Related papers: The Basic Reproduction Number for Bounded Linear O…
We study the denseness of Crawford number attaining operators on Banach spaces. Mainly, we prove that if a Banach space has the RNP, then the set of Crawford number attaining operators is dense in the space of bounded linear operators. We…
It is essential to understand the dynamics of epidemics in the presence of coexisting pathogens. There are various phenomenon that can effect the dynamics. In this paper, we formulate a mathematical model using different assumptions to…
We study an SIR epidemic model with a seasonal contact rate and saturated treatment function. It is shown that the basic reproduction number $(\mathcal {R}_0)$ cannot be acted as a threshold that predicts the spread of an infection. Based…
The process of recombination in population genetics, in its deterministic limit, leads to a nonlinear ODE in the Banach space of finite measures on a locally compact product space. It has an embedding into a larger family of nonlinear ODEs…
In this paper, we study the existence of the random fixed points for lower semicontinuous condensing random operators defined on Banach spaces. Our results extend corresponding ones present in literature.
We establish a general result about extending a right invertible row over a Banach algebra to an invertible matrix. This is applied to the computation of right topological stable rank of a split exact sequence. We also introduce a…
We study the relationship between the residuality of the set of norm attaining functionals on a Banach space and the residuality and the denseness of the set of norm attaining operators between Banach spaces. Our first main result says that…
Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the R0 alternative"…
A replicator equation with explicit space and global regulation is considered. This model provides a natural framework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the…
We investigate steady states of a quasilinear first order hyperbolic partial integro-differential equation. The model describes the evolution of a hierarchical structured population with distributed states at birth. Hierarchical…
This paper is concerned with the study of a class of nonlinear nonlocal functional evolution problems defined in an abstract Banach algebra. We introduce an abstract functional setting that encompasses a wide range of structured population…
The main aim of this paper is to provide characterizations of Birkhoff-James orthogonality (BJ-orthogonality in short) in a number of families of Banach spaces in terms of the elements of significant subsets of the unit ball of their dual…
In this paper we explore the properties of a bounded linear operator defined on a Banach space, in light of operator norm attainment. Using Birkhoff-James orthogonality techniques, we give a necessary condition for a bounded linear operator…
We consider linear control systems of the form $\dot{y}(t)=Ay(t)-\mu B C y(t)$ where $\mu$ is a positive real parameter, $A$ is the state operator and generates a linear $C_0-$semigroup of contractions $S(t) $ on a Banach space $X$, $B$ and…
We introduce a positive linear operator acting on the Banach space of all continuous functions on the unit interval via the Moran model studied in population genetics. We show that this operator, named the Moran operator, uniformly…
We introduce the concept of essential numerical range $W_{\!e}(T)$ for unbounded Hilbert space operators $T$ and study its fundamental properties including possible equivalent characterizations and perturbation results. Many of the…
We extend a recent investigation by Meehan et al. (2019) regarding the global stability properties of the general Kermack-McKendrick (renewal) model to the multi-strain case. We demonstrate that the basic reproduction number of each strain…
In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.
The recursion operators admitted by different operator Burgers equations, in the framework of the study of nonlinear evolution equations, are here con- sidered. Specifically, evolution equations wherein the unknown is an operator acting on…
The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case…