We propose a numerical method for a general integro-differential system of equations which includes a number of age-of-infection epidemic models in the literature [1, 2]. The numerical solution is obtained by a non-standard discretization of the nonlinear terms in the system, and agrees with the analytical solution in many important qualitative aspects. Both the behaviour at finite time and the asymptotic properties of the solution are preserved for any value of the discretization parameter.

In this paper we analyze the stability of the problem of performing a rational QZ$step with a shift that is an eigenvalue of a given regular pencil H-lambda K in unreduced Hessenberg-Hessenberg form. In exact arithmetic, the backward rational QZ step moves the eigenvalue to the top of the pencil, while the rest of the pencil is maintained in Hessenberg-Hessenberg form, which then yields a deflation of the given shift. But in finite-precision the rational QZ step gets ``blurred'' and precludes the deflation of the given shift at the top of the pencil.

We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest-neighbor pairwise potentials, with bonds modeled as linearized elastic springs. Within this framework, we introduce plastic slip fields, whose discrete circulation around each tri-angle detects the possible presence of an edge dislocation.

This paper deals with the limit cases for s-fractional heat flows in a cylindrical domain, with homogeneous Dirichlet boundary conditions, as s-+ 0+ and s-+ 1-. We describe the fractional heat flows as minimizing move-ments of the corresponding Gagliardo seminorms, with re-spect to the L2 metric. To this end, we first provide a Gamma-convergence analysis for the s-Gagliardo seminorms as s-+ 0+ and s-+ 1-; then, we exploit an abstract stability result for minimizing movements in Hilbert spaces, with respect to a sequence of Gamma-converging uniformly lambda-convex energy function-als.

In this manuscript we propose a numerical method for non-linear integro-differential systems arising in age-of-infection models in a heterogeneously mixed population. The discrete scheme is based on direct quadrature methods and provides an unconditionally positive and bounded solution. Furthermore, we prove the existence of the numerical final size of the epidemic and show that it tends to its continuous equivalent as the discretization steplength vanishes.

In this paper we consider a non-standard discretization to a Volterra integro-dierential system which includes a number of age-of-infection models in the literature. The aim is to provide a general framework to analyze the proposed scheme for the numerical solution of a class of problems whose continuous dynamic is well known in the literature and allow a deeper analysis in cases where the theory lacks

Mortality shocks, such as pandemics, threaten the consolidated longevity improvements, confirmed in the last decades for the majority of western countries. Indeed, just before the COVID-19 pandemic, mortality was falling for all ages, with a different behavior according to different ages and countries. It is indubitable that the changes in the population longevity induced by shock events, even transitory ones, affecting demographic projections, have financial implications in public spending as well as in pension plans and life insurance.

We study the asymptotic behavior, as the lattice spacing ? tends to zero, of the discrete elastic energy induced by topological singularities in an inhomogeneous ? periodic medium within a two-dimensional model for screw dislocations in the square lattice. We focus on the |log?| regime which, as ?->0 allows the emergence of a finite number of limiting topological singularities.

The aim of this work is to propose a fast and reliable algorithm for computing integrals of the type $$\int_{-\infty}^{\infty} f(x) e^{\scriptstyle -x^2 -\frac{\scriptstyle 1}{\scriptstyle x^2}} dx,$$ where $f(x)$ is a sufficiently smooth function, in floating point arithmetic. The algorithm is based on a product integration rule, whose rate of convergence depends only on the regularity of $f$, since the coefficients of the rule are ``exactly'' computed by means of suitable recurrence relations here derived. We prove stability and convergence in the space of locally continuous functions