If S is a semigroup, then an S-set AS is a set A together with a representation of S by mappings of A into itself. In this article, the theory of injective envelopes is carried from R-modules to S-sets. These results are known to hold in every Grothendieck category, but the category EnsS of (right) S-sets is not even additive.

Chikungunya virus (CHIKV) has caused several major epidemics globally over the last two decades and is quickly expanding into new areas. Although this mosquito-borne disease is self-limiting and is not associated with high mortality, it can lead to severe, chronic and disabling arthritis, thereby posing a heavy burden to healthcare systems. The two main vectors for CHIKV are Aedes aegypti and Aedes albopictus (Asian tiger mosquito); however, many other mosquito species have been described as competent CHIKV vectors in scientific literature. With climate change, globalization and unfettered urban planning affecting many areas, CHIKV poses a significant public health risk to many countries. A scoping review was conducted to collate and categorize all pertinent information gleaned from published scientific literature on a priori defined aspects of CHIKV and its competent vectors. After developing a sensitive and specific search algorithm for the research question, seven databases were searched and data was extracted from 1920 relevant articles. Results show that CHIKV research is reported predominantly in areas after major epidemics have occurred. There has been an upsurge in CHIKV publications since 2011, especially after first reports of CHIKV emergence in the Americas. A list of hosts and vectors that could potentially be involved in the sylvatic and urban transmission cycles of CHIKV has been compiled in this scoping review. In addition, a repository of CHIKV mutations associated with evolutionary fitness and adaptation has been created by compiling and characterizing these genetic variants as reported in scientific literature.

Background: Severe acute respiratory syndrome virus 2 (SARS-CoV-2), likely a bat-origin coronavirus, spilled over from wildlife to humans in China in late 2019, manifesting as a respiratory disease. Coronavirus disease 2019 (COVID-19) spread initially within China and then globally, resulting in a pandemic. Objective: This article describes predictive modelling of COVID-19 in general, and efforts within the Public Health Agency of Canada to model the effects of non-pharmaceutical interventions (NPIs) on transmission of SARS-CoV-2 in the Canadian population to support public health decisions.Methods: The broad objectives of two modelling approaches, 1) an agent-based model and 2) a deterministic compartmental model, are described and a synopsis of studies is illustrated using a model developed in Analytica 5.3 software.Results: Without intervention, more than 70% of the Canadian population may become infected. Non-pharmaceutical interventions, applied with an intensity insufficient to cause the epidemic to die out, reduce the attack rate to 50% or less, and the epidemic is longer with a lower peak. If NPIs are lifted early, the epidemic may rebound, resulting in high percentages (more than 70%) of the population affected. If NPIs are applied with intensity high enough to cause the epidemic to die out, the attack rate can be reduced to between 1% and 25% of the population. Conclusion:Applying NPIs with intensity high enough to cause the epidemic to die out would seem to be the preferred choice. Lifting disruptive NPIs such as shut-downs must be accompanied by enhancements to other NPIs to prevent new introductions and to identify and control any new transmission chains.

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