Thiago Yukio Tanaka | Searcharxiv

arXiv2024

Controls insensitizing the norm of solution of a Schrödinger type system with mixed dispersion

The main goal of this manuscript is to prove the existence of insensitizing controls for the fourth-order dispersive nonlinear Schrödinger equation with cubic nonlinearity. To obtain the main result we prove a null controllability property for a coupled fourth-order Schrödinger cascade type system with zero-order coupling which is equivalent to the insensitizing control problem. Precisely, employing a new Carleman estimate, we first obtain a null controllability result for the linearized system around zero, and then the null controllability for the nonlinear case is extended using an inverse mapping theorem.

math.AP↗

arXiv2020

SEIRD model in heterogenous populations: The role of commuting and social inequalities in the COVID-19 dynamics

In this paper we analyze the effects of commuting and social inequalities for the epidemic development of the novel coronavirus (COVID-19). With this aim we consider a SEIRD (susceptible, exposed, infected, recovered and dead by disease) model without vital dynamics in a population divided into patches that have different economic resources and in which the individuals can commute from one patch to another (bilaterally). In the modeling we choose the social and commuting parameters arbitrarily. We calculate the basic reproductive number $R_0$ with the next generation approach and analyze the sensitivity of $R_0$ with respect to the parameters. Furthermore, we run numerical simulations considering a population divided into two patches to bring some conclusions on the number of total infected individuals and cumulative deaths for our model considering heterogeneous populations.

q-bio.PE↗