Necibe Tuncer

Necibe Tuncer
Florida Atlantic University | FAU · Department of Mathematical Sciences

About

49
Publications
8,192
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476
Citations
Introduction
Necibe Tuncer currently works at the Department of Mathematical Sciences, Florida Atlantic University. Necibe does research in Applied Mathematics. Their current project is 'Immuno-epidemiological Modeling'.
Additional affiliations
May 2018 - present
Florida Atlantic University
Position
  • Professor (Associate)
August 2014 - present
Florida Atlantic University
Position
  • Professor (Assistant)
Education
January 2002 - May 2007
Auburn University
Field of study
  • Mathematics

Publications

Publications (49)
Article
Full-text available
Determining accurate estimates for the characteristics of the severe acute respiratory syndrome coronavirus 2 in the upper and lower respiratory tracts, by fitting mathematical models to data, is made difficult by the lack of measurements early in the infection. To determine the sensitivity of the parameter estimates to the noise in the data, we de...
Preprint
Determining accurate estimates for the characteristics of the severe acute respiratory syndrome coronavirus 2 in the upper and lower respiratory tracts, by fitting mathematical models to data, is made difficult by the lack of measurements early in the infection. To determine the sensitivity of viral predictions to the noise in the data, we develope...
Preprint
Full-text available
We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium solutions of nonlinear parabolic PDEs. The parameterization method provides an infinitesimal invariance equation...
Article
Full-text available
Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the...
Article
Full-text available
In this paper, we present a multi-scale co-affection model of HIV infection and opioid addiction. The population scale epidemiological model is linked to the within-host model which describes the HIV and opioid dynamics in a co-affected individual. CD4 cells and viral load data obtained from morphine addicted SIV-infected monkeys are used to valida...
Article
Full-text available
We propose two models inspired by the COVID-19 pandemic: a coupled disease-human behaviour (or disease-game theoretic), and a coupled disease-human behaviour-economic model, both of which account for the impact of social-distancing on disease control and economic growth. The models exhibit rich dynamical behaviour including multistable equilibria,...
Article
Full-text available
In this paper, we introduce three within-host and one within-vector models of Zika virus. The within-host models are the target cell limited model, the target cell limited model with natural killer (NK) cells class, and a within-host-within-fetus model of a pregnant individual. The within-vector model includes the Zika virus dynamics in the midgut...
Preprint
Full-text available
Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the...
Article
Full-text available
In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial di erential equation and obtain an explicit formula for the basic reproduction number R0. The diseases-free equilibrium i...
Preprint
In this paper, we introduce a SEIR type COVID-19 model where the infected class is further divided into subclasses with individuals in intensive care (ICUs) and ventilation units. The model is validated with the symptomatic COVID-19 cases, deaths, and the number of patients in ICUs and ventilation units as reported by Republic of Turkey, Ministry o...
Article
In this paper we formulate a multi-scale nested immuno-epidemiological model of HIV on complex networks. The system is described by ordinary differential equations coupled with a partial differential equation. First, we prove the existence and uniqueness of the immunological model and then establish the well-posedness of the multi-scale model. We d...
Article
Traditionally, the monolayer (two-dimensional) cell cultures are used for initial evaluation of the effectiveness of anticancer drugs. In particular, these experiments provide the \(\hbox {IC}_{50}\) curves that determine drug concentration that can inhibit growth of a tumor colony by half when compared to the cells grown with no exposure to the dr...
Preprint
Full-text available
Traditionally, the monolayer (two-dimensional) cell cultures are used for initial evaluation of the effectiveness of anticancer drugs. In particular, these experiments provide the IC50 curves that determine drug concentration that can inhibit growth of a tumor colony by half when compared to the cells grown with no exposure to the drug. Low IC50 va...
Article
Full-text available
A new method for approximating unstable manifolds for parabolic PDEs is introduced, which combines the parameterization method for invariant manifolds with finite element analysis and formal Taylor series expansions, and is applicable to problems posed on irregular spatial domains. The param-eterization method centers on an infinitesimal invariance...
Article
Full-text available
This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic...
Article
Full-text available
The largest outbreak of Ebola to date is the 2014 West Africa Ebola outbreak, with more than 10,000 cases and over 4000 deaths reported in Liberia alone. To control the spread of the outbreak, multiple interventions were implemented: identification and isolation of cases, contact tracing, quarantining of suspected contacts, proper personal protecti...
Article
The Zika virus (ZIKV) epidemic has caused an ongoing threat to global health security and spurred new investigations of the virus. Use of epidemiological models for arbovirus diseases can be a powerful tool to assist in prevention and control of the emerging disease. In this article, we introduce six models of ZIKV, beginning with a general vector-...
Research
Full-text available
Traditionally, the monolayer (two-dimensional) cell cultures are used for initial evaluation of the effectiveness of anticancer therapies. In particular, these experiments provide the IC50 curves that determine drug concentration that can inhibit growth of a tumor colony by half. The multicellular spheroid (three-dimensional) cultures have a histol...
Article
Full-text available
Leishmaniasis is a vector-borne disease of worldwide distribution, currently present in 98 countries. Since late 2010, an unusual increase of human visceral and cutaneous leishmaniasis cases has been observed in the south-western Madrid region, totaling more than 600 cases until 2015. Some hosts, such as human, domestic dog and cat, rabbit (Oryctol...
Data
Model of the leishmaniasis dynamic in dogs with and without insecticide impregnated collar. Legend: Vector: V1) Non infected, V2) Infected but not infective; V3) Infected and infective; Dogs: Sd) Susceptible; Ld) Latent with visceral leishmaniasis, Ad) Asymptomatic; Dd) Sick with visceral leishmaniasis; Rd) Recovered; Dogs with collar: Sdc) Suscept...
Data
Equations of dogs and vectors adapted for using vaccine and insecticide impregnated collar in dogs. (DOCX)
Article
Full-text available
Malaria is one of the most common mosquito-borne diseases widespread in the tropical and subtropical regions. Few models coupling the within-host malaria dynamics with the between-host mosquito-human dynamics have been developed. In this paper, by adopting the nested approach, a malaria transmission model with immune response of the host is formula...
Article
The focus of this article is to present the projected finite element method for solving systems of reaction-diffusion equations on evolving closed spheroidal surfaces with applications to pattern formation. The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discret...
Article
In this paper, we introduce a malaria model with an asymptomatic class in human population and exposed classes in both human and vector populations. The model assumes that asymptomatic individuals can get re-infected and move to the symptomatic class. In the case of an incomplete treatment, symptomatic individuals move to the asymptomatic class. If...
Chapter
Full-text available
This chapter introduces an avian influenza model which includes the dynamics of low pathogenic avian influenza (LPAI) and high pathogenic avian influenza (HPAI). The model structures the LPAI-recovered individuals by time-since-recovery and involves the crossimmunity that LPAI infection generates toward the HPAI. Reproduction numbers (R0LW, R0HW) a...
Article
Full-text available
Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host's immune system influence the pathogen's transmission potential between hosts via vectors. Yet there are few theoretical s...
Article
Full-text available
This paper introduces a time-since-recovery structured, multi-strain, multi-population model of avian influenza. Influenza A viruses infect many species of wild and domestic birds and are classified into two groups based on their ability to cause disease: low pathogenic avian influenza (LPAI) and high pathogenic avian influenza (HPAI). Prior infect...
Article
Full-text available
This paper investigates a two strain SIS model with diffusion, spatially heterogeneous coefficients of the reaction part and distinct diffusion rates of the separate epidemiological classes. First, it is shown that the model has bounded classical solutions. Next, it is established that the model with spatially homogeneous coefficients leads to comp...
Article
In this article, we discuss the structural and practical identifiability of a nested immuno-epidemiological model of arbovirus diseases, where host–vector transmission rate, host recovery, and disease-induced death rates are governed by the within-host immune system. We incorporate the newest ideas and the most up-to-date features of numerical meth...
Article
Full-text available
In this paper, we use a two-host one pathogen immuno-epidemiological model to argue that the principle for host evolution, when the host is subjected to a fatal disease, is minimization of the case fatality proportion F. This principle is valid whether the disease is chronic or leads to recovery. In the case of continuum of hosts, stratified by the...
Article
Full-text available
Biological processes occur at distinct but interlinked scalesof organization. Yet, mathematical models are often focused on a single scale. Recently, there has been a significant interest in creating and using models that link the within-host dynamics and population level dynamics of infectious diseases. These types of multi-scale models, called im...
Article
Full-text available
In this paper we present a robust, efficient and accurate finite element method for solving reaction-diffusion systems on stationary spheroidal surfaces (these are surfaces which are deformations of the sphere such as ellipsoids, dumbbells, and heart-shaped surfaces) with potential applications in the areas of developmental biology, cancer research...
Article
In this paper, the spatiotemporal patterns of a reaction-diffusion substrate-inhibition chemical Seelig model are considered. We first prove that this parabolic Seelig model has an invariant rectangle in the phase plane which attracts all the solutions of the model regardless of the initial values. Then, we consider the long time behaviors of the s...
Article
The highly pathogenic avian influenza (HPAI) strain H5N1, which first appeared in Hong Kong in 1997, achieved bird-to-human transmission, causing a severe disease with high mortality to humans [18]. According to the World Health Organization (WHO), a total of 637 cases were reported in fifteen countries, including 378 deaths, corresponding to a cas...
Article
Avian influenza H5N1 is at present the most dangerous zoonotic disease infecting wild and domestic birds. Should the virus mutate and become efficiently human-to-human transmittable, a pandemic will occur with high mortality. Avian influenza H5N1 exists in two forms: Low pathogenic (LPAI) and high pathogenic (HPAI). In this talk we build a model of...
Article
One of the main challenges in mathematical modeling of infectious diseases is to estimate the model parameters realistically. It is crucial to have accurate parameters in order to analyze the control strategies and to predict the outcome of the disease. In particular, the transmission rate of infectious diseases is very difficult to estimate. We pr...
Article
Full-text available
The number of cases of H5N1 avian influenza in birds and humans exhibit seasonality which peaks during the winter months. What causes the seasonality in H5N1 cases is still being investigated. This article addresses the question of modeling the periodicity in cumulative number of human cases of H5N1. Three potential drivers of influenza seasonality...
Article
This chapter introduces an avian influenza model which includes the dynamics of low pathogenic avian influenza (LPAI) and high pathogenic avian influenza (HPAI). The model structures the LPAI-recovered individuals by time-since-recovery and involves the cross-immunity that LPAI infection generates toward the HPAI. Reproduction numbers ( RLw0 ,RHw0...
Article
Full-text available
This article introduces a two-strain spatially explicit SIS epidemic model with space-dependent transmission parameters. We define reproduction numbers of the two strains, and show that the disease-free equilibrium will be globally stable if both reproduction numbers are below one. We also introduce the invasion numbers of the two strains which det...
Article
A nonlinear minimization problem ‖F(d)−u‖⟶min, ‖u−uδ‖≤δ, is a typical mathematical model of various applied inverse problems. In order to solve this problem numerically in the lack of regularity, we introduce iteratively regularized Gauss–Newton procedure with a nonlinear regularization term (IRGN–NRT). The new algorithm combines two very powerful...
Article
Full-text available
We describe and analyze a new finite element discretization for domains with spheroidal geometry. In particular, we describe how the method can be used to approximate solutions as well as eigenvalues and eigenfunctions of partial differential equations posed on the sphere, ellipsoidal shells, and cylindrical shells. These novel, so-called “radially...
Article
The estimates for the number of operations needed to implement two different iteratively regularized Gauss-Newton methods as well as the iteratively regularized gradient scheme are given. The operation count is illustrated by simulations for a two dimensional version of the exponentially ill-posed optical tomography inverse problem for the diffusio...
Article
We are concerned with the linear singular two-point boundary value problem (x α y ' (x)) ' =f(x),y(0)=a,y(1)=b, where 0<α<1. We use the linear shooting method on equidistant meshes to approximate the solution and the convergence is accelerated by means of extrapolation methods. Numerical results are presented for different cases of α.
Article
The convergence properties of q-Bernstein polynomials are investigated. When q⩾1 is fixed the generalized Bernstein polynomials nf of f, a one parameter family of Bernstein polynomials, converge to f as n→∞ if f is a polynomial. It is proved that, if the parameter 0<q<1 is fixed, then nf→f if and only if f is linear. The iterates of nf are also con...
Article
Full-text available
We discuss here recent developments on the convergence of the q-Bernstein polynomials B(sub n)f which replaces the classical Bernstein polynomial with a one parameter family of polynomials. In addition, the convergence of iterates and iterated Boolean sum of q-Bernstein polynomial will be considered. Moreover a q-difference operator D(sub q)f defin...

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Projects

Projects (4)
Archived project
Create usable models for avian influenza