Thomas Goetz

• Dr. rer. nat.
• Professor at University Koblenz

Robots are increasingly being used across various sectors, from industry and healthcare to household applications. In practice, a pivotal challenge is the reaction to unexpected external disturbances, whose real-time feedback often relies on (noisy) sensor measurements. Subsequent inverse-dynamics calculations demand noise-amplifying numerical diff...

In this paper, we extend the classical SIRS (Susceptible-Infectious-Recovered-Susceptible) model from mathematical epidemiology by incorporating a vaccinated compartment, V, accounting for an imperfect vaccine with waning efficacy over time. The SIRSV-model divides the population into four compartments and introduces periodic re-vaccination for wan...

During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article explores one among the many possibilities of a coupled opinion-epidemic system. The findings reveal either intric...

During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article explores one among the many possibilities of coupled opinion–epidemic systems. The findings reveal either intrica...

In this study, we focus on modeling the local spread of COVID-19 infections. As the pandemic continues and new variants or future pandemics can emerge, modelling the early stages of infection spread becomes crucial, especially as limited medical data might be available initially. Therefore, our aim is to gain a better understanding of the diffusion...

In this study, we present an integro-differential model to simulate the local spread of infections. The model incorporates a standard susceptible-infected-recovered (\textit{SIR}-) model enhanced by an integral kernel, allowing for non-homogeneous mixing between susceptibles and infectives. We define requirements for the kernel function and derive...

In this study, we present an integro-differential model to simulate the local spread of infections. The model incorporates a standard susceptible-infected-recovered (\textit{SIR}-) model enhanced by an integral kernel, allowing for non-homogeneous mixing between susceptibles and infectives. We define requirements for the kernel function and derive...

The study of the spread of epidemics has gained significant attention in recent years, due to ongoing and recurring outbreaks of diseases such as COVID‐19, dengue, Ebola, and West Nile virus. In particular, modeling the spatial spread of these epidemics is crucial. This article explores the use of fractional diffusion as a means of describing non‐l...

Households play an important role in disease dynamics. Many infections happening there due to the close contact, while mitigation measures mainly target the transmission between households. Therefore, one can see households as boosting the transmission depending on household size. To study the effect of household size and size distribution, we diff...

The current pandemic situation due to COVID-19 demonstrates the need for epidemiologic models to represent infection events as accurately as possible. An important factor is the mobility of the affected individuals which can be investigated with discrete or continuous spatial models. In this contribution, parameter estimation via adjoint functions...

Dengue is the most critical mosquito-borne viral disease that has rapidly spread within recent years. Understanding of the seasonal pattern of dengue cases and relationship with climate data could be useful in deciding control mechanisms. In this study, monthly dengue cases, average rainfall data, average temperature data and relative humidity data...

Background COVID-19 continues to disrupt social lives and the economy of many countries and challenges their healthcare capacities. Looking back at the situation in Germany in 2020, the number of cases increased exponentially in early March. Social restrictions were imposed by closing e.g. schools, shops, cafés and restaurants, as well as borders f...

The Covid-19 pandemic has spread across the world at a rate never seen before, affecting different countries and having a huge impact not only on health care systems but also on economic systems. Never as in this situation the continuous exchange of views between scientists of different disciplines must be considered the keystone to overcome this e...

The Covid-19 pandemic has spread across the world at a rate never seen before, affecting different countries and having a huge impact not only on health care systems but also on economic systems. Never as in this situation the continuous exchange of views between scientists of different disciplines must be considered the keystone to overcome this e...

An epidemic model where disease transmission can occur either through global contacts or through local, nearest neighbor interactions is considered. The classical SIR--model describing the global interactions is extended by adding additional equations for the density of local pairs in different epidemic states. A locality parameter $p\in [0,1]$ cha...

The primary goal of this paper is to model and study the behavior of ellipsoidal microplastic particles in a 3D lid-driven cavity. An Eulerian equation for the hydrodynamics is solved toward stationarity under the Reynolds number 1000 and coupled with a Lagrangian system governing the particle dynamics. The key points of departure in the modeling a...

At the end of 2019, an outbreak of a new coronavirus, called SARS–CoV–2, was reported in China and later in other parts of the world. First infection reported in Germany by the end of January 2020 and on March 16th, 2020 the federal government announced a partial lockdown in order to mitigate the spread. Since the dynamics of new infections started...

This paper stresses its base contribution on a new SIR-type model including direct and fomite transmission as well as the effect of distinct household structures. The model derivation is modulated by several mechanistic processes inherent from typical airborne diseases. The notion of minimum contact radius is included in the direct transmission, fa...

Models and Parameter Estimation of COVID-19 in Germany (March-May 2020)

In this article, we combine a multipatch SIRUV model with seasonal mosquito breeding rate in order to develop a seasonal SIR model via a time-scale separation. The model is applied to commuting and dengue incident data in Jakarta to forecast dengue outbreaks. Qualitatively, the analysis is in good agreement with the actual outbreaks.

Vector-borne diseases can usually be examined with a vector–host model like the [Formula: see text] model. This, however, depends on parameters that contain detailed information about the mosquito population that we usually do not know. For this reason, in this article, we reduce the [Formula: see text] model to an [Formula: see text] model with a...

COVID–19 continues to disrupt social lives and the economy of many countries and challenges their healthcare capacities. In Germany, the number of cases increased exponentially in early March 2020. As a political reaction, social restrictions were imposed by closing e.g. schools, shops, cafés and restaurants, as well as borders for travellers. This...

Background COVID–19 continues to disrupt social lives and the economy of many countries and challenges their healthcare capacities. InGermany, the number of cases increased exponentially in early March 2020. As a political reaction, social restrictions wereimposed by closing e.g. schools, shops, cafés and restaurants, as well as borders for travell...

Microplastic in freshwater has been known to absorb, adsorb, and later desorb persistent organic pollutants as well as in its tiny size acts as an infiltrator to vital tissues; it may therefore corrupt physiological processes of organic lives. The fate of microplastic particles can be understood by revealing to what extent certain material properti...

The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum...

Currently, due to the COVID-19 pandemic the public life in most European countries stopped almost completely due to measures against the spread of the virus. Efforts to limit the number of new infections are threatened by the advent of new variants of the SARS-COV-2 virus, most prominent the B.1.1.7 strain with higher infectivity. In this article w...

A time-dependent predator-prey system is introduced where food sharing among predators leads to a dynamically stable endemic. The predator population is split into the adult and juvenile sub-population. Food sharing refers to the process in which food is delivered from adults to juveniles. The populations differ in their ability to procure food and...

Together with emerging infectious diseases, dengue fever continues to ravage tropical and subtropical countries amidst weak health systems. Vertical and sexual transmission have been shown to exhibit synergism in the endemic maintenance during inter-epidemics. This work presents a SISUV model modulating horizontal transmission, also vertical and se...

Medical statistics reveal a significant dependence of hospitalized dengue patients on their age. We extend an ODE system governing dengue epidemics to a hyperbolic PDE system to incorporate age dependence. The equilibrium distributions are determined by the fixed points of the resulting integro-differential equation. The basic reproductive number i...

Abstract Since the end of 2019 an outbreak of a new strain of coronavirus, called SARS-CoV-2, is reported from China and later other parts of the world. Since January 21, World Health Organization (WHO) reports daily data on confirmed cases and deaths from both China and other countries ( www.who.int/emergencies/diseases/novel-coronavirus-2019/situ...

Since the beginning of the corona pandemic in March 2020, various parameters for describing the spread of the disease have been specified for Germany in addition to the daily infection figures (new infections and total infections), which are also used for political decisions. In addition to excess mortality and the weekly incidence, these include t...

The maximum running speed of legged animals is one evident factor for evolutionary selection—for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum...

At the end of 2019, an outbreak of a new coronavirus, called SARS-CoV-2, was reported in China and later in other parts of the world. First infections were reported in Germany by the end of January and on March 16th the federal government announced a partial lockdown in order to mitigate the spread. Since the dynamics of new infections started to s...

At the end of 2019, an outbreak of a new coronavirus, called SARS--CoV--2, was reported in China and later in other parts of the world. First infections were reported in Germany by the end of January and on March 16th the federal government announced a partial lockdown in order to mitigate the spread. Since the dynamics of new infections started to...

Since the end of 2019 an outbreak of a new strain of coronavirus, called SARS--CoV--2, is reported from China and later also from other parts of the world. Since 21 January 2020, World Health Organization (WHO) reports daily data on confirmed cases and deaths from both China and other countries~\cite{WHO20}. The Johns Hopkins University~\cite{CSSE}...

The benefits of optimization-based modeling for parameter estimation of Hill-type muscle models are demonstrated. Therefore, we examined the model and data of Günther et al. (2007), who analyzed isometric, concentric, and quick-release contractions of a piglet calf muscle. We found that the isometric experiments are suitable for derivative-based pa...

This article thematizes the qualitative estimation of transmission dynamics of Dengue fever. At first, a single-compartment vector-host model for the total infective cases in one homogeneous area has been set up and simplified using a steady-state approximation. Seasonality has been considered in the transmission parameter which is modelled by a Fo...

In this paper, we developed a mathematical model for the sedimentation process of small particles in a lid-driven cavity flow with an obstacle to model the transport of microplastic particles in rivers. A stationary incompressible Navier-Stokes simulation at moderate Reynolds-numbers provides the background flow field. Spherical particles are injec...

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diph...

This paper stresses its base contribution on a new SIR-type model for COVID-19 including direct and fomite transmission as well as the effect of distinct household structures. To what extent increasing the physical-distancing-related contact radius and enhancing mass control (public curfew, lockdown, workplace clearance, and school closure) reduce...

Since the end of 2019 an outbreak of a new strain of coronavirus, called SARS– CoV–2, is reported from China and later other parts of the world. Since January 21, WHO reports daily data on confirmed cases and deaths from both China and other countries [1]. The Johns Hopkins University [5] collects those data from various sources worldwide on a dail...

On the basis of a semi-realistic SIR microsimulation for Germany and Poland, we show that the R 0 parameter interval for which the COVID-19 epidemic stays overcritical but below the capacity limit of the health care system to reach herd immunity is so narrow that a successful implementation of this strategy is likely to fail. Our microsimulation is...

Since the end of 2019 an outbreak of a new strain of coronavirus, called 2019--nCoV, is reported from China and later other parts of the world. Since January 21, WHO reports daily data on confirmed cases and deaths from both China and other countries. In this work we present some discrete and continuous models to discribe the disease dynamics in Ch...

Medical statistics reveal a significant dependence of hospitalized dengue patient on the patient's age. To incorporate an age-dependence into a mathematical model, we extend the classical ODE system of disease dynamics to a PDE system. The equilibrium distribution is then determined by the fixed points of resulting integro-differential equations. I...

In this article, we combine a multipatch SIRUV model with seasonal mosquito breeding rate in order to develop a seasonal SIR model via a timescale separation. The model is applied to commuting and dengue incident data in Jakarta to forecast dengue outbreaks

Dengue incidence has been increasing dramatically in last few years with nearly four hundred million annual cases worldwide. It has been postulated that the wide-spread of dengue be due to climate change and increased exposure following the increasing human population in the affected regions. Climate change impacts on ecosystem have also set a crit...

Vector control is regarded an efficient approach for preventing and reducing the spread of malaria. For several decades, insecticides have been used to suppress the population of Anopheles mosquitoes throughout the globe. It turns out that continual usage of a single compounded insecticide has massively contributed to the rise of resistant mosquito...

In this paper we investigate the parameter estimation of the fiber lay-down process in the production of nonwovens. The parameter estimation is based on the mass per unit area data, which is available at least on an industrial scale. We introduce a stochastic model to represent the fiber lay-down and through the model's parameters we characterize t...

There are nowadays a huge load of publications about dengue epidemic models, which mostly employ deterministic differential equations. The analytical properties of deterministic models are always of particular interest by many experts, but their validity - if they can indeed track some empirical data - is an increasing demand by many practitioners....

There are nowadays a huge load of publications about dengue epidemic models, which mostly employ deterministic differential equations. The analytical properties of deterministic models are always of particular interest by many experts, but their validity - if they can indeed track some empirical data - is an increasing demand by many practitioners....

[This corrects the article DOI: 10.1155/2015/585409.].

Equilibrium analysis in autonomous evolutionary models is of central importance for developing long term treatments. This task typically includes checks on the existence and stability of some equilibria. Prior to touching on the stability, one often attempts to determine the existence where the basic reproductive number ℛ0 plays a critical role as...

In recent decades, Dengue fever and its deadly complications, such as Dengue hemorrhagic fever, have become one of the major mosquito-transmitted diseases, with an estimate of 390 million cases occurring annually in over 100 tropical and subtropical countries, most of which belonging to the developing world. Empirical evidence indicates that the mo...

The Strategic Partnership for the Development of Training Workshops and Modeling Clinic for In- dustrial Mathematics (acronym MODCLIM) is a strategic partnership for higher education project, approved in 2014 by Erasmus+ program, Key Action 2: Cooperation for innovation and the exchange of good practices. MODCLIM develops a project focused on math...

Dengue fever is a viral mosquito-borne infection which in recent years has become a major international public health concern, a leading cause of illness and death in tropical and subtropical regions. Models from mathematical epidemiology, like the classical SIR-model and its variants, are used to describe the spread of dengue in a given population...

Optimization problems, e.g. arising from epidemiology models, often ask for solutions minimizing multi-criteria objective functions. In this paper we discuss a novel approach for solving bi–objective optimal control problems. The set of non–dominated points is constructed via a decreasing sequence of rectangles. Particular attention is paid to a pr...

We model the connectivity between Thai provinces in terms of human mobility via a radiation model in order to describe dengue fever spreading in Thailand, for which long term epidemiological data are available.

We mathematically compared two models of mammalian striated muscle activation dynamics proposed by Hatze and Zajac. Both models are representative for a broad variety of biomechanical models formulated as ordinary differential equations (ODEs). These models incorporate parameters that directly represent known physiological properties. Other paramet...

Reduced one-dimensional equations for the stationary, isothermal rotational spinning process of slender fibers are considered for the case of large Reynolds ($\delta=3/\text{Re}\ll 1$) and small Rossby numbers ($\varepsilon \ll 1$). Surface tension is included in the model using the parameter $\kappa=\sqrt{\pi}/(2 \text{We})$ related to the inverse...

Mathematical simulations are of increasing relevance for applications in engineering and the life sciences. Disciplines like epidemiology, biomechanics, medical image processing, just to name a few, are subject of academic research since decades. With modern numerical methods and the advent of increasing computing power not just simulations of biol...

It is preliminarily known that Aedes mosquitoes are very close to humans and their dwellings, also give rises to a broad spectrum of diseases: dengue, yellow fever, chikungunya. In this paper, we explore a multi-age-class model for mosquito population secondarily classi- fied into indoor-outdoor dynamics. We accentuate a novel design for the model...

Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies

In this paper, we mathematically compared two models of mammalian striated muscle activation dynamics proposed by Hatze and Zajac. Both models are representative of a broad variety of biomechanical models formulated as ordinary differential equations (ODEs). The models incorporate some parameters that directly represent known physiological properti...

Aedes aegypti is known as the responsible vector in transmitting dengue flavivirus. Unavailability of medication to cure the transmission in human blood becomes a global health issue in recent decades. World epidemiologists are encouraged to focus on investigation toward an effective and inexpensive way to prevent dengue transmission, i.e. mosquito...

Modellierungsveranstaltungen am Fachbereich Mathematik der TU Kaiserslautern haben eine lange Tradition. Seit Mitte der 1980er Jahre werden regelmäßig Modellierungsseminare für Studierende im Grund- sowie Hauptstudium angeboten. Als Gründungsmitglied des ECMI (European Consortium for Mathematics in Industry) veranstaltet der Fachbereich Mathematik...

An optimal control model of Aedes aegypti population dynamics concerning classification of indoor-outdoor life cycles is taken into account in this paper. A dengue epidemics measure, the basic mosquito offspring, is obtained from the well-known next-generation matrix. The number is used to analyse the stability of the mosquito-free equilibrium. Thi...

An optimal control problem for a host-vector Dengue transmission model is discussed here. In the model, treatments with mosquito repellent are given to adults and children and those who undergo treatment are classified in treated compartments. With this classification, the model consists of eleven dynamic equations. The basic reproductive ratio tha...

The stationary, isothermal rotational spinning process of fibers is considered. The investigations are concerned with the case of large Reynolds (δ = 3/Re ≪ 1) and small Rossby numbers (ε ≪ 1). Modelling the fibers as a Newtonian fluid and applying slender body approximations, the process is described by a two-point boundary value problem of ODEs....

We derive an equation to compute directly the expected occupation time of the centered Ornstein-Uhlenbeck process. This allows us to identify the parameters of the Ornstein-Uhlenbeck process for available occupation times via a standard least squares minimization. To test the method, we generate occupation times via Monte-Carlo simulations and reco...

A mathematical model describing the melt spinning process of polymer fibers is considered. Newtonian and non-Newtonian models are used to describe the rheology of the polymeric material. Two key questions related to the industrial application of melt spinning are considered: the optimization and the stability of the process. Concerning the optimiza...

An optimal-control problem for a mathematical model of a melt-spinning process is considered. Newtonian models with constant viscosity and temperature-dependent viscosity are used to describe the rheology of the polymeric material, the fiber is made of. The extrusion velocity of the polymer at the spinneret, as well as the velocity and temperature...

We present an optimal control approach for the isothermal film casting process with free surfaces described by averaged Navier–Stokes equations. We control the thickness of the film at the take-up point using the shape of the nozzle and the initial thickness. The control goal consists in finding an even thickness profile.

We investigate the stability of the melt spinning process with respect to variations of external parameters such as the velocity and temperature of the quench air. Newtonian and non-Newtonian models are used to describe the rheology of the polymer the fiber is made of. The critical draw ratio, indicating the onset of instabilities, is computed nume...

We consider an isothermal model for the film casting process. The aim of this study is to determine a shape of the die that leads to a uniform thickness of the film. Thanks to a decoupling of the equations for the thickness and the velocities of the film, we are able to solve the reverse thickness equation. This reverse equation describes the depen...

AIP Conference Proceedings 1168(1), 1046 (2009) DOI: http://doi.org/10.1063/1.3241230

We present an optimal control approach for the isothermal film casting process with free surfaces described by averaged Navier–Stokes equations. We control the thickness of the film at the take-up point using the shape of the nozzle and the initial thickness. The control goal consists in finding an even thickness profile. To achieve this goal, we m...

We consider a model for the production of glass fibers in a rotating spinning device. The model depends on two small parameters, namely the Reynolds-number δ and the Rossby-number ε. For small Rossby-numbers, i.e., a fast rotating spinning drum, numerical difficulties arise. To overcome this problems, asymptotic expansions are carried out for the s...

Nowadays artificial fibres made of polymers or glass are of increasing industrial importance. Worldwide a total amount of 37.9 million tons of chemical fibres was produced in 2004 and the production still increases by around 5% annually.

We consider the convection-diffusion process of charged particles in a fluid which is described by the Navier-Stokes equations. Assuming a Hagen-Poiseuille flow profile, a one-dimensional. model is derived. For stationary cases, the positivity of the concentrations is proven. Unique equilibrium solutions are shown to exist for a certain range of Di...

A stochastic model for the turbulent fiber lay-down in the industrial production of nonwoven materials is extended by including a moving conveyor belt. In the hydrodynamic limit corresponding to large noise values, the transient and stationary joint probability distributions are determined using the method of multiple scales and the Chapman-Enskog...

We present and investigate a stochastic model and its associated Fokker-Planck equation for the lay-down of fibers on a conveyor belt in the production process of nonwoven materials. The model is based on a stochastic differential equation taking into account the motion of the fiber under the influence of turbulence. A reformulation as a stochastic...

In this paper an optimal control problem for polymer crystallization is investigated. The crystallization is described by a non–isothermal Avrami–Kolmogorov model. The boundary temperature serves as control variable. The cost functional takes the spatial variation of the crystallinity and the final degree of crystallization into account. The result...

In this paper an optimal control problem for polymer crystallization is investigated. The crystallization is described by a non-isothermal Avrami–Kolmogorov model and the temperature at the boundary of the domain serves as control variable. The cost functional takes into account the spatial variation of the crystallinity and the final degree of cry...

In this paper an optimal control problem for polymer crystallization is investigated. The crystallization is described by a non–isothermal Avrami–Kolmogorov model. The boundary temperature serves as control variable. The cost functional takes the spatial variation of the crystallinity and the final degree of crystallization into account. The result...

The oscillatory flow of a viscoelastic fluid in a circular pipe under the influence of a transversal magnetic field is studied. Exact solutions for the axial velocity and flow rate are presented. The velocity enhancement and the resonance behaviour are analysed both numerically and asymptotically in the case of small pipe radii. Approximations for...

Recently, Burger and Capasso [1]derived a coupled system of partial differential equations to describe nonisothermal crystallization of polymers. The system is based on a spatial averaging of the underlying stochastic birth-and-growth process describing the nucleation and growth of single crystals. In the present work, we reconsider the scaling pro...

Porous-media flow of polymers with Carreau-law viscosities and their application to enhanced oil recovery (EOR) is considered. Applying the homogenization method leads to a nonlinear two-scale problem. In case of a small difference between the Carreau and the Newtonian case an asymptotic expansion based on the small deviation of the viscosity from...

We consider low-Reynolds number flow past an ensemble of particles. The singularity method is applied to represent the flow field. The strength and positions of the poles of the fundamental solution are obtained by minimizing the L2-error in the boundary conditions. Numerical simulations are carried out for ensembles of spheres immersed in a unifor...

Recently, Burger and Capasso [M AS 11 (2001) 1029--1053] derived a coupled system of partial di#erential equations to describe non--isothermal crystallization of polymers. The system is based on a spatial averaging of the underlying stochastic birth--and--growth process describing the nucleation and growth of single crystals. In the present work we...

Simplified PN (SPN) approximations to the equations of radiative heat transfer are derived for optically thick, diffusive systems, and appropriate boundary conditions are formulated. The SPN equations are derived by an asymptotic analysis, while the boundary conditions are obtained from a variational analysis. Numerical comparisons of the SPN, equi...

A collocation method is presented for solving a singular integral equation of the second kind arsing in the slender-body approximation of viscous flow past slender bodies. When the spectral representation of the integral operator is explicitly known, the collocation method is shown to recover the spectrum of the continuous operator. The approximati...

In this paper, we discuss numerical and analytical approximations of radiative heat transfer equations used to model cooling processes of molten glass. Simplified diffusion type approximations are discussed and investigated numerically. These approximations are also used to develop acceleration methods for the iterative solution of the full radiati...

A method to compute combined heat conduction and radiative transfer in a semitransparent medium is proposed. The heat equation is solved by an implicit finite-difference scheme and the radiation is simulated using a ray-tracing method. Stability and convergence for the coupling of both methods is shown. The crucial point for ray-tracing as well as...

An asymptotic method to determine the air-flow around slender fibers in the case of low Reynolds numbers is presented. Based on the equations for linearized flow, the force acting on a fiber is approximated as the superposition of fundamental solutions. Matching asymptotic expansions valid in different regions of the flow field leads to an integral...