 have been shown to return positive results when performed to individuals who are past the infectious stage of the disease. Meanwhile, antigen-based tests are often treated as a less accurate substitute for RT-PCR, however, new evidence suggests they may better reflect infectiousness. Consequently, the two test types may each be most optimally deployed in different settings. Here, we present an epidemiological model with surveillance testing and coordinated isolation in two congregate living settings (a nursing home and a university dormitory system) that considers test metrics with respect to viral culture, a proxy for infectiousness. Simulations show that antigen-based surveillance testing coupled with isolation greatly reduces disease burden and carries a lower economic cost than RT-PCR-based strategies. Antigen and RT-PCR tests perform different functions toward the goal of reducing infectious disease burden and should be used accordingly.

Association Between Contact Precautions and Transmission of Methicillin-Resistant Staphylococcus aureus in Veterans Affairs Hospitals.

Importance: The effectiveness and importance of contact precautions for endemic pathogens has long been debated, and their use has broad implications for infection control of other pathogens. Objective: To estimate the association between contact precautions and transmission of methicillin-resistant Staphylococcus aureus (MRSA) across US Department of Veterans Affairs (VA) hospitals. Design, Setting, and Participants: This retrospective cohort study used mathematical models applied to data from a population-based sample of adults hospitalized in 108 VA acute care hospitals for at least 24 hours from January 1, 2008, to December 31, 2017. Data were analyzed from May 2, 2019, to December 11, 2020. Exposures: A positive MRSA test result, presumed to indicate contact precautions use according to the VA MRSA Prevention Initiative. Main Outcomes and Measures: The main outcome was the association between contact precautions and MRSA transmission, defined as the relative transmissibility attributed to contact precautions. A contact precaution effect estimate (<1 indicates a reduction in transmission associated with contact precautions) was estimated for each hospital and then pooled over time and across hospitals using meta-regression. Results: In this cohort study of 108 VA hospitals, more than 2 million unique individuals had over 5.6 million admissions, of which 14.1% were presumed to have contact precautions with more than 8.4 million MRSA surveillance tests. Pooled estimates found associations between contact precautions and transmission to be stable from 2008 to 2017, with estimated transmission reductions ranging from 43% (95% credible interval [CrI], 38%-48%) to 51% (95% CrI, 46%-55%). Over the entire 10-year study period, contact precautions reduced transmission 47% (95% CrI, 45%-49%), and the intrafacility autocorrelation coefficient estimate was 0.99, suggesting consistent estimates over time within facilities. Larger facilities and those with higher admission screening compliance observed additional reductions in transmission associated with contact precautions (relative rate, 0.84; 95% CI, 0.74-0.96 and 0.74; 95% CI, 0.58-0.96, respectively) compared with smaller facilities and those with lower admission screening compliance. Facilities in the southern US had a smaller transmission reduction attributable to contact precautions (relative rate, 1.14; 95% CI, 1.01-1.28) compared with facilities in other regions in the US. Conclusions and Relevance: In this cohort study of adults in VA hospitals, transmissibility of MRSA was found to be reduced by approximately 50% among patients with contact precautions. These results provide an explanation for decreasing acquisition rates in VA hospitals since the MRSA Prevention Initiative.

High variability in transmission of SARS-CoV-2 within households and implications for control.

BACKGROUND: Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) poses a high risk of transmission in close-contact indoor settings, which may include households. Prior studies have found a wide range of household secondary attack rates and may contain biases due to simplifying assumptions about transmission variability and test accuracy. METHODS: We compiled serological SARS-CoV-2 antibody test data and prior SARS-CoV-2 test reporting from members of 9,224 Utah households. We paired these data with a probabilistic model of household importation and transmission. We calculated a maximum likelihood estimate of the importation probability, mean and variability of household transmission probability, and sensitivity and specificity of test data. Given our household transmission estimates, we estimated the threshold of non-household transmission required for epidemic growth in the population. RESULTS: We estimated that individuals in our study households had a 0.41% (95% CI 0.32%- 0.51%) chance of acquiring SARS-CoV-2 infection outside their household. Our household secondary attack rate estimate was 36% (27%- 48%), substantially higher than the crude estimate of 16% unadjusted for imperfect serological test specificity and other factors. We found evidence for high variability in individual transmissibility, with higher probability of no transmissions or many transmissions compared to standard models. With household transmission at our estimates, the average number of non-household transmissions per case must be kept below 0.41 (0.33-0.52) to avoid continued growth of the pandemic in Utah. CONCLUSIONS: Our findings suggest that crude estimates of household secondary attack rate based on serology data without accounting for false positive tests may underestimate the true average transmissibility, even when test specificity is high. Our finding of potential high variability (overdispersion) in transmissibility of infected individuals is consistent with characterizing SARS-CoV-2 transmission being largely driven by superspreading from a minority of infected individuals. Mitigation efforts targeting large households and other locations where many people congregate indoors might curb continued spread of the virus.

Continued need for non-pharmaceutical interventions after COVID-19 vaccination in long-term-care facilities.

Long-term care facilities (LTCFs) bear disproportionate burden of COVID-19 and are prioritized for vaccine deployment. LTCF outbreaks could continue occurring during vaccine rollout due to incomplete population coverage, and the effect of vaccines on viral transmission are currently unknown. Declining adherence to non-pharmaceutical interventions (NPIs) against within-facility transmission could therefore limit the effectiveness of vaccination. We built a stochastic model to simulate outbreaks in LTCF populations with differing vaccination coverage and NPI adherence to evaluate their interacting effects. Vaccination combined with strong NPI adherence produced the least morbidity and mortality. Healthcare worker vaccination improved outcomes in unvaccinated LTCF residents but was less impactful with declining NPI adherence. To prevent further illness and deaths, there is a continued need for NPIs in LTCFs during vaccine rollout.

Modeling the potential impact of administering vaccines against Clostridioides difficile infection to individuals in healthcare facilities.

BACKGROUND: A vaccine against Clostridioides difficile infection (CDI) is in development. While the vaccine has potential to both directly protect those vaccinated and mitigate transmission by reducing environmental contamination, the impact of the vaccine on C. difficile colonization remains unclear. Consequently, the transmission-reduction effect of the vaccine depends on the contribution of symptomatic CDI to overall transmission of C. difficile. METHODS: We designed a simulation model of CDI among patients in a network of 10 hospitals and nursing homes and calibrated the model using estimates of transmissibility from whole genome sequencing studies that estimated the fraction of CDI attributable to transmission from other CDI patients. We assumed the vaccine reduced the rate of progression to CDI among carriers by 25-95% after completion of a 3-dose vaccine course administered to randomly chosen patients at facility discharge. We simulated the administration of this vaccination campaign and tallied effects over 5 years. RESULTS: We estimated 30 times higher infectivity of CDI patients compared to other carriers. Simulations of the vaccination campaign produced an average reduction of 3-16 CDI cases per 1000 vaccinated patients, with 2-11 of those cases prevented among those vaccinated and 1-5 prevented among unvaccinated patients. CONCLUSIONS: Our findings demonstrate potential for a vaccine against CDI to reduce transmissions in healthcare facilities, even with no direct effect on carriage susceptibility. The vaccine's population impact will increase if received by individuals at risk for CDI onset in high-transmission settings.

Variation and trends in transmission dynamics of Methicillin-resistant Staphylococcus aureus in veterans affairs hospitals and nursing homes.

Variation and differences of MRSA transmission within and between healthcare settings are not well understood. This variability is critical for understanding the potential impact of infection control interventions and could aid in the evaluation of future intervention strategies. We fit a Bayesian transmission model to detailed individual-level MRSA surveillance data from over 230 Veterans Affairs (VA) hospitals and nursing homes. Our approach disentangles the effects of potential confounders, including length of stay, admission prevalence, and clearance, estimating dynamic transmission model parameters and temporal trends. The median baseline transmission rate in hospitals was approximately four-fold higher than in nursing homes, and declined in 46% of hospitals and 9% of nursing homes, resulting in a median transmission rate reduction of 43% across hospitals and an increase of 2% in nursing homes. For first admissions into an acute care facility, the median (range) importation probability was 10.5% (5.9%-18.4%), and was nearly twice as large, 18.7% (9.2%-37.4%), in nursing homes. This analysis found differences within and between hospitals and nursing homes. The transmission rate declined substantially in hospitals and remained stable in nursing homes, while admission prevalence was considerably higher in nursing homes than in hospitals.

Limit cycles in a chemostat model for a single species with age structure.

We model an age-structured population feeding on an abiotic resource by combining the Gurtin-MacCamy [Math. Biosci. 43 (1979) 199] approach with a standard chemostat model. Limit cycles arise by Hopf bifurcations at low values of the chemostat dilution rate, even for simple maternity functions for which the original Gurtin-MacCamy model has no oscillatory solutions. We find the exact location in parameter space of the Hopf bifurcations for special cases of our model. The onset of cycling is largely independent of both the form of the resource uptake function and the shape of the maternity function.

Estimates of the risk of large or long-lasting outbreaks of Middle East respiratory syndrome after importations outside the Arabian Peninsula.

We quantify outbreak risk after importations of Middle East respiratory syndrome outside the Arabian Peninsula. Data from 31 importation events show strong statistical support for lower transmissibility after early transmission generations. Our model projects the risk of ≥10, 100, and 500 transmissions as 11%, 2%, and 0.02%, and ≥1, 2, 3, and 4 generations as 23%, 14%, 0.9%, and 0.05%, respectively. Our results suggest tempered risk of large, long-lasting outbreaks with appropriate control measures.