Optimal distribution of vaccines to achieve high population immunity levels is a desirable aim in infectious disease epidemiology. A distributed optimal control epidemiological model that accounts for vaccination was developed and applied to the case of the COVID-19 pandemic. The model proposed here is nonstandard and takes into account the heterogeneity of the infected sub-population with respect to the time since infection, which is essential in the case of COVID-19. Based on the epidemiological characteristics of COVID-19 we analyze several vaccination scenarios and an optimal vaccination policy. In particular we consider random vaccination over the whole population and the prioritization of age groups such as the elderly and compare the effects with the optimal solution. Numerical results of the model show that random vaccination is efficient in reducing the overall number of infected individuals. Prioritization of the elderly leads to lower mortality though. The optimal strategy in terms of total deaths is early prioritization of those groups having the highest contact rates.
Festuca L. is one of the most complicated genera in Poaceae. Polyacrylamide gel electrophoresis was used to study the isoenzyme variation of glutamate-oxaloacetate transaminase, malate dehydrogenase, glutamate dehydrogenase, isocitrate dehydrogenase and 6-phosphogluconate dehydrogenase in natural populations of F. valesiaca Schleich. ex Gaud., F. rupicola Heuff., F. dalmatica (Hack.) K. Richt. and F. stojanovii (Acht.) Kozuharov ex Foggi & Petrova. The aim of the present study was to assess isoenzyme variation and genetic affinities among the four species of the genus Festuca. Genetic identities (I) and distances (D) were calculated to evaluate qualitative genetic affinities and systematic relationships among the species. Considering the patterns of isoenzyme variation in the studied group, it is evident that F. dalmatica and F. stojanovii are closely related species. The species F. valesiaca and F. rupicola are isoenzymatically well characterized as distinct genetic entities. The obtained results generally support recent narrow species concept in the genus Festuca.
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