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.

Input: Consider Input: 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.

Output: Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period


Input: Consider Input: | The ancient biological 'arms race' between microbial pathogens and humans has shaped genetic variation in modern populations, and this has important implications for the growing field of medical genomics. As humans migrated throughout the world, populations encountered distinct pathogens, and natural selection increased the prevalence of alleles that are advantageous in the new ecosystems in both host and pathogens. This ancient history now influences human infectious disease susceptibility and microbiome homeostasis, and contributes to common diseases that show geographical disparities, such as autoimmune and metabolic disorders. Using new high-throughput technologies, analytical methods and expanding public data resources, the investigation of natural selection is leading to new insights into the function and dysfunction of human biology. www.nature.com/reviews/genetics

Output: Natural selection and infectious disease in human populations


Input: Consider Input: Strategies for containing an emerging infectious disease outbreak must be nonpharmaceutical when drugs or vaccines for the pathogen do not yet exist or are unavailable. The success of these non-pharmaceutical strategies will depend not only on the effectiveness of quarantine or other isolation measures but also on the epidemiological characteristics of the infection. However, there is currently no systematic framework to assess the relationship between different containment strategies and the natural history and epidemiological dynamics of the pathogen. Here, we compare the effectiveness of quarantine and symptom monitoring, implemented via contact tracing, in controlling epidemics using an agent-based branching model. We examine the relationship between epidemic containment and the disease dynamics of symptoms and infectiousness for seven case study diseases with diverse natural histories including Ebola, Influenza A, and Severe Acute Respiratory Syndrome (SARS). We show that the comparative effectiveness of symptom monitoring and quarantine depends critically on the natural history of the infectious disease, its inherent transmissibility, and the intervention feasibility in the particular healthcare setting. The benefit of quarantine over symptom monitoring is generally maximized for fast-course diseases, but we show the conditions under which symptom monitoring alone can control certain outbreaks. This quantitative framework can guide policy-makers on how best to use non-pharmaceutical interventions to contain emerging outbreaks and prioritize research during an outbreak of a novel pathogen.


Output: TITLE Containing Emerging Epidemics: a Quantitative Comparison of Quarantine and Symptom Monitoring