PubMed · 13308554
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C R BLACKBURN. 1956-02-18. Infectious hepatitis.. https://pubmed.ncbi.nlm.nih.gov/13308554/
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We formulate compartmental differential susceptibility (DS) susceptible-infective-removed (SIR) models by dividing the susceptible population into multiple subgroups according to the susceptibility of individuals in each group. We analyze the impact of disease-induced mortality in the situations where the number of contacts per individual is either constant or proportional to the total population. We derive an explicit formula for the reproductive number of infection for each model by investigating the local stability of the infection-free equilibrium. We further prove that the infection-free equilibrium of each model is globally asymptotically stable by qualitative analysis of the dynamics of the model system and by utilizing an appropriately chosen Liapunov function. We show that if the reproductive number is greater than one, then there exists a unique endemic equilibrium for all of the DS models studied in this paper. We prove that the endemic equilibrium is locally asymptotically stable for the models with no disease-induced mortality and the models with contact numbers proportional to the total population. We also provide sufficient conditions for the stability of the endemic equilibrium for other situations. We briefly discuss applications of the DS models to optimal vaccine strategies and the connections between the DS models and predator-prey models with multiple prey populations or host-parasitic interaction models with multiple hosts are also given.
OBJECTIVE: Controversy surrounds the use of parenteral nutrition in critical illness. Previous overviews used composite scales to identify high-quality trials, which may mask important differences in true methodological quality. Using a component-based approach this meta-analysis investigated the effect of trial quality on overall conclusions reached when standard enteral nutrition is compared to standard parenteral nutrition in critically ill patients. METHODS: An extensive literature search was undertaken to identify all eligible trials. We retrieved 465 publications, and 11 qualified for inclusion. Nine trials presented complete follow-up, allowing the conduct of an intention to treat analysis. RESULTS: Aggregation revealed a mortality benefit in favour of parenteral nutrition, with no heterogeneity. A priori specified subgroup analysis demonstrated the presence of a potentially important treatment-subgroup interaction between studies of parenteral vs. early enteral nutrition compared to parenteral vs. late enteral. Six trials with complete follow-up reported infectious complications. Infectious complications were increased with parenteral use. The I(2) measure of heterogeneity was 37.7%. CONCLUSIONS: Intention to treat trials demonstrated reduced mortality associated with parenteral nutrition use. A priori subgroup analysis attributed this reduction to trials comparing parenteral to delayed enteral nutrition. Despite an association with increased infectious complications, a grade B+ evidence-based recommendation (level II trials, no heterogeneity) can be generated for parenteral nutrition use in patients in whom enteral nutrition cannot be initiated within 24 h of ICU admission or injury.
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