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.

Pure coconut oil, lanolin, and acetaminophen were vaporized at rates of 1–50 mg/min, using a porous network exhibiting a temperature gradient from 5000 to 5500 K/mm, without incurring noticeable chemical changes due to combustion, oxidation, or other thermally-induced chemical structural changes. The newly coined term “ereptiospiration” is used here to describe this combination of thermal transpiration at high temperature gradients since the process can force the creation of thermal aerosols by rapid heating in a localized zone. Experimental data were generated for these materials using two different supports for metering the materials to the battery powered coil: namely, a stainless steel fiber bundle and a 3-D printed steel cartridge. Heating coconut oil, lanolin, or acetaminophen in a beaker to lower temperatures than those achieved at the surface of the coil showed noticeable and rapid degradation in the samples, while visual and olfactory observations for ereptiospiration showed no noticeable degradation in lanolin and coconut oil while HPLC chromatograms along with visual observation confirm that within the limit of detection, acetaminophen remains chemically unaltered by ereptiospiration.