RESUMO

The role of lockdown measures in mitigating COVID-19 in Mexico is investigated using a comprehensive nonlinear ODE model. The model includes both asymptomatic and presymptomatic populations with the latter leading to sickness (with recovery, hospitalization and death as possible outcomes). We consider situations involving the application of social-distancing and other intervention measures in the time series of interest. We find optimal parametric fits to the time series of deaths (only), as well as to the time series of deaths and cumulative infections. We discuss the merits and disadvantages of each approach, we interpret the parameters of the model and assess the realistic nature of the parameters resulting from the optimization procedure. Importantly, we explore a model involving two sub-populations (younger and older than a specific age), to more accurately reflect the observed impact as concerns symptoms and behavior in different age groups. For definiteness and to separate people that are (typically) in the active workforce, our partition of population is with respect to members younger vs. older than the age of 65. The basic reproduction number of the model is computed for both the single- and the two-population variant. Finally, we consider what would be the impact of partial lockdown (involving only the older population) and full lockdown (involving the entire population) on the number of deaths and cumulative infections.

Assuntos

COVID-19/epidemiologia , COVID-19/prevenção & controle , Surtos de Doenças/prevenção & controle , Surtos de Doenças/estatística & dados numéricos , Adulto , Idoso , Idoso de 80 Anos ou mais , Humanos , México/epidemiologia , Pessoa de Meia-Idade , Modelos Estatísticos

RESUMO

We examine theoretically and experimentally the localized electrical modes existing in a bi-inductive electrical lattice containing a bulk or a surface capacitive impurity. By means of the formalism of lattice Green's functions, we are able to obtain closed-form expressions for the frequencies of the impurity (bound-state) eigenmodes and for their associated spatial profiles. This affords us a systematic understanding of how these mode properties change as a function of the system parameters. We test these analytical results against experimental measurements, in both the bulk and surface cases, and find very good agreement. Last, we turn to a series of quench experiments, where either a parameter of the lattice or the lattice geometry itself is rapidly switched between two values or configurations. In all cases, we are able to naturally explain the results of such quench experiments from the larger analytical picture that emerges as a result of the detailed characterization of the impurity-mode solution branches.

RESUMO

It is shown that the tight-binding approximation of the nonlinear Schrödinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present nonstandard possibilities, among which we mention a quasilinear regime, where the pulse dynamics obeys essentially the linear Schrödinger equation. We analyze the properties of such models both in connection to their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.