Contributions to the mathematical theory of epidemics—II. The problem of endemicity

(1) A mathematical investigation has been made of the prevalence of a disease in a population from which certain individuals are being removed as the result of the disease, whilst fresh individuals are being introduced as the result of birth or immigration. Allowance is made for the effects of the immunity produced as the result of an attack of the disease, but the effect of deaths from other causes is not taken into account, and the action of the disease is supposed to be independent of the age of the individual. (2) As a special case of the above, results have been obtained for a closed population in which no deaths occur and to which no fresh individuals are added, but in which the individuals after being infected acquire immunity, and then may be again infected. A threshold density of population exists analogous to that described in the previous paper, which is such that no disease can exist in a population, the density of which is below the threshold. (3) In other special cases investigated when either immigration or birth is operative in the supply of fresh individuals, as well as in the general case, only one steady state of disease is possible. To reach this state the population must be of a certain density which will be determined by the functions characterizing the infectivity, morbidity, etc., of the disease. (4) Increase of the immigration rate or of the birth-rate results in an increase in the rate of infection of the healthy individuals and also in the percentage rate of infection, the percentage of sick, and in the percentage of mortality from the disease. This result is, of course, a necessary consequence of our assumption that the disease is the only cause of death. (5) More particular results have been obtained by substituting constants in the place of the undetermined functions assumed in the general theory. Further, under these conditions the nature of the steady states has been more fully investigated and it has been shown that in all cases, except one, the steady states are stable ones. In the exception, a disturbance would result in purely periodic oscillations about the steady state.     

The Synthesis of α-Methylamino Acids

α-Methyltryptophan, α-methylhistidine, and α-methyldopa were prepared by the reaction of α-isocyanopropionates with gramine methiodide, the acetoxymethylimidazole derivative, and protected 3,4-dihydroxybenzyl bromides, respectively.     

The Synthesis of Dilnethyl α-Sorigenin

1,6,8-Trimethoxy-3-hydroxymethyl-2-naphthoic acid lactone (IV) was synthesized from benzoic acid in 21 steps. This lactone (IV) was completely identical with authentic dimethyl α-sorigenin, obtained by the methylation of natural α-sorigenin. Herewith the structure of α-sorigenin was confirmed to be 1,8-dihydroxy-6-methoxy-3-hydroxymethyl-2-naphthoic acid lactone (III).     

The Synthesis of αβ Imidothymidine Diphospate

Abstract

It has been shown by many workers that nucleotides containing an ap methylene link have interesting biochemical properties compared to those containing an αβ 0x0 linkage.¹ In our laboratory af3 methylene thymidine triphosphate has been shown to be a more powerful inhibitorof thymidine kinase than thymidine triphosphate but a weaker inhibitor of ribonucleotide reductase and cytidine deaminase. We have been interested in examining the properties of the af3 imido analogue. Several routes to prepare the unknown ap imidothymidine triphosphate were unsuccessfully tried:

1. Reaction of 3′-O-Acetylthymidine with the tributylammonium salt of dicyclohexylcarbodiimide.

2. Reaction of 5′-O-tosylthymidine with the tributylammonium salt 3 of imidodiphosphoric acid in hot dimethylacetamide.

     

The anthropology of ontology (religious science?)

Through engagement with a range of recent publications, this article offers a mini‐ethnography of wonder discourses in the anthropology of ontology, leading to a rethink of the concept of religion. It has sometimes been suggested that science and religion are antithetical orientations to the experience of wonder: whereas science seeks to banish wonder by replacing it with knowledge, religion remains open to wonder in the face of the unknowable. With this criterion of difference in view, this article identifies certain trends in the anthropology of ontology that appear to enjoin and pursue open‐ended wonder in ways that might be read as constituting anthropology as religious science. This coincidence of supposed opposites recommends, I conclude, a relational account of religion.     

The role of major virulence factors of AIEC involved in inflammatory bowl disease—a mini-review

Applied Microbiology and Biotechnology - Adherent-invasive Escherichia coli (AIEC) has recently attracted more attention because it is closely related to the pathogenicity of human inflammatory...     

The problem of natural antibodies, 1894–1905

As we have seen, natural antibodies first emerged as an experimental phenomenon without a plausible theoretical explanation. They were originally denied the status of antibody; then, adjustments to the side-chain theory transformed them from a curiosity into a foundation of the theory. However, in accommodating natural antibodies, Ehrlich had opened several holes in his mechanism of antibody formation.Thus, by 1905, natural antibodies were clearly established as problematic. From the practical standpoint, it seemed unwise to maintain an identity between normal and immune antibodies, given the therapeutic differences in their avidity. With the decline of Ehrlich's theory of antibody formation and the spread of Landsteiner's hapten technique for the production of antibodies against artificial antigens after World War I, the theoretical possibility of their existence as other than anomaly seemed more remote than ever. However, outside the theory and despite clinical considerations, natural antibodies remained a perplexing experimental phenomenon.⁴⁹     

The synthesis of a major α′-mycolic acid of Mycobacterium smegmatis

The synthesis of (2R,3R,Z)-2-docosyl-3-hydroxytetracont-21-enoic acid, a significant α′-mycolic acid of Mycobacterium smegmatis and other mycobacteria is reported.