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: Reproduction numbers, defined as averages of the number of people infected by a typical case, play a central role in tracking infectious disease outbreaks. The aim of this paper is to develop methods for estimating reproduction numbers which are simple enough that they could be applied with limited data or in real time during an outbreak. I present a new estimator for the individual reproduction number, which describes the state of the epidemic at a point in time rather than tracking individuals over time, and discuss some potential benefits. Then, to capture more of the detail that micro-simulations have shown is important in outbreak dynamics, I analyse a model of transmission within and between households, and develop a method to estimate the household reproduction number, defined as the number of households infected by each infected household. This method is validated by numerical simulations of the spread of influenza and measles using historical data, and estimates are obtained for would-be emerging epidemics of these viruses. I argue that the household reproduction number is useful in assessing the impact of measures that target the household for isolation, quarantine, vaccination or prophylactic treatment, and measures such as social distancing and school or workplace closures which limit between-household transmission, all of which play a key role in current thinking on future infectious disease mitigation.

A: Estimating Individual and Household Reproduction Numbers in an Emerging Epidemic
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Q: This article reviews the pulmonary route of administration, aerosol delivery devices, characterization of pulmonary drug delivery systems, and discusses the rationale for inhaled delivery of siRNA. Diseases with known protein malfunctions may be mitigated through the use of siRNA therapeutics. The inhalation route of administration provides local delivery of siRNA therapeutics for the treatment of various pulmonary diseases, however barriers to pulmonary delivery and intracellular delivery of siRNA exists. siRNA loaded nanocarriers can be used to overcome the barriers associated with the pulmonary route, such as anatomical barriers, mucociliary clearance, and alveolar macrophage clearance. Apart from naked siRNA aerosol delivery, previously studied siRNA carrier systems comprise of lipidic, polymeric, peptide, or inorganic origin. Such siRNA delivery systems formulated as aerosols can be successfully delivered via an inhaler or nebulizer to the pulmonary region. Preclinical animal investigations of inhaled siRNA therapeutics rely on intratracheal and intranasal siRNA and siRNA nanocarrier delivery. Aerosolized siRNA delivery systems may be characterized using in vitro techniques, such as dissolution test, inertial cascade impaction, delivered dose uniformity assay, laser diffraction, and laser Doppler velocimetry. The ex vivo techniques used to characterize pulmonary administered formulations include the isolated perfused lung model. In vivo techniques like gamma scintigraphy, 3D SPECT, PET, MRI, fluorescence imaging and pharmacokinetic/pharmacodynamics analysis may be used for evaluation of aerosolized siRNA delivery systems. The use of inhalable siRNA delivery systems encounters barriers to their delivery, however overcoming the barriers while formulating a safe and effective delivery system will offer unique advances to the field of inhaled medicine.

A:
Aerosol Delivery of siRNA to the Lungs. Part 1: Rationale for Gene Delivery Systems
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