No abstract

A new extension operator for a virtual coarse space is presented which can be used in domain decomposition methods for nodal elliptic problems in two dimensions. In particular, a two-level overlapping Schwarz algorithm is considered and a bound for the condition number of the preconditioned system is obtained. This bound is independent of discontinuities across the interface. The extension operator saves computational time compared to previous studies where discrete harmonic extensions are required and it is suitable for general polygonal meshes and irregular subdomains. Numerical experiments that verify the result are shown, including some with regular and irregular polygonal elements and with subdomains obtained by a mesh partitioner.

We formulate an age-structured three-staged nonlinear partial differential equation model that features nonlinear recidivism to the infected (infectious) class from the temporarily recovered class. Equilibria are computed, as well as local and global stability of the infection-free equilibrium. As a result, a backward-bifurcation exists under necessary and sufficient conditions. A generalized numerical framework is established and numerical experiments are explored for two positive solutions to exist in the infectious class.

A bound is obtained for the condition number of a BDDC algorithm for problems posed in H(curl) in two dimensions, where the subdomains are only assumed to be uniform in the sense of Peter Jones. For the primal variable space, a continuity constraint for the tangential average over each interior subdomain edge is imposed. For the averaging operator, a new technique named deluxe scaling is used. Our bound is independent of jumps in the coefficients across the interface between the subdomains and depends only on a few geometric parameters of the decomposition. Numerical results that verify the result are shown, including some with subdomains with fractal edges and others obtained by a mesh partitioner.

For countries starting to receive steady supplies of vaccines against SARS-CoV-2, the course of Covid-19 for the following months will be determined by the emergence of new variants and successful roll-out of vaccination campaigns. To anticipate this scenario, we used a multilayer network model developed to forecast the transmission dynamics of Covid-19 in Costa Rica, and to estimate the impact of the introduction of the Delta variant in the country, under two plausible vaccination scenarios, one sustaining Costa Rica’s July 2021 vaccination pace of 30,000 doses per day and with high acceptance from the population and another with declining vaccination pace to 13,000 doses per day and with lower acceptance. Results suggest that the introduction and gradual dominance of the Delta variant would increase Covid-19 hospitalizations and ICU admissions by $$35\%$$ 35 % and $$33.25\%$$ 33.25 % , respectively, from August 2021 to December 2021, depending on vaccine administration and acceptance. In the presence of the Delta variant, new Covid-19 hospitalizations and ICU admissions are estimated to increase around $$24.26\%$$ 24.26 % and $$27.19\%$$ 27.19 % , respectively, in the same period if the vaccination pace drops. Our results can help decision-makers better prepare for the Covid-19 pandemic in the months to come.