The large-scale use of antivirals during influenza pandemics poses a significant selection pressure for drug-resistant pathogens to emerge and spread in a population. This requires treatment strategies to minimize total infections as well as the emergence of resistance. Here we propose a mathematical model in which individuals infected with wild-type influenza, if treated, can develop de novo resistance and further spread the resistant pathogen. Our main purpose is to explore the impact of two important factors influencing treatment effectiveness: i) the relative transmissibility of the drug-resistant strain to wild-type, and ii) the frequency of de novo resistance. For the endemic scenario, we find a condition between these two parameters that indicates whether treatment regimes will be most beneficial at intermediate or more extreme values (e.g., the fraction of infected that are treated). Moreover, we present analytical expressions for effective treatment regimes and provide evidence of its applicability across a range of modeling scenarios: endemic behavior with deterministic homogeneous mixing, and single-epidemic behavior with deterministic homogeneous mixing and stochastic heterogeneous mixing. Therefore, our results provide insights for the control of drug-resistance in influenza across time scales.

The production, characterization, and antioxidant capacity of the carotenoid fucoxanthin from the marine diatom Odontella aurita were investigated. The results showed that low light and nitrogen-replete culture medium enhanced the biosynthesis of fucoxanthin. The maximum biomass concentration of 6.36 g L^-1 and maximum fucoxanthin concentration of 18.47 mg g^-1 were obtained in cultures grown in a bubble column photobioreactor (Ø 3.0 cm inner diameter), resulting in a fucoxanthin volumetric productivity of 7.96 mg L^-1 day^-1. A slight reduction in biomass production was observed in the scaling up of O. aurita culture in a flat plate photobioreactor, yet yielded a comparable fucoxanthin volumetric productivity. A rapid method was developed for extraction and purification of fucoxanthin. The purified fucoxanthin was identified as all-trans-fucoxanthin, which exhibited strong antioxidant properties, with the effective concentration for 50% scavenging (EC₅₀) of 1,1-dihpenyl-2-picrylhydrazyl (DPPH) radical and 2,2′-Azino-bis(3-ethylbenzthiazoline-6-sulfonic acid (ABTS) radical being 0.14 and 0.03 mg mL^-1, respectively. Our results suggested that O. aurita can be a natural source of fucoxanthin for human health and nutrition.