RESUMO
In this paper, a mathematical model for COVID-19 that involves contact tracing is studied. The contact tracing-induced reproduction number R q and equilibrium for the model are determined and stabilities are examined. The global stabilities results are achieved by constructing Lyapunov functions. The contact tracing-induced reproduction number R q is compared with the basic reproduction number R 0 for the model in the absence of any intervention to assess the possible benefits of the contact tracing strategy.
RESUMO
The use of nanoparticles, in combination with ionizing radiation, is considered a promising method to improve the performance of radiation therapies. In this work, we engineered mono- and bimetallic core-shell gold-platinum nanoparticles (NPs) grafted with poly (ethylene glycol) (PEG). Their radio-enhancing properties were investigated using plasmids as bio-nanomolecular probes and gamma radiation. We found that the presence of bimetallic Au:Pt-PEG NPs increased by 90% the induction of double-strand breaks, the signature of nanosize biodamage, and the most difficult cell lesion to repair. The radio-enhancement of Au:Pt-PEG NPs were found three times higher than that of Au-PEG NPs. This effect was scavenged by 80% in the presence of dimethyl sulfoxide, demonstrating the major role of hydroxyl radicals in the damage induction. Geant4-DNA Monte Carlo simulations were used to elucidate the physical processes involved in the radio-enhancement. We predicted enhancement factors of 40% and 45% for the induction of nanosize damage, respectively, for mono- and bimetallic nanoparticles, which is attributed to secondary electron impact processes. This work contributed to a better understanding of the interplay between energy deposition and the induction of nanosize biomolecular damage, being Monte Carlo simulations a simple method to guide the synthesis of new radio-enhancing agents.
Assuntos
DNA/efeitos da radiação , Ouro/química , Nanopartículas Metálicas/química , Modelos Teóricos , Imagens de Fantasmas , Platina/química , Radiossensibilizantes/química , Simulação por Computador , Humanos , Método de Monte Carlo , Radiação IonizanteRESUMO
We consider a stochastic model describing the spread of a vector borne disease in a community where individuals (hosts and vectors) die and new individuals (hosts and vectors) are born. The time to extinction of the disease, TQ, starting in quasi-stationary (conditional on non extinction) is studied. Properties of the limiting distribution are used to obtain an approximate expression for E(TQ), the mean-parameter in the exponential distribution of the time to extinction, for a finite population. It is then investigated numerically and by means of simulations how E(TQ) and its approximations depend on the different model parameters.
