In this task, you're given a paragraph from the research paper and your task is to generate a suitable title for the research paper based on the given paper. Under 100 words is a good title length.

Q: In this paper, we analyze a delayed SEIR epidemic model in which the latent and infected states are infective. The model has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number R 0 , is less than or equal to unity. We investigate the effect of the time delay on the stability of endemic equilibrium when R 0 > 1. We give criteria that ensure that endemic equilibrium is asymptotically stable for all time delays and a Hopf bifurcation occurs as time delay exceeds the critical value. We give formulae for the direction of Hopf bifurcations and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold reduction for functional differential equations. Numerical simulations are presented to illustrate the analytical results.

A: Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period
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Q: ('filoviruses') that cause severe hemorrhagic fever with human case fatality rates of up to 90%. Filovirus infection requires fusion of the host cell and virus membranes, a process that is mediated by the envelope glycoprotein (GP). GP contains two subunits, the surface subunit (GP1), which is responsible for cell attachment, and the transmembrane subunit (GP2), which catalyzes membrane fusion. The GP2 ectodomain contains two heptad repeat regions, N-terminal and C-terminal (NHR and CHR, respectively) that adopt a six-helix bundle during the fusion process. The refolding of this six-helix bundle provides the thermodynamic driving force to overcome barriers associated with membrane fusion. Here we report the crystal structure of the MARV GP2 core domain in its post-fusion (six-helix bundle) conformation at 1.9 Å resolution. The MARV GP2 core domain backbone conformation is virtually identical to that of EBOV GP2 (reported previously), and consists of a central NHR core trimeric coiled-coil packed against peripheral CHR α-helices and an intervening loop/helix-turn-helix segment. We previously reported that the stability of the MARV GP2 post-fusion structure is highly pH-dependent, with increasing stability at lower pH [Harrison, J.S.; Koellhoffer, J. K.; Chandran, K.; and Lai, J. R. Biochemistry, 2012Biochemistry, , 51, 2515Biochemistry, -2525. We hypothesized that this pH-dependent stability provides a mechanism for conformational control such that the post-fusion six helix bundle is promoted in the environments of appropriately matured endosomes. In this report, a structural rationale for this pH-dependent stability is described, and involves a high-density array of core and surface acidic side chains at the midsection of the structure, termed the 'anion stripe.' In addition, many surface-exposed salt bridges likely contribute to stabilizing the post-fusion structure at low pH. These results provide structural insights into the mechanism of MARV GP2-mediated membrane fusion.

A: Crystal Structure of the Marburg Virus GP2 Core Domain in its Post-Fusion Conformation †
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Q: Infectious diseases are a leading cause of death globally. Decisions surrounding how to control an infectious disease outbreak currently rely on a subjective process involving surveillance and expert opinion. However, there are many situations where neither may be available. Modeling can fill gaps in the decision making process by using available data to provide quantitative estimates of outbreak trajectories. Effective reduction of the spread of infectious diseases can be achieved through collaboration between the modeling community and public health policy community. However, such collaboration is rare, resulting in a lack of models that meet the needs of the public health community. Here we show a Susceptible-Infectious-Recovered (SIR) model modified to include control measures that allows parameter ranges, rather than parameter point estimates, and includes a web user interface for broad adoption. We apply the model to three diseases, measles, norovirus and influenza, to show the feasibility of its use and describe a research agenda to further promote interactions between decision makers and the modeling community. Despite substantial public health improvements in the last century, infectious diseases remain one of the leading causes of both morbidity and mortality 1,2 . When confronted with an infectious disease outbreak, public health officials typically work to control the outbreak by performing assessments, analyzing surveillance data, identifying resources and interacting with subject mater experts 2-4 . Control measures are then implemented based on the cumulative information collected. These approaches rely heavily on good surveillance systems, access to experts, and good intuition about which control measures to use. As such, they are largely subjective, time consuming, and the infrastructure required is often not present in high disease burden areas. Modeling is an attractive supplemental method because of the ability to estimate an outbreak's trajectory and the effects of possible control measures in a timely manner. Compartmental models are historically common; they divide individuals into categories based on their disease status. The most common variant is the SIR model, named after the categories used-"susceptible", "infectious" and "recovered". Models of this nature have small computational requirements, and are thus commonly used as first pass attempts to characterize outbreaks or infections quickly 5 . For example, after the sudden emergence of Severe Acute Respiratory Syndrome (SARS) in the early 2000s, researchers used modeling to characterize the virus' epidemiology. Several used compartmental models with control measures like quarantine or isolation in various settings (e.g., hospitals or cities) to describe effects of possible interventions 6-9 . Similar work exists for essentially all well known infectious diseases. For example, Mandal et al. provide a review of models used for malaria 10 and Bauch et al. explore model use with respect to SARS and other emerging infectious diseases 6 . Methods among these groups are often similar, but tend to focus on specific diseases and locations of interest. In contrast, agent-based models use a bottom-up approach where the agents (these are often people) interact with particular rules to simulate outbreaks 11 . This allows simulations at high resolutions, but requires large amounts of data to parameterize the models, as well as substantial computational power. It is thought that they may reflect real world scenarios more accurately, but the lack of available epidemiological data necessitates assumptions that are difficult or impossible to test 11 . These models further require computational resources inaccessible to an average health department. Both agent-based and compartmental models exhibit additional features that are problematic to wide-spread model adoption. The first is the focus on particular disease-location pairs. This emphasis precludes application to

A:
An approach to and web-based tool for infectious disease outbreak intervention analysis OPEN
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