@misc{BestehornBestehornMichelitschetal., author = {Bestehorn, Michael and Bestehorn, Michael and Michelitsch, Thomas M. and Collet, Bernard A. and Riascos, Alejandro P. and Nowakowski, Andrzej. F.}, title = {Simple model of epidemic dynamics with memory effects}, series = {Physical Review E}, volume = {105}, journal = {Physical Review E}, number = {2}, issn = {2470-0045}, doi = {10.1103/PhysRevE.105.024205}, pages = {024205-1 -- 024205-10}, abstract = {We introduce a compartment model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states S=susceptible, I=infected, or R=recovered (SIR model). In state R an individual is assumed to stay immune within a finite-time interval. In the first part, we introduce a random lifetime or duration of immunity which is drawn from a certain probability density function. Once the time of immunity is elapsed an individual makes an instantaneous transition to the susceptible state. By introducing a random duration of immunity a memory effect is introduced into the process which crucially determines the epidemic dynamics. In the second part, we investigate the influence of the memory effect on the space-time dynamics of the epidemic spreading by implementing this approach into computer simulations and employ a multiple random walker's model. If a susceptible walker meets an infectious one on the same site, then the susceptible one gets infected with a certain probability. The computer experiments allow us to identify relevant parameters for spread or extinction of an epidemic. In both parts, the finite duration of immunity causes persistent oscillations in the number of infected individuals with ongoing epidemic activity preventing the system from relaxation to a steady state solution. Such oscillatory behavior is supported by real-life observations and not captured by the classical standard SIR model.}, language = {en} } @article{BestehornFantzFriedrichetal., author = {Bestehorn, Michael and Fantz, M. and Friedrich, R. and Haken, H. and P{\´e}rez-Garc{\´i}a, C.}, title = {Spiral Patterns in Thermal Convection}, language = {en} } @article{BestehornFantzFriedrichetal., author = {Bestehorn, Michael and Fantz, M. and Friedrich, R. and Haken, H.}, title = {Pattern formation in rotating B{\´e}nard convection}, language = {en} } @inproceedings{VaerenberghLegrosColinetetal., author = {Vaerenbergh, S. van and Legros, J. C. and Colinet, P. and Velarde, M. G. and Bestehorn, Michael and Lebon, G. and Thess, A. and Karcher, C.}, title = {Processes With Double Diffusive Instabilities Studied in Microgravity}, series = {The 2nd European Symposium on Utilisation of the International Space Station, 16 - 18 November 1998, ESTEC, Noordwijk, The Netherlands}, booktitle = {The 2nd European Symposium on Utilisation of the International Space Station, 16 - 18 November 1998, ESTEC, Noordwijk, The Netherlands}, publisher = {ESA Publ.}, address = {Noordwijk}, isbn = {92-9092-732-1}, pages = {241 -- 248}, language = {en} } @article{BestehornFantzFriedrichetal., author = {Bestehorn, Michael and Fantz, M. and Friedrich, R. and Haken, H.}, title = {Hexagonal and Spiral Patterns of Thermal Convection}, language = {en} } @article{BestehornNeufeldFriedrichetal., author = {Bestehorn, Michael and Neufeld, M. and Friedrich, R. and Haken, H.}, title = {Pattern formation in rotating B{\´e}nard convection}, language = {en} } @article{ThieleVelardeNeufferetal., author = {Thiele, Uwe and Velarde, M. G. and Neuffer, Kai and Bestehorn, Michael and Pomeau, Y.}, title = {Sliding drops in the diffusive interface model coupled to hydrodynamics}, series = {Physical Review E}, volume = {64}, journal = {Physical Review E}, number = {4}, issn = {1550-2376}, pages = {061601}, language = {en} } @article{ThieleNeufferBestehornetal., author = {Thiele, Uwe and Neuffer, Kai and Bestehorn, Michael and Pomeau, Y. and Velarde, M. G.}, title = {Sliding drops on an inclined plane}, series = {Colloids and Surfaces A}, volume = {206}, journal = {Colloids and Surfaces A}, number = {1-3}, pages = {87 -- 104}, language = {en} } @article{MillanRodriguezPerezGarciaBestehornetal., author = {Mill{\´a}n-Rodriguez, J. and P{\´e}rez-Garc{\´i}a, C. and Bestehorn, Michael and Fantz, M. and Friedrich, R.}, title = {Pattern Formation in Convection of Rotating Fluids with Broken Vertical Symmetry}, language = {en} } @article{MillanRodriguezBestehornPerezGarciaetal., author = {Mill{\´a}n-Rodriguez, J. and Bestehorn, Michael and P{\´e}rez-Garc{\´i}a, C. and Friedrich, R. and Neufeld, M.}, title = {Defects Motion in Rotating Fluids}, language = {en} } @article{MillanRodriguezBestehornPerezGarciaetal., author = {Mill{\´a}n-Rodriguez, J. and Bestehorn, Michael and P{\´e}rez-Garc{\´i}a, C. and Neufeld, M. and Friedrich, R.}, title = {Motion of Defects in Rotating Fluids}, language = {en} } @article{BestehornNeufeldFriedrichetal., author = {Bestehorn, Michael and Neufeld, M. and Friedrich, R. and Haken, H.}, title = {Comment on Spiral pattern formation in Rayleigh-B{\´e}nard Convection}, language = {en} } @misc{BestehornTyvandMichelitsch, author = {Bestehorn, Michael and Tyvand, Peder A. and Michelitsch, Thomas M.}, title = {Dimension-Reduced Model for Deep-Water Waves}, series = {Journal of Applied Mathematics and Physics}, volume = {7}, journal = {Journal of Applied Mathematics and Physics}, number = {1}, issn = {2327-4379}, doi = {10.4236/jamp.2019.71007}, pages = {72 -- 92}, abstract = {Starting from the 2D Euler equations for an incompressible potential flow, a dimension-reduced model describing deep-water surface waves is derived. Similar to the Shallow-Water case, the z-dependence of the dependent variables is found explicitly from the Laplace equation and a set of two one- dimensional equations in x for the surface velocity and the surface elevation remains. The model is nonlocal and can be formulated in conservative form, describing waves over an infinitely deep layer. Finally, numerical solutions are presented for several initial conditions. The side-band instability of Stokes waves and stable envelope solitons are obtained in agreement with other work. The conservation of the total energy is checked.}, language = {en} } @misc{GrangerMichelitschBestehornetal., author = {Granger, T{\´e}o and Michelitsch, Thomas M. and Bestehorn, Michael and Riascos, Alejandro P. and Collet, Bernard A.}, title = {Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks}, series = {Entropy}, volume = {26}, journal = {Entropy}, number = {5}, issn = {1099-4300}, doi = {10.3390/e26050362}, abstract = {We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barab{\´a}si-Albert (BA), Erd{\"o}s-R{\´e}nyi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0with and without mortality, respectively, and prove that RM1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.}, language = {en} } @misc{GrangerMichelitschBestehornetal., author = {Granger, T{\´e}o and Michelitsch, Thomas M. and Bestehorn, Michael and Riascos, Alejandro P. and Collet, Bernard A.}, title = {Four-compartment epidemic model with retarded transition rates}, series = {Physical Review E}, volume = {107}, journal = {Physical Review E}, number = {4}, issn = {2470-0045}, doi = {10.1103/PhysRevE.107.044207}, pages = {044207-1 -- 044207-15}, abstract = {We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the following compartments: susceptible S; incubated, i.e., infected yet not infectious, C; infected and infectious I; and recovered, i.e., immune, R. An infection is visible only when an individual is in state I. Upon infection, an individual performs the transition pathway S→C→I→R→S, remaining in compartments C, I, and R for a certain random waiting time tC, tI, and tR, respectively. The waiting times for each compartment are independent and drawn from specific probability density functions (PDFs) introducing memory into the model. The first part of the paper is devoted to the macroscopic S-C-I-R-S model. We derive memory evolution equations involving convolutions (time derivatives of general fractional type). We consider several cases. The memoryless case is represented by exponentially distributed waiting times. Cases of long waiting times with fat-tailed waiting-time distributions are considered as well where the S-C-I-R-S evolution equations take the form of time-fractional ordinary differential equations. We obtain formulas for the endemic equilibrium and a condition of its existence for cases when the waiting-time PDFs have existing means. We analyze the stability of healthy and endemic equilibria and derive conditions for which the endemic state becomes oscillatory (Hopf) unstable. In the second part, we implement a simple multiple-random-walker approach (microscopic model of Brownian motion of Z independent walkers) with random S-C-I-R-S waiting times in computer simulations. Infections occur with a certain probability by collisions of walkers in compartments I and S. We compare the endemic states predicted in the macroscopic model with the numerical results of the simulations and find accordance of high accuracy. We conclude that a simple random-walker approach offers an appropriate microscopic description for the macroscopic model. The S-C-I-R-S-type models open a wide field of applications allowing the identification of pertinent parameters governing the phenomenology of epidemic dynamics such as extinction, convergence to a stable endemic equilibrium, or persistent oscillatory behavior.}, language = {en} } @misc{BestehornRiascosMichelitschetal., author = {Bestehorn, Michael and Riascos, Alejandro P. and Michelitsch, Thomas M. and Collet, Bernard A.}, title = {A Markovian random walk model of epidemic spreading}, series = {Continuum Mechanics and Thermodynamics}, volume = {33}, journal = {Continuum Mechanics and Thermodynamics}, number = {4}, issn = {1432-0959}, doi = {10.1007/s00161-021-00970-z}, pages = {1207 -- 1221}, abstract = {We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time Markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then, we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on the same node, there is a certain probability for the susceptible walker to get infected. By implementing this hypothesis in computer simulations, we study the space-time evolution of the emerging infection patterns. Generally, random walk approaches seem to have a large potential to study epidemic spreading and to identify the pertinent parameters in epidemic dynamics.}, language = {en} } @misc{BestehornMichelitsch, author = {Bestehorn, Michael and Michelitsch, Thomas M.}, title = {Oscillating Behavior of a Compartmental Model with Retarded Noisy Dynamic Infection Rate}, series = {International Journal of Bifurcation and Chaos}, volume = {33}, journal = {International Journal of Bifurcation and Chaos}, number = {5}, issn = {1793-6551}, doi = {10.1142/S0218127423500566}, abstract = {Our study is based on an epidemiological compartmental model, the SIRS model. In the SIRS model, each individual is in one of the states susceptible (S), infected (I) or recovered (R), depending on its state of health. In compartment R, an individual is assumed to stay immune within a finite time interval only and then transfers back to the S compartment. We extend the model and allow for a feedback control of the infection rate by mitigation measures which are related to the number of infections. A finite response time of the feedback mechanism is supposed that changes the low-dimensional SIRS model into an infinite-dimensional set of integro-differential (delay-differential) equations. It turns out that the retarded feedback renders the originally stable endemic equilibrium of SIRS (stable focus) to an unstable focus if the delay exceeds a certain critical value. Nonlinear solutions show persistent regular oscillations of the number of infected and susceptible individuals. In the last part we include noise effects from the environment and allow for a fluctuating infection rate. This results in multiplicative noise terms and our model turns into a set of stochastic nonlinear integro-differential equations. Numerical solutions reveal an irregular behavior of repeated disease outbreaks in the form of infection waves with a variety of frequencies and amplitudes.}, language = {en} } @misc{HarlanderSchoenBorciaetal., author = {Harlander, U. and Sch{\"o}n, F.-T. and Borcia, I. D. and Richter, S. and Borcia, R. and Bestehorn, M.}, title = {Resonant water-waves in ducts with different geometries: forced KdV solutions}, series = {European Journal of Mechanics - B/Fluids}, volume = {106}, journal = {European Journal of Mechanics - B/Fluids}, number = {July-August 2024}, issn = {0997-7546}, doi = {10.1016/j.euromechflu.2024.03.008}, pages = {107 -- 115}, language = {en} } @misc{BorciaBestehornBorciaetal., author = {Borcia, I. D. and Bestehorn, M. and Borcia, R. and Sch{\"o}n, F.-T. and Harlander, U. and Richter, S.}, title = {Mean flow generated by asymmetric periodic excitation in an annular channel}, series = {The European Physical Journal Special Topics}, volume = {233 (2024)}, journal = {The European Physical Journal Special Topics}, publisher = {Springer}, doi = {10.1140/epjs/s11734-024-01181-8}, pages = {1665 -- 1672}, language = {en} } @misc{SchoenBorciaHarlanderetal., author = {Sch{\"o}n, F.-T. and Borcia, I. D. and Harlander, U. and Borcia, R. and Richter, S. and Bestehorn, M.}, title = {Resonant surface waves in an oscillating periodic tank with a submerged hill}, series = {Journal of Fluid Mechanics}, volume = {999 (2024)}, journal = {Journal of Fluid Mechanics}, doi = {10.1017/jfm.2024.885}, pages = {1 -- 18}, language = {en} }